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1 Package:·python-statsmodels-doc1 Package:·python-statsmodels-doc
2 Source:·statsmodels2 Source:·statsmodels
3 Version:·0.14.5+dfsg-13 Version:·0.14.5+dfsg-1
4 Architecture:·all4 Architecture:·all
5 Maintainer:·Debian·Science·Maintainers·<debian-science-maintainers@lists.alioth.debian.org>5 Maintainer:·Debian·Science·Maintainers·<debian-science-maintainers@lists.alioth.debian.org>
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 48 ····················"output_type":·"stream",
 49 ····················"text":·[
 50 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 51 ························"Traceback·(most·recent·call·last):\n",
 52 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 53 ························"····f.result()\n",
 54 ························"····~~~~~~~~^^\n",
 55 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 56 ························"····await·self.process_control(msg)\n",
 57 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 58 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 59 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 60 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 61 ························"····raise·ValueError(msg)\n",
 62 ························"ValueError:·DELIM·not·in·msg_list\n"
 63 ····················]
 64 ················},
 65 ················{
 66 ····················"name":·"stderr",
 67 ····················"output_type":·"stream",
 68 ····················"text":·[
 69 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 70 ························"Traceback·(most·recent·call·last):\n",
 71 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 72 ························"····f.result()\n",
 73 ························"····~~~~~~~~^^\n",
 74 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 75 ························"····await·self.process_control(msg)\n",
 76 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 77 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 78 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 79 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 80 ························"····raise·ValueError(msg)\n",
 81 ························"ValueError:·DELIM·not·in·msg_list\n"
 82 ····················]
 83 ················},
 84 ················{
 85 ····················"name":·"stderr",
 86 ····················"output_type":·"stream",
 87 ····················"text":·[
 88 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 89 ························"Traceback·(most·recent·call·last):\n",
 90 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 91 ························"····f.result()\n",
 92 ························"····~~~~~~~~^^\n",
 93 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 94 ························"····await·self.process_control(msg)\n",
 95 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 96 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 97 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 98 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 99 ························"····raise·ValueError(msg)\n",
 100 ························"ValueError:·DELIM·not·in·msg_list\n"
 101 ····················]
 102 ················},
 103 ················{
 104 ····················"name":·"stderr",
 105 ····················"output_type":·"stream",
 106 ····················"text":·[
 107 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 108 ························"Traceback·(most·recent·call·last):\n",
 109 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 110 ························"····f.result()\n",
 111 ························"····~~~~~~~~^^\n",
 112 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 113 ························"····await·self.process_control(msg)\n",
 114 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 115 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 116 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 117 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 118 ························"····raise·ValueError(msg)\n",
 119 ························"ValueError:·DELIM·not·in·msg_list\n"
 120 ····················]
 121 ················},
 122 ················{
 123 ····················"name":·"stderr",
 124 ····················"output_type":·"stream",
 125 ····················"text":·[
 126 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 127 ························"Traceback·(most·recent·call·last):\n",
 128 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 129 ························"····f.result()\n",
 130 ························"····~~~~~~~~^^\n",
 131 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 132 ························"····await·self.process_control(msg)\n",
 133 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 134 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 135 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 136 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 137 ························"····raise·ValueError(msg)\n",
 138 ························"ValueError:·DELIM·not·in·msg_list\n",
 139 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 140 ························"Traceback·(most·recent·call·last):\n",
 141 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 142 ························"····f.result()\n",
 143 ························"····~~~~~~~~^^\n",
 144 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 145 ························"····await·self.process_control(msg)\n",
 146 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 147 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 148 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 149 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 150 ························"····raise·ValueError(msg)\n",
 151 ························"ValueError:·DELIM·not·in·msg_list\n"
 152 ····················]
 153 ················},
 154 ················{
 155 ····················"name":·"stderr",
 156 ····················"output_type":·"stream",
 157 ····················"text":·[
 158 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 159 ························"Traceback·(most·recent·call·last):\n",
 160 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 161 ························"····f.result()\n",
 162 ························"····~~~~~~~~^^\n",
 163 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 164 ························"····await·self.process_control(msg)\n",
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./usr/share/doc/python-statsmodels-doc/html/_sources/examples/notebooks/generated/discrete_choice_example.ipynb.txt
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269 ························"==================================================================================="269 ························"===================================================================================\n"
270 ····················] 
271 ················}, 
272 ················{ 
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274 ····················"output_type":·"stream", 
275 ····················"text":·[ 
276 ························"\n" 
277 ····················]270 ····················]
278 ················}271 ················}
279 ············],272 ············],
280 ············"source":·[273 ············"source":·[
281 ················"print(affair_mod.summary())"274 ················"print(affair_mod.summary())"
282 ············]275 ············]
283 ········},276 ········},
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./usr/share/doc/python-statsmodels-doc/html/_sources/examples/notebooks/generated/distributed_estimation.ipynb.txt
    
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875 ····················"output_type":·"execute_result"875 ····················"output_type":·"execute_result"
876 ················},876 ················},
877 ················{877 ················{
 878 ····················"name":·"stderr",
 879 ····················"output_type":·"stream",
 880 ····················"text":·[
 881 ························"/usr/lib/python3/dist-packages/IPython/core/pylabtools.py:170:·UserWarning:·Creating·legend·with·loc=\"best\"·can·be·slow·with·large·amounts·of·data.\n",
 882 ························"··fig.canvas.print_figure(bytes_io,·**kw)\n"
 883 ····················]
 884 ················},
 885 ················{
878 ····················"data":·{886 ····················"data":·{
879 ························"image/png":·"iVBORw0KGgoAAAANSUhEUgAAA9oAAAKTCAYAAADmN3BXAAAAQHRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjErZGZzZzEsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvzRIYmAAAAAlwSFlzAAAPYQAAD2EBqD+naQABAABJREFUeJzsvXecXXWd//8659x7z23Tk8wkIb2AITTpSAlKsYC0FSWsLra1rYpdvyy7KIqKZVX4LbvYQBEQRN111wUUAUVKQugkSElC2iSTTLv99N8fN+/PfM6dSTIDCclMXs/HYx5J5rYz93zm5rw+79f79TaiKIpACCGEEEIIIYSQ3YK5tw+AEEIIIYQQQgiZSFBoE0IIIYQQQgghuxEKbUIIIYQQQgghZDdCoU0IIYQQQgghhOxGKLQJIYQQQgghhJDdCIU2IYQQQgghhBCyG6HQJoQQQgghhBBCdiOJvX0Ar4QwDLFp0yY0NTXBMIy9fTiEEEIIIYQQQiY4URShWCxi2rRpMM2d16zHpdDetGkTZsyYsbcPgxBCCCGEEELIfsb69etxwAEH7PQ+41JoNzU1Aaj/gM3NzXv5aAghhBBCCCGETHQKhQJmzJih9OjOGJdCW+zizc3NFNqEEEIIIYQQQl4zRtO+zDA0QgghhBBCCCFkN0KhTQghhBBCCCGE7EYotAkhhBBCCCGEkN3IuOzRHi1BEMDzvL19GGQ/JZlMwrKsvX0YhBBCCCGEkNeYCSm0oyjC5s2bMTAwsLcPhezntLa2oquri/PeCSGEEEII2Y+YkEJbRPaUKVOQzWYpcshrThRFqFQq6OnpAQBMnTp1Lx8RIYQQQggh5LViwgntIAiUyO7o6Njbh0P2YzKZDACgp6cHU6ZMoY2cEEIIIYSQ/YQJF4YmPdnZbHYvHwkhQ+uQWQGEEEIIIYTsP0w4oS3QLk72BbgOCSGEEEII2f+YsEKbEEIIIYQQQgjZG1Bok3HB2rVrYRgGnnjiCQDAfffdB8MwXlWy/O54DkIIIYQQQghphEKbjEtOOOEEdHd3o6WlZVT3X7JkCS699NJX9RyEEEIIIYQQMhootMlryu4KBUulUq96PvXueA5CCCGEEEIIaYRCex9iyZIl+PjHP45LL70UbW1t6OzsxPXXX49yuYz3vve9aGpqwrx58/B///d/scetXLkSb33rW5HP59HZ2Yl3v/vd2LZtm7r9zjvvxIknnojW1lZ0dHTgrLPOwksvvaRuF1v2r3/9a5x66qnIZrM47LDD8NBDD+30eA3DwHXXXYe3vOUtyGQymDNnDm6//fZhz3vbbbdhyZIlSKfTuOmmmwAAP/3pT/G6170O6XQaBx10EP793/899tzLli3DEUccgXQ6jaOOOgqPP/547PaRbN9//etfccoppyCbzaKtrQ1nnnkm+vv7cckll+D+++/H97//fRiGAcMwsHbt2hGf44477sDBBx8M27Yxe/ZsfOc734m97uzZs3HVVVfhfe97H5qamjBz5kxcf/31O32fCCGEEEIIIfsX+4XQjqIIFdffK19RFI3pWG+88UZMmjQJy5Ytw8c//nF85CMfwTve8Q6ccMIJeOyxx3DmmWfi3e9+NyqVCgCgu7sbp5xyCg4//HA8+uijuPPOO7FlyxZceOGF6jnL5TI+/elPY/ny5bjnnntgmibOO+88hGEYe+3LLrsMn/3sZ/HEE09g4cKFuOiii+D7/k6P9/LLL8cFF1yAJ598En//93+Piy66CKtWrYrd5wtf+AI+8YlPYNWqVTjzzDPxwx/+EJdddhm+9rWvYdWqVbjqqqtw+eWX48Ybb1THe9ZZZ+HAAw/EihUrcMUVV+Czn/3sTo/jiSeewJve9CYcfPDBeOihh/DAAw/g7LPPRhAE+P73v4/jjz8eH/zgB9Hd3Y3u7m7MmDFj2HOsWLECF154Id71rnfh6aefxhVXXIHLL78cN9xwQ+x+3/nOd5T4/+hHP4qPfOQjeO6553Z6fIQQQgghhJD9ByMaqxLcBygUCmhpacHg4CCam5tjt9VqNaxZswZz5sxBOp0GAFRcH4v+5a69cahY+ZUzkU0lRnXfJUuWIAgC/OUvfwEABEGAlpYWnH/++fjZz34GANi8eTOmTp2Khx56CMcddxz+5V/+BY888gjuumvo59uwYQNmzJiBv/3tb1i4cOGw19m6dSumTJmCp59+GosXL8batWsxZ84c/OhHP8L73//++nGvXImDDz4Yq1atwkEHHTTi8RqGgQ9/+MO47rrr1PeOO+44vP71r8e///u/q+f93ve+h09+8pPqPjNnzsQ3v/lNXHTRRep7X/3qV/H73/8eDz74IK6//np86Utfwvr169Uc6v/4j//ARz7yETz++OM4/PDDcd999+HUU09Ff38/WltbsXTpUqxbtw4PPPDADt/bww8/HN/73vfU9xqf4+KLL8bWrVtx9913q/t8/vOfx//+7//i2WefBVCvaJ900kn4+c9/DqC+idPV1YUvf/nL+PCHPzzsdUdaj4QQQgghhJDxx850aCP7RUV7PHHooYeqv1uWhY6ODhxyyCHqe52dnQCAnp4eAPUq7L333ot8Pq++RBiLPfyll17C0qVLMXfuXDQ3N2POnDkAgHXr1u3wtadOnRp7nR1x/PHHD/t3Y0X7qKOOUn/funUr1q9fj/e///2xY/7qV7+qjnfVqlU47LDDlMge6XUakYr2q2HVqlV4wxveEPveG97wBrzwwgsIgkB9T3+fDMNAV1fXLt8nQgghhBBCyP7D6Eqt45xM0sLKr5y51157LCSTydi/DcOIfU+Cu8T2HYYhzj77bHzzm98c9lwils8++2zMmDEDP/zhDzFt2jSEYYjFixfDdd0dvnbj64yFxnCxXC6n/i7P98Mf/hDHHnts7H6WVX+vXonJIpPJjPkxjURRNOzYRzqWkc7RK3mfCCGEEEIIIROT/UJoG4Yxavv2eOP1r3897rjjDsyePRuJxPCfsbe3F6tWrcJ//ud/4qSTTgKAHdqrXwkPP/ww3vOe98T+fcQRR+zw/p2dnZg+fTpWr16Niy++eMT7LFq0CD//+c9RrVaVgH744Yd3ehyHHnoo7rnnHnz5y18e8fZUKhWrSu/odRvfmwcffBALFy5UmwCEEEIIIYQQsitoHR/nfOxjH0NfXx8uuugiLFu2DKtXr8bdd9+N973vfQiCAG1tbejo6MD111+PF198EX/605/w6U9/ere9/u23346f/OQneP755/Gv//qvWLZsGf7pn/5pp4+54oor8PWvfx3f//738fzzz+Ppp5/GT3/6U3z3u98FACxduhSmaeL9738/Vq5cid///vf49re/vdPn/NKXvoTly5fjox/9KJ566ik899xzuO6661T6+uzZs/HII49g7dq12LZt24gV6M985jO45557cOWVV+L555/HjTfeiGuvvXaXQWyEEEIIIYQQokOhPc6ZNm0a/vrXvyIIApx55plYvHgxPvnJT6KlpQWmacI0Tdx6661YsWIFFi9ejE996lP41re+tdte/8tf/jJuvfVWHHroobjxxhvxi1/8AosWLdrpYz7wgQ/gRz/6EW644QYccsghOOWUU3DDDTeo3vF8Po/f/e53WLlyJY444ghcdtllI1rjdRYuXIi7774bTz75JI455hgcf/zx+K//+i9V5f/sZz8Ly7KwaNEiTJ48eVh/OlB3B9x222249dZbsXjxYvzLv/wLvvKVr+CSSy55ZW8OIYQQQgghZL9kv0gdJ3sGwzDwm9/8Bueee+7ePpR9Fq5HQgghhBBCJgZMHSeEEEIIIYQQQvYSFNqEEEIIIYQQQshuZGJGcZPXhHHYdUAIIYQQQgghrwjHcUZ9X1a0CSGEEEIIIYSQXeD7/qjvS6FNCCGEEEIIIYTshDAMRxwRvCMotAkhhBBCCCGEkJ0wlmo2QKFNCCGEEEIIIYTsFAptQgghhBBCCCFkNxFFEYIgGNNjKLQJIYQQQgghhJAdINVs0xy9fKbQJiNyxRVX4PDDD9/bh/GquO+++2AYBgYGBvb2oRBCCCGEEELGKSK0E4nRT8em0N6HKBaLuPTSSzFr1ixkMhmccMIJWL58eew+l1xyCQzDiH0dd9xxsft8+tOfRnt7O2bOnIlbb701dtttt92Gs88+e5fH8tnPfhb33HPPmI5/9uzZ+N73vjemxxBCCCGEEELIvopuGx+L0B79Pcke5wMf+ACeeeYZ/PznP8e0adNw00034bTTTsPKlSsxffp0db83v/nN+OlPf6r+nUql1N9/97vf4eabb8bdd9+NF154Ae9973tx+umno6OjAwMDA7jssstGJaDz+Tzy+fzu/QFHieu6sZ+JEEIIIYQQQvYGQRAgiiIYhgHLskb9OFa09xGq1SruuOMOXH311Tj55JMxf/58XHHFFZgzZw6uu+662H1t20ZXV5f6am9vV7etWrUKS5YswVFHHYWLLroIzc3NWL16NQDg85//PD760Y9i5syZuzyeRuv4JZdcgnPPPRff/va3MXXqVHR0dOBjH/sYPM8DACxZsgQvv/wyPvWpT6lKu/Dggw/i5JNPRiaTwYwZM/CJT3wC5XJZ3T579mx89atfxSWXXIKWlhZ88IMfxPHHH48vfvGLsWPaunUrkskk7r33XgDATTfdhKOOOgpNTU3o6urC0qVL0dPTM8p3nBBCCCGEEEJ2ziuxjQP7mdCuuP4Ov2pesNvvOxZ830cQBEin07HvZzIZPPDAA7Hv3XfffZgyZQoWLlyID37wgzFxedhhh+HRRx9Ff38/VqxYgWq1ivnz5+OBBx7AY489hk984hNjOi6de++9Fy+99BLuvfde3Hjjjbjhhhtwww03AAB+/etf44ADDsBXvvIVdHd3o7u7GwDw9NNP48wzz8T555+Pp556Cr/85S/xwAMP4J/+6Z9iz/2tb30LixcvxooVK3D55Zfj4osvxi233IIoitR9fvnLX6KzsxOnnHIKgHrl+8orr8STTz6J3/72t1izZg0uueSSV/zzEUIIIYQQQojOKxXa+5V1fNG/3LXD2049cDJ++t5j1L+PvPKPqHojR7gfO6cdv/zQ8erfJ37zXvSV3WH3W/uNt4362JqamnD88cfjyiuvxOte9zp0dnbilltuwSOPPIIFCxao+73lLW/BO97xDsyaNQtr1qzB5Zdfjje+8Y1YsWIFbNvGmWeeib//+7/H0UcfjUwmgxtvvBG5XA4f+chHcMMNN+C6667DNddcg0mTJuH666/HwQcfPOpjbGtrw7XXXgvLsnDQQQfhbW97G+655x588IMfRHt7OyzLUtVl4Vvf+haWLl2KSy+9FACwYMEC/OAHP8App5yC6667Tm0svPGNb8RnP/tZ9bh3vvOd+NSnPoUHHngAJ510EgDg5ptvxtKlS1Xa3/ve9z51/7lz5+IHP/gBjjnmGJRKpb1meyeEEEIIIYRMDMQ2DmBMtnFgP6to7+v8/Oc/RxRFmD59Omzbxg9+8AMsXbo0dlLf+c534m1vexsWL16Ms88+G//3f/+H559/Hv/7v/+r7nPFFVfgxRdfxNNPP43zzjsPV111FU477TQkk0l89atfxQMPPIAPfOADeM973jOm4zv44INjxzJ16tRdWrVXrFiBG264QfV85/N5nHnmmQjDEGvWrFH3O+qoo2KPmzx5Mk4//XT84he/AACsWbMGDz30EC6++GJ1n8cffxznnHMOZs2ahaamJixZsgQAsG7dujH9XIQQQgghhBDSiF7NNgwDrju8uLoj9quK9sqvnLnD20ytpxgAVlx+2qjv+8AXTn11B7adefPm4f7770e5XEahUMDUqVPxzne+E3PmzNnhY6ZOnYpZs2bhhRdeGPH25557Dr/4xS/w+OOP4yc/+QlOPvlkTJ48GRdeeCHe9773oVAooLm5eVTHl0wmY/82DANhGO70MWEY4kMf+tCIlnW9VzyXyw27/eKLL8YnP/lJXHPNNbj55ptx8MEH47DDDgMAlMtlnHHGGTjjjDNw0003YfLkyVi3bh3OPPPMMf0CEEIIIYQQQshINNrGKbR3QDY1+h93T913NORyOeRyOfT39+Ouu+7C1VdfvcP79vb2Yv369Zg6deqw26Iowj/+4z/iO9/5DvL5PIIgUOFl8ueuhPJYSKVSKvpeeP3rX49nn30W8+fPH/PznXvuufjQhz6EO++8EzfffDPe/e53q9uee+45bNu2Dd/4xjcwY8YMAMCjjz766n4AQgghhBBCCEFdJ4lWSiQSCIIAjuOM+vG0ju9D3HXXXbjzzjuxZs0a/OEPf8Cpp56KAw88EO9973sBAKVSCZ/97Gfx0EMPYe3atbjvvvtw9tlnY9KkSTjvvPOGPd8Pf/hDTJkyBW9/+9sBAG94wxvwpz/9CQ8//DD+7d/+DYsWLUJra+tuO/7Zs2fjz3/+MzZu3Iht27YBAL7whS/goYcewsc+9jE88cQTeOGFF/Df//3f+PjHP77L58vlcjjnnHNw+eWXY9WqVVi6dKm6bebMmUilUrjmmmuwevVq/Pd//zeuvPLK3fazEEIIIYQQQvZfpJptWRYMw4Dneep7o4FCex9icHAQH/vYx3DQQQfhPe95D0488UTcfffdyrJtWRaefvppnHPOOVi4cCH+4R/+AQsXLsRDDz2Epqam2HNt2bIFV111FX7wgx+o7x1zzDH4zGc+g7e97W247bbbYrO4dwdf+cpXsHbtWsybNw+TJ08GABx66KG4//778cILL+Ckk07CEUccgcsvv3zECvxIXHzxxXjyySdx0kknxazmkydPxg033IDbb78dixYtwje+8Q18+9vf3q0/DyGEEEIIIWT/RLeNR1EEx3FiE5F2hRGN5d77CIVCAS0tLRgcHBzWX1yr1bBmzRrMmTNn2KgsQl5ruB4JIYQQQggZX0RRhFKpBKDusg3DEAMDA+jv78fChQtH1KGNsKJNCCGEEEIIIYRsR3KnTNOEaZrKNj6WWdoU2oQQQgghhBBCyHZ2ZBun0CaEEEIIIYQQQl4ButCWarZpmkilUqN+DgptQgghhBBCCCEEddt4FEUwDAOWZcHzPARBgGQyOaaK9n41R5sQQgghhBBCCNkR+livMAzheR7CMFQ28tHCijYhhBBCCCGEEIKRbeOWZSGZTMIwjFE/D4U2IYQQQgghhJD9njAMEYYhgCGhrdvGHccZ9XNRaBNCCCGEEEII2e/RbeNBEKh+bcuykEgk1O2jYcxC+89//jPOPvtsTJs2DYZh4Le//W3s9iiKcMUVV2DatGnIZDJYsmQJnn322dh9HMfBxz/+cUyaNAm5XA5vf/vbsWHDhrEeCiGEEEIIIYQQsltotI17nodEIoFkMgkAqto9GsYstMvlMg477DBce+21I95+9dVX47vf/S6uvfZaLF++HF1dXTj99NNRLBbVfS699FL85je/wa233ooHHngApVIJZ511lhoMToZYsmQJLr300r19GIQQQgghhBAyYYmiSOlRy7Lg+z6CIEAikUAikRizVh2z0H7LW96Cr371qzj//PNHPLjvfe97uOyyy3D++edj8eLFuPHGG1GpVHDzzTcDAAYHB/HjH/8Y3/nOd3DaaafhiCOOwE033YSnn34af/zjH8d6OETjvvvug2EYGBgY2NuHQgghhBBCCCHjBqlmm6aJIAhU9fqV2MaB3dyjvWbNGmzevBlnnHGG+p5t2zjllFPw4IMPAgBWrFgBz/Ni95k2bRoWL16s7tOI4zgoFAqxL0IIIYQQQgghZHeg28Z931e2ccuyYBjGnq9o74zNmzcDADo7O2Pf7+zsVLdt3rwZqVQKbW1tO7xPI1//+tfR0tKivmbMmLE7D3ufoVwu4z3veQ/y+TymTp2K73znO7Hbb7rpJhx11FFoampCV1cXli5dip6eHgDA2rVrceqppwIA2traYBgGLrnkEgDAnXfeiRNPPBGtra3o6OjAWWedhZdeeuk1/dkIIYQQQgghZF8kiqJhFW1JG08mk4iiaEz92cAeSh1vnC8WRdEuZ47t7D5f+tKXMDg4qL7Wr18/tgOKIsAt752vMQw1/9znPod7770Xv/nNb3D33Xfjvvvuw4oVK9TtruviyiuvxJNPPonf/va3WLNmjRLTM2bMwB133AEA+Nvf/obu7m58//vfB1AX8J/+9KexfPly3HPPPTBNE+edd96YFwshhBBCCCGETDSkWm0YhhrxZRgGDMOI2cZNc/TyObE7D7CrqwtAvWo9depU9f2enh5V5e7q6oLruujv749VtXt6enDCCSeM+Ly2bcO27Vd+YF4FuGraK3/8q+H/bQJSuV3erVQq4cc//jF+9rOf4fTTTwcA3HjjjTjggAPUfd73vvepv8+dOxc/+MEPcMwxx6BUKiGfz6O9vR0AMGXKFLS2tqr7XnDBBbHX+vGPf4wpU6Zg5cqVWLx48av56QghhBBCCCFkXNOYNu77/oi28URi9PJ5t1a058yZg66uLvzhD39Q33NdF/fff78S0UceeSSSyWTsPt3d3XjmmWd2KLT3B1566SW4rovjjz9efa+9vR0HHnig+vfjjz+Oc845B7NmzUJTUxOWLFkCAFi3bt0un3vp0qWYO3cumpubMWfOnFE9jhBCCCGEEEImOnrQmaSP62O99Pnao2XMFe1SqYQXX3xR/XvNmjV44okn0N7ejpkzZ+LSSy/FVVddhQULFmDBggW46qqrkM1msXTpUgBAS0sL3v/+9+Mzn/kMOjo60N7ejs9+9rM45JBDcNppp431cEZHMluvLO8NktlR3S3ahcW8XC7jjDPOwBlnnIGbbroJkydPxrp163DmmWfCdd2dPvbss8/GjBkz8MMf/hDTpk1DGIZYvHjxLh9HCCGEEEIIIROZIAiUFhPbuGmayjYehqG6fY8K7UcffVSFbgHApz/9aQDAP/zDP+CGG27A5z//eVSrVXz0ox9Ff38/jj32WNx9991oampSj/m3f/s3JBIJXHjhhahWq3jTm96EG264YUwHPiYMY1T27b3J/PnzkUwm8fDDD2PmzJkAgP7+fjz//PM45ZRT8Nxzz2Hbtm34xje+ocLgHn300dhzpFIpAIgl4vX29mLVqlX4z//8T5x00kkAgAceeOC1+JEIIYQQQgghZJ9Gr1YHQTDMNq7fvqviqM6YhfaSJUt2+gKGYeCKK67AFVdcscP7pNNpXHPNNbjmmmvG+vITlnw+j/e///343Oc+h46ODnR2duKyyy5TDfczZ85EKpXCNddcgw9/+MN45plncOWVV8aeY9asWTAMA//zP/+Dt771rchkMmhra0NHRweuv/56TJ06FevWrcMXv/jFvfEjEkIIIYQQQsg+ReN87DAMkUqlVD+2LrTHMkt7j6SOk1fGt771LZx88sl4+9vfjtNOOw0nnngijjzySADA5MmTccMNN+D222/HokWL8I1vfAPf/va3Y4+fPn06vvzlL+OLX/wiOjs78U//9E8wTRO33norVqxYgcWLF+NTn/oUvvWtb+2NH48QQgghhBBC9hnEKg5AjfCSQqf0Z4tbeKzuayMaS/17H6FQKKClpQWDg4Nobm6O3Var1bBmzRrMmTMH6XR6Lx0hIXW4HgkhhBBCCNk3cV0XjuPAMAxEUQTXdVUIWjabRRiGKJfLAOoO5GKxuEMd2ggr2oQQQgghhBBC9jvECq7Xnk3THNE2bhjGmJ6bQpsQQgghhBBCyH6FjPESwjBUYlqE9iu1jQMU2oQQQgghhBBC9jMaq9kyO9uyLNWnLUJbhPdYoNAmhBBCCCGEELJfMZJtXGZnA/H52iK8x8KEFdrjMOONTEC4DgkhhBBCCNm3iKIIvu8jiqJhaeONtvFEIjHm/mxgAgptiWGvVCp7+UgIGVqHsi4JIYQQQgghexcR0UEQwLIshGEIy7JGtI2/kv5sABi72Xwfx7IstLa2oqenBwCQzWZf0Q4EIa+GKIpQqVTQ09OD1tbWV/wLSgghhBBCCNm9iG1caAxBk4o3QKEdo6urCwCU2CZkb9Ha2qrWIyGEEEIIIWTv4/s+wjAEUBfVjUJbbjMMg0JbxzAMTJ06FVOmTIHneXv7cMh+SjKZZCWbEEIIIYSQfQgJOfN9H8lkckTb+KutZgMTVGgL8oYRQgghhBBCJi56VZKQnaGnjRuGMayaDbz6/mxgAoahEUIIIYQQQvYfHMdBqVRS4oiQneH7PoIggGmaI9rGoyja4fzssawxCm1CCCGEEELIuKVaraJarbJllOySMAwRhiF831ci2jAMmKY5LG1cvq/juu6oX4tCmxBCCCGEEDIuCYIAjuOoPwnZGTI7OwzDWKuBPop3R7bxKIrGtMYotAkhhBBCCCHjEsdxVEI0reNkV4htXET0zvqzR7KNs6JNCCGEEEIImfDoFcbG2ciE6Ejvted5SCQSSmTrtnG9P7uxou04Dj5y23Ojfj0KbUIIIYQQQsi4Q0STIP23hIyE2MajKIr1Xo9UzR6pP/vBF7fib1uro349Cm1CCCGEEELIuMPzPARBgDAMUavVEAQB7eNkh/i+D9/31bzsKIoAjNyf3WgbD8MQtz/WPabXo9AmhBBCCCGEjDscx1EVSsMwKLTJDmm0jQu6bRwYaj9otI139xXxpxf6x/SaFNqEEEIIIYSQcUUYhqqinUqlYFmWGttESCNBECjruGVZI4agSRp54/cB4Lbl6+CHEQ7qyo36NSm0CSGEEEIIIeMKsQGHYYhkMgnTNCm0yQ7RbeOWZSnng24bl7VjmmZs9JfvB7jjiS0AgHccecCoX5NCmxBCCCGEEDKukNnZhmHAsiwkEolYYjQhOp7nwff9HaaNAzuen12qVnH+oZOwqDOHsw4bvdBO7PouhBBCCCGEELJvEEURXNeF7/tIp9MwDENVtz3PUz3bhABx27hsyAAjz8ke6fuh5+Ki13fiAyfNHdPrsqJNCCGEEEIIGTc02sbDMFRiWwQVIYJuG08mkyMKan00nF7RDoJAzWrPZDJjel0KbUIIIYQQQsi4wfM8uK4L0zTVqCYRTUweJ43otnFB1o4ga6axP/tXy1/G/63qhR+ZsX7u0UDrOCGEEEIIIWRcEEURarUafN+HbduqQilJ0lEUwff9MYsiMjEJwxCu6wIAUqnUmGzjYRjh+/euxqZBBynbxt9P6xzTa7OiTQghhBBCCBkXBEEA13URhiFs21ZhVlKJZPI40Wm0jcvaaBTaI83Pvve5zdg06KDJtvD2w2cAqFfHRwuFNiGEEEIIIWRc4HkeHMeBZVmwbTtm+eUsbdKI67oxxwMAlVQvhGGoKt36929+ZB0A4G0HT0JT1gZAoU0IIYQQQgiZgIhtPJFIwLbtWICVzEceixgiExdpMwCAdDo94uxsID7WS8R490AV9z2/DQDwrqMOUG6JsfT/U2gTQgghhBBC9nmCIECtVkMURWqsFzBUzZYeXCaPE2BorJdpmkilUmOyjd+y7GUEEXDYtDwWHdAeu99oodAmhBBCCCGE7PP4vq9s49lsNiaQJHlchLZUusn+i2zK6MK60TYODA9CC8IItz26AQDwd4d3qu9TaBNCCCGEEEImHNVqVSWK61ZgEdoioDjiiwCI2cZFJDfaxvX+bAnW21asYUarjZa0hbccMhWmaSKKojGvKY73IoQQQgghhOzThGGISqUCAMhkMqpnFqhXIsMwVIJbqtqpVGpvHjLZi/i+D8/zYBgGbNtGtVoFsHPbuLQitKZN/H9/dyAKNR9N2XTsfvqM7V3BijYhhBBCCCFkn0ZPG9dt4zLWyzRNVZFkIBqRavZYbePAUFJ5ez6tvi/riWFohBBCCCGEkAlDpVJBEAQqbVy3jQNDIkqq2xTa+zdSwc5kMmotNFazAQxbRw++0IPNAxUYhoFkMgnLsmK2cdd1R30MFNqEEEIIIYSQfZYoipRtPJfLwTTNESuRpmkimUwiiiIK7f0Y3/eV48G27R32ZwdBgCiK1CaNH4S49LYn8ebrVuCZzVV1f902LgJ+NFBoE0IIIYQQQvZZHMeB53kwTRPZbBZRFMXmZwsyxonJ4/s3Iob1Hv2d2cbl+/es2oKeootm28JhM1qGpY27rjumDRwKbUIIIYQQQsg+S7VaRRAEsG0byWRyWH+2ICO+AFBo78eMlDY+km28cX72TQ+/DAA46+BJSKeGbOO60B4LFNqEEEIIIYSQfRJJG4+iCJlMJmYbb6xQSuo4gFc0jomMf0ZrG9fXRyKRwPq+Ch54sRcAcMHhXUgkEjAMI2Ybl/aF0UKhTQghhBBCCNknqdVq8H0flmWpsV4j9WcDULO05T7s097/aLSN6z3YOuJ2kMT6mx95GRGAY2Y2Y+6UJnV/vZotI+RGC4U2IYQQQgghZJ9Et41LovhI/dnAUB+uZVkIw3DMVl8yvomiSNnGM5nMqG3jXhDi9hUbAADnHzoZhmEgkUjEbOMi4HO53KiPh0KbEEIIIYQQss8RBAEcx0EURUin6zONpZrd2J8tMHl8/8XzPPi+D8MwkEqldiq0dVfEyk0FFGs+JuWSeONBk9VMdnm8Pi4um82O+niGvyohhBBCCCGE7GWq1aqyjdu2vVPbuCDJ49VqFZ7nKeswmfhINbvRNt64VvT+bMuycPDUPO75xLF4btMA0qnksLRxz/MQBAGSySTS6fSoj4cVbUIIIYQQQsg+RRRFcBwnljYODB/J1Igkj4uYYvL4/kEYhnAcB8Cu08ZlDUl/tud5aE4ncPgBzSPaxmu1mgrjG8umDYU2IYQQQgghZJ/C8zxVkR5Nf7YggWgAR3ztT/i+jyAIYFnWmGzj24o19VhJGrcsS93HcRyEYahmuHOONiGEEEIIIWTc4jgOPM9DMplEMpkcNtZrR5VFfZa23ltLJjZSdZZq9I7SxoEhS7gfGTj93/6Mi3/6ODYXarAsS60dWTciwm3bhmVZYwrYo9AmhBBCCCGE7DP4vq/GKaVSqVHbxgGoICvLshBFEZPH9wOCIFDnOZ1OxyrWjRsyURQpl8M9z21Ff8XD5qKDSXlbPUZs42EYqj9t2x7zpg2FNiGEEEIIIWSfQcKngLrwaQyn2tUsY7EPc8TX/oGsl0QigWQyOSrbuGmauHnZegDAuYd2wk7W79toG5fvGYahvkYLhTYhhBBCCCFkn0DGcrmuq0S2zMWOogjAcKFdqHn48/Nb1e16IJqILjIxEddCGIaqgj0a2/jLfTU8sqYPpgFccHiXCkEzDGNY2ngqlVLi27btUR8bhTYhhBBCCCFkn0BmIQP1imQqlYqN9RqpP/sffrIMH/jZo1jxcj+A+CxtBqJNbHzfh+d5MAwDtm3H1s5I1WdZR7c9tgkAcPL8dkxtqY/sknYDaV3Qbeb6ps9oodAmhBBCCCGE7BO4rgvf91VFcle28fV9FTy+bgCuH6KzuS6Y9EA0jvia2OiJ4YlEYqe2cRHOjh/it090AwDeccRUJcgTiQSCIEAURajVajBNMzaL27ZthqERQgghhBBCxhdSfQ6CAIZhIJlMKmG9oyC0W5evAwCcOL8DM9qzAIYLbXksmVhIm0EQBEgmk8o2Dozcxy8i/E/P92Kg6mFqs40T53cAGArR831fzWD3fV85KDKZjLp9tAyX+oQQQgghhBDyGqOHoIlYNk1zh/3ZXhDitkc3AADOO3QKfN9XjxGBJIFoY+mtJeMDaTMQ58PO0saBoc2atyzuQsIEvCBCwjJVfzdQF+O1Wg2GYaBWqyGXy6nkexHho4UVbUIIIYQQQsheRUYp+b6vRLZelQaG92ffs2oLthYdtOeS+P2zPVjynT9jQ38FQLxPm8njExMR2o22cRkH14haRwZw+kGTcdYhXbEebBHSjuMgDEOYpgnDMJDL5QAM9YOPFgptQgghhBBCyF5FBIz00Y5mrJeMZzrv0E6s769hQ38Vq7qLAIaEdhiGY55/TPZ9pCVA+rN3ZRsPw1CJavlTNm0kD0A2ejzPg+d5SKVSsTnu0g8+Wii0CSGEEEIIIXsVqU7KrGI94Xmk/uz1fRX85YWtAICzFrVjXkfdGr5yUwHA8OTxsVh+yb6PPjtbQsuAndvGq16Av/vhClz357WoeUEsBA2oC+lKpYIgCGCaJmzbRjqdhmmaStSPJViPQpsQQgghhBCy19ADqADE0sZ31J+dsxO49E0LcM6hnejKJ7BgUgYAsLJ7EACF9kRGzqluGxfXwo5s477v466VW/G3njJ++9QWZNOpWE+3iOhKpd56kEqlYNu2WnN6P/hoYRgaIYQQQgghZK8hPdQyLzuVSo1oG9crle25FD62ZC5KpRIqlQrmtscr2iLWRcBLlZKMf2QEl7QY7Mo2Lo+57bH6SK+/O7wLCcuCq23sOI6DWq0G3/dh2zay2WwsvV6EPedoE0IIIYQQQvZ5ZJyXCOEwDGFZ1i7HegFD4sf3fcxurQui9f1VFGoeDMNQI5uCIGCf9gRCbOOyJnZlGw/DEM9tLuLpTUUkTAPnHT5V3SaP8X0fhUJBWcZFYFuWFbONU2gTQgghhBBC9nl0ASxCRhdMur1X+M7df8Odz3Sj6riqr7stm8LkXP0+z3UXY33eMm+ZjH9Gso2L60FfIzq+7+P27dXsNx7YgaltuWG28Vqthmq1CtM00dzcrDZqRIR7nodEIrFDa/pI0DpOCCGEEEJ2O67rwnEcZLPZMVWByP6DLoDFNq6njev92WL7Xt9XwTV/ehEA8PuPHIW84SphfnBnFlurIfwgVI9JpVJwHIcjviYIejq9tBPoFe2RKFQd/M8zPQCAdxwxFYlEQq0Hy7Lgui4GBwdhWRay2awS7/J80p9t2/aYwtAotAkhhBBCyG5HLmTH2tdI9h+k11aEUhAESKfTO+3PvnX5OgDAifPa0dWURKnkqCr45W+ahtbWVnR0dACA6rGt1WoU2hMEz/NGtHDvyDYOAP/z5GaU3QAz2tI4fl6HEsvSWlAsFuE4DhKJBFpaWmLtCkEQqDA9y7LG1OdPoU0IIYQQQnYrIqAAjKkCRPYv9BA02ZDRxUxjf7YXhLjt0Q0AgAuOmDpMiEuFPAxDJaJSqZTqA4+iaIdijOz7yCxs3/eRTCaVEAZ2XM0OggCLp+Vx1sEdOGR6K+xUKmY1dxxHjfRqaWmBbduo1WoAhqrdum18LC0IFNqEEEIIIWS3IheyAIU2GRkRv8CQbVwf6wUM78++Z9UWbC06mJRP4ZT5bSgXC0oAGYYBy7Lqs5BrLrJpW1W09eTxHQkysu+ji1yZtz4aoT1/Ugb/cuZcZDIZWJYVE9KFQgG1Wg2pVAq5XC6WXi4bQJKEn0wmUS6XR328DEMjhBBCCCG7lUahzRnGpBERTaZpKiGs92frrgipcP/ikbpt/IIjpsFEpCrUkhJtGAY+dPsLOOzKP+GlrSWYpqkq5GIBJuMXz/MQRdEw+/bObOOSOG9ZFpLJpNr4ExEtI73S6TQymcww27jruoiiSFXQRaSPBgptQgghhBCy25AxODoU2kRHD0ETESwV6ZFs44ZhYH1fBX95YRsA4LzDOlXauAgoSRg3ECGIIqzsLsSeU0QTGZ9In7Q4H2QUHLCzEDQXV/xuFZ7dVFBuCdlsMQxDJY0nEglkMhmkUqlYhVyfnS0ivVqtjvqYKbQJIYQQQshuQ+9/bJyFTAgwJJqkCqn3Z+9orFd/xcVhM1px0oJJmN5iw3VdJYBEeCWTSczrSAMAVnYXAEAJLI74Gt/o6fQyemtXQvu/Ht+IXz7WjX+9c01MaMuIMJnHnUqlkMlkYu4by7JU2rjen10oFEZ9zGxSIIQQQgghuw1daEtfLPu0iY6IpkQiocSO2L+FxiC0Qw9oxX997A0YKFURhZ6ymqfTdWEt/dhz2lMAgJWbhoR2KpWC53kU2uMUEcb65ow+0msk23gURfjFsnqrwfmHTVHV6iiK4LquGvsmGzS6bTyRSCAMQ7VeZDNncHCQ1nFCCCGEEPLaI6nAQP1iVWzAFNpE0EPQpCopo5NG6s9uHOOUModEl6SKe56HWq0G0zSxYHtFe9X2irYI8DAMaR0fp8jmnZzz0czOfmL9AJ7bXELKMnD24k4kk0kVbCZrTj6XJCRNT7GXjRnZqPF9H6VSiUKbEEIIIYS89jSOW6LQJo2I2BXxKz23O7ON3/lMNwYrnurRFdu4bOYUCgX09/cjiiLM7cjANIBtJRc9xVpsxJcu8sn4QbeNAxiVbfzm7cF5b1zQhimtOZimCc/z1LxscdtYloVcLgcg7qIQp4W0wBQKBfT19Y0pUI9CmxBCCCGE7BZ02ziAmNBmIBoRCzAAVWGUHtgd2cbX9Vbw4Zsew3FfvwfbCvUgKs/zYJombNtGEAQolUqoVqtwXRe5dBIHtNgA6vZxmact4oz28fHFSJsjjSO4GhmsevjdU5sAAOcdOhm2bSMMQziOgzAMVbCZtCw0ppEbhqHSxqMoQqVSQaFQgOM4wxwWO4NCmxBCCCGEvGqk2gjEhbZcCLOqTfQ+W8MwYhXtHQntW5fXK5NHzW5DLhnftLFtG9VqVYlnz/OQTCZxwqw83rJoEloyQ/O1xRrMEV/ji8bZ2cCQ0E4mkyM+5jePbUDNCzG3I40jDmhWWQB6gJ6kh2ez2WG2cdd1UalU4DiO2hxyHAfAjivoI8EwNEIIIYQQ8qqRC1WpHgoyWikMwzFVg8jEQ0ST9Lzqo5r0sV4ixkMYuO3RDQCAi46ZEbONy5c+bikIAqTTaXzwmMlobm7G5MltAIYS8DlLe/yh28alR3tXtvFkwsTkfBLnHjIJmUwGhmGgVCoBgApF8zwPiUQC2WwWwNC6C4IA5XIZtVoNqVQKtm3D8zz1+mP5DKPQJoQQQgghr5pG27igC22y/yI9sUC9ElmpVFQP7I6q2X9cuQXbSg4mN9lYsqADgefCdV2Ypol0Oq16bi3LUj3YlmUpwRSGIUzTjI12YiDa+KExaVxnR7ZxALjo6Bk4+YAkwjBCOp2G4zjqvOdyOfT19SEMQ2Qymdh8bM/zYNu2CtZraWlBPp/Hli1bUKlUYBgGbNse9fHvEet4sVjEpZdeilmzZiGTyeCEE07A8uXL1e1RFOGKK67AtGnTkMlksGTJEjz77LN74lAIIYQQQsgeRu+9HUloA7SO7+/oI70k8Xmk/mzdwnvz9vFMFx51AIwonhRt2zYcx1GVST2J2rIsOK6H5zcPwvXDWCAahfb4QXfJyLndlW0cQD3wzDSQsetjuSqVCgAgnU7DMAyVHJ7P59VsbH1dJJNJ5PN5ZDIZuK4Lx3FQq9VgWZaqgI+GPSK0P/CBD+APf/gDfv7zn+Ppp5/GGWecgdNOOw0bN24EAFx99dX47ne/i2uvvRbLly9HV1cXTj/9dBSLxT1xOIQQQgghZA8iVUjph9Wh0CZRFMVmEottXHr49TUja2njoIO/vLANhgG886gZqhot/d2maarAqlQqpZ5DqtjvumkV3vyDB7Gyu6BGfOmVbrJvo68ZqVzvaqzXQMXFH1ZuQalSbydIp9Oo1WrwfR+WZSGTyaBcLqvnDYIAjuPA932YpolcLqc2bRKJhHJeVKtVZRuXhPLRsNuFdrVaxR133IGrr74aJ598MubPn48rrrgCc+bMwXXXXYcoivC9730Pl112Gc4//3wsXrwYN954IyqVCm6++ebdfTiEEEIIIWQPs6NqNoCYAGLy+P6JXpkUC7cegtY41sswDDyxYRCWaeCkBZMxbXuKuMw1TqfTKqBKBHSpVIqFqx3QnAJQn6etvw6Tx8cHI1WzhR3Zxn+1YgM++LNH8Ynbn1WPlZYF27ZhmiYGBgZQrVZjI+WkVzuVSqnQM9u2VeJ4qVSCaZrIZrN7t6ItvzjpdDr2/UwmgwceeABr1qzB5s2bccYZZ6jbbNvGKaecggcffHDE53QcB4VCIfZFCCGEEEL2DXYmtKUCCbCqvb8ittxkMqmqyrvqzz7viAPw0BffiH8563Vqfemp9p7nKdt4sVhErVZDuVyG7/tIpVKY21HXIis3FVQFnIFo4wfZDJFzBmCn1ewoilSrwYlzWlT1W9ZZEAQoFosqFK2pqQnpdFqljguyUZNKpVCr1VTvdiKRQFNT05h+ht0utJuamnD88cfjyiuvxKZNmxAEAW666SY88sgj6O7uxubNmwEAnZ2dscd1dnaq2xr5+te/jpaWFvU1Y8aM3X3YhBBCCCHkFaAHFu0oBZj28f0X3aottnGZTyziV9D7swFgSnMa86c0wfd9eJ4X68GW55Hnb6yUz2uvV7RXdtcLdIlEQlU4KbT3bfTZ2foEA2Gk/uxH1vRh9dYyMkkTZx7Yrr7vuq4a61apVBCGIXK5HNra2pBMJmOv47quWkuJRALValWFoKXTaWQymWEzvXfGHunR/vnPf44oijB9+nTYto0f/OAHWLp0aewXqbHcv6NEOQD40pe+hMHBQfW1fv36PXHYhBBCCCFkjOysmi1QaO+/6CFohmEo0dM41kufw76tPGTtFkEtVUURR67rIpFIKKuvYRiqUm6aJua11yvaz3UXEIaRGvFF6/i+jzgg5Hzp7Mg2fvMj9Wr2mQd1IJ2of9ZUKhW1fqQynk6n0draqnSp3q4gaymdTiMIAhWSJin3MpZutOwRoT1v3jzcf//9KJVKWL9+PZYtWwbP8zBnzhx0dXUBwLDqdU9Pz7Aqt2DbNpqbm2NfhBBCCCFk77Mjoa0LJwrt/RM90CqVSql0+pFs47I21vfXcOLV9+HdP34EXhCOaBuX9HC9Qi3fC8MQhmFgVkcGKctA2Q2wrq+i7MD6MZF9D5lxDWBEYTvShl5vycH/PdMNADjrda0olUoIgkC1DKRSKWQyGVWt1vus9eeXDSAJQavVagjDEOl0GrZtIwgClVg+GvaI0BZyuRymTp2K/v5+3HXXXTjnnHOU2P7DH/6g7ue6Lu6//36ccMIJe/JwCCGEEELIbiQIgpidV8dxHFVREqE9FtslGf+IYNL7o2UDRgLKBBE8v3lyC8KoXmFMWqYS0SLExTYu1XG5TSra8j07mcCc9nqI2ioteVwq2tz02TeRqrI+sk0PQxtJaP9qxQZ4QYTXTcliWrq+NlKplAovS6fTyjZu27aaha0HNErlWzaABgYG1PqVx8jn2WjZscfnVXDXXXchiiIceOCBePHFF/G5z30OBx54IN773vfCMAxceumluOqqq7BgwQIsWLAAV111FbLZLJYuXbonDocQQgghhOwB9Gq2bufUq4ZBECCVSqnv76xdkEws9JFeAGI91CON9fKCEL9+ol6ZXHrMTCXMHceJ9XPL5o2Ip0wmg2q1GqtwJxIJvPnAVpyyIIF5U/Kxx0tlXdYl2TfwPE9txtm2rdaPfGZIu4GO7/t4bG0vAOBtB7UgiiJks1l0dHSovv4oilCtVmEYBnK53Igp91KpTqfTcBwH1WpVrRHLsoYJ/tGwR4T24OAgvvSlL2HDhg1ob2/HBRdcgK997Wvql+zzn/88qtUqPvrRj6K/vx/HHnss7r777jEnuRFCCCGEkL3HjmzjeuVaqo1SnQrDcFj1m0w8GkPQAOzQNi5V7j8934vesovJTTbe9Lop8H1PPU5swHpLglSmk8kkSqUSDMNQYi2RSOCcRW3I5/OYMqWuMWSkk4hxCu19B9lQAaBGce3MNi7j3cIwxLfPfx0uWj0JHSkfuUwKLS0tsCwL1Wp9nrbe05/JZGLPAQyFr0l7wbZt25T1XNaIrDn98btijwjtCy+8EBdeeOEObzcMA1dccQWuuOKKPfHyhBBCCCFkD6PbeRuFtu/7uHNlD25atgnfuWAR5mcyqtpIob1/oFezxdYtGy2pVGrE/uxfPV6vZl941AFIWibKNV/Ze6WiKYKnWq2qnttkMolUKgXTNOE4DnzfVz25subEOi7WcyaP71s4jqOS6FOplPp8kY06ACpZ3nXd2GZeIpHAwdOaUCgUYNt2LB1cBHwURbBtO7a5IvcR27iMn5MxcSL2s9msEt2yGTAa9miPNiGEEEIImZjoo5gareBVx8XnfvMcntxYwEtbywAYiLY/obcO6NVsOfeNtnHf97Gur4qH1wzAMIB3HT1TiSypZosIk0qjVDOTyaQKqzIMIxaIZpomthRq+MOz3Sg5fix5nEJ730EPQEun62nxcn70VhOZay0C2Q1NhAk7Fo6XTqeVIJfH12o1WJYVC0GTDZzGwL5CoQDP82JZALLGZB73aKHQJoQQQgghY2ZHtvEwDHH/C/WeybZsEkfPalEVRbmdTGwaQ9AAqCqyiF19cyYIAvz2qfpEopMWTMaM9mysx19Es1jHHceB53kxYaXbjUUMWZaFj9zxIj70iyfw9IbBmNCWEVJk7yP90clkMrZegPr5r1arsSp2MplELpfDrY9147ir/oT/uO9FBEGATCajNlykSi0V8EahrdvGxWWj9/3LZk0ymUQ2mx12XKNhj1jHCSGEEELIxEXvkx3JNn7H43XRdNaiDhhRGLOLM3l84tNYzRbhInOMR+rP/uAbZmLh1FbMaM8BGLLziuVct41LNVsXVplMRlW+XddVCdLzO9LoLrhY2V3A0bNaVPK4biknew/dgSBp4HIOpQ3ANE3Yth1rEQjDCLcuX4eqF6AlXQ8ry2Qyw9LtPc+DYRjD1p3e5w/UN2U8z1Nry3EcJBIJ5HI5Ffboed6YRsNxZRFCCCGEkDEhVR2pMuqs6y3hgZf6AAAnzWvFAy/2ouJ46n6vJL2XjB92FIIm59wwjBEFTzaVwDuOmonj5nbEbOMAlEVcerylT1aEl1Qe5fVc14Xv+0gmk5i3fcTXyk31EV9ynyAIuOmzl9HPpZxHoN5/L1VsEdlNTU1Ip9Pqc+QvL27D+r4qmmwLb1rYpm4byTbeODsbQKziDUCFp+mVc9u2kc/n1e36Oh4NrGgTQgghhJAxsSPbeBRFuOOxjYgAHD2rBV/63UvorXi4ra0Jx8zPMHl8P0As2RKCBgzZxsWeq2/OSPVxpJnauhCWSmWlUoHjOEilUqqCmUwmEQSBek0R2qlUCnPb6+FXMktbjkGEtghv8tojIlsC0IC6+C4WiwDqayiTySCzPUxR5+ZHXgYAvOV17cimEqoaLu0DslEjYWbS+w3EQ9AEwzBQKpVi61eq4HqP+FhaDljRJoQQQggho0avAjWKlJrj4tdP1G3jf3fEVCzsrFeRVnbXL5zZpz2xGWltiIV3pLFeALB6axHnXb8Cv1i+UVULddu4PE5uq9VqyiYszyW917ZtI5FIwPM81Q8+r6MuwF7oKcL16xs8EmrFQLS9h578LiI4iiIUi0Vl6c9ms6pKrbOlUMMfV/UAAM47ZLKadS3zrsMwVGPe9HWhvzaAmA3cdV1UKhWYpgnDMJDNZpX4TyQSqNVqal2NFgptQgghhBAyanZmG3+5twQAaMkkcMq8Vsxrr19Ar+ouqMcAFNoTlR2FoAFQqeGN/dm3r9iEl7ZV8JcX+5TjQRfBjZXqarWqQtCkP1uq1HoQllQtp7dmkE+Z8IIIL/aUkEgkVEWbQnvvoM/M1gPQpC9beqr1EDydW5etQxBGOGxaHgdObVG367bxIAjgOA4sy4pVs+U22RQKggCmaaJQGHI8yBqVKrnYysc6Fo5CmxBCCCGEjJod2cYB4IAWG//zodfjpxcfAgshFkzOAACe21JSgVYAA9EmKvqYJEEXMyKchKrjqbTxpcfOVPcH4r3eYt8tl8tqDreIb6mci/24MVU8kUhg/qT6OlzVXVDVbwrtvYfnecMC0CRdPAgCdR6B4a6ZKIpw+6PrAQDnHzoZyWRSrSn9vMqGjVjA9ccHQaDWh6xP3YkhGzcy711Eu/SMjxb2aBNCCCGEkFGxs7RxqRIhCjF/Sh61Wg1ztwdRPd9Thu8HrGhPYPQ52bI2pGoowWSNY73uXrkZfWUPk/MpvPGgKep5xP6rjwMLggDFYlGNcRIBJlZx13Vj9xUxl0gkcMEh7Tj/iKk4YX6Hsq/LsTF5/LVFD0ATB0IURahWq2p+dTqd3uHnjOd5+Om7D8NvHt+EtxwyVT1eNnF834+1Dti2HcuDUDO4t4eeSSo5gGGbNoZhIJVKYWBgQN2fPdqEEEIIIWS3I2Ja7Lo6L2wehOvHLZlT8xZSloGqF2Jtb4nJ4xMYfaSXCBcRNSJmG0XTL5dvAAC848gDkLTM2NoxDENVNw3DUNZdy7JiI5dM01QjmfRUcRkblUwmceLsJpy5sBVTWzLDbO3c9HltEZEtIXbyPenHF8s4MLw9RUR6Z1MKH3zDDGRSiWHVbD0ELZFIIJPJxF5fPsNc10WpVFJp9lJFl883mcsOAJVKRQltfaNoV1BoE0IIIYSQUbEj23gYRnjfzx7Dmdcuw0u9zpAN0zIxp61uI165qQDDMNSFKgXOxGFHAXlSVdZ7aIU1W0t4aE0/DAAXHRO3jYtYEnFuGEasmi191slkEp7nxUaHiTCXmccyN1tmZ+uCnyO+XltGCkCTCrTneWpE147CFqvVqvq7rAs59zJ+SzZ8oihS498aj0GCz6QNQezh8tkk6yiZTKJaraJWq6nNHAptQgghhBCy29mR0P7z8z3YNOjA8UPMm5JX4sU0TZx/cCv++fRZOHR6k/oeQKE9kRBxI8nPgp4a3mgbv2XZOgDAifPaMaMjByBuG3ddF5ZlIZVKwXVdNfIpl8vFqpiu6w4TTrrokqro4xsK+PFfVqO3PGQx14UZ2bPITGug3sNvmqb6nu6Skc8FOfeC67r4/+5bgw/f8jSe2FhfC7KJIn8XIS8WdD1oTY4hDEMUCgU1/s22bSXWRUjL4xKJBCqVCgqFgnqOsYyDY482IYQQQgjZJaoHGxhmGxfR9NZFHUhZBsrbq5iWZWHJ3Cbkcjm05VPqsZxhPLHQZw8LjYFUjZszpyxox9ptRZx7+DQAiNnG5XHZbBaJRAL9/f3KNp7NZpVoj6JIVUP1tSmiS2zKiUQC375vNVb31jCvsxlHTUsrkcZAtNcG13WVoBYBLSJb1oiM4wIQCzALwxDlag2/erwbPSUX5x7WCaBZbbjoa0HWXWMIGjCURC4J462trSqlXirpknieTCbhui76+/uVmB/r5xUr2oQQQgghZJfo1Wy9MtlTrOGe57YCAM4/rEtVEXVxpVt0WdGeWIiwMQxj2Kxi+T4w3AVxxAHN+M75i3D6oi4AQ/3cElClh5YVi0UYhqGq2VKtrNVqqNVqsZRqsYY3Jo/LPO2VmwqxEV+0ju959HMhAWiu66o1os+/lvvovdmO4+D+F3rRU3LRnkviTQdOUhVxIG4blzU3km28Wq2qFgTbttHU1ATHcVQgmmRHyHoaHBxEpVJRDgj9NUcDhTYhhBBCCNklO7KN/+rRDfDDCIun5nDQ1OZYD2YikUAymcSTG4v4xbINGKy4FNoTDLFeN27ASHVaqs+6cNLT6xvnbQNQtvFMJoNKpaJ6c/P5vLpPGIaoVCpKVIkIEoEu1Wo5hvky031zfMSXPkaM7BnEMi4bJHryuKwPPTVeF8hSpb79sW4AwLmHdiFpmaoCDgwlz+vnu9E27vs+KpUKSqUSbNtGS0tLLHVc1q7YycvlMkqlkqp2v5JsCQptQgghhBCyUyRMCogL7TCMcOvyum383MWTYmnipmmqC+xv3LcJ3/zjGjy1YYDJ4xMI3XqtiyPd/i1WbuHl3jKu/J9nsaa3EkuVFpEka03EkogdsQKLMNNnakulW9aTvJ5UOVOplBo1JxVtfaY7hfaeQ84rUN98k1FewNAmi7hgxLYtRFEEx3GwcaCGB9f0AwD+7oi6A0ICzIC6dVySy8VZoT9PEAQol8uqn1+q2bVaTWUIyHPZtg3P85RbIpPJKLENDG0ajAYKbUIIIYQQslNETDUGWj2xYQDr+qrIpSyc8bpJqjqkX7iGYYi5Knl8kMnjEwg9BE2vWOvV6UZL+c3L1uEnf30Z37z7pVg1W4S5PkvZ930MDtbXTDabVRVr13XVazc3N6NWq6mAK7GW6zOVLcvC3Pb6Gny5r4KKF8ZEHtfhnmGkADQZuybrQlLAk8nkMMu49HD/+onNiCLghLntmNGWiYWgGYahNnz0EW+y5sIwRLVaRRAEqFarqmIt60gq6bqY9jxPVdzlOYC6YB9LTz+FNiGEEEII2Sk7so2/fmYbfvWBI/Gl02Yhn07FrJzVahWe5yEIAszZLnJWdtfTe+WClv2x4xt9draOVDH1dHAAcP0Qv3p0++zs108dZhuX+cYitAcHB+G6LgzDQFNTk3pNEUFNTU0wTRPFYlGFYclGjvTtOo4DwzAwqSmNSbkkogh4fktR9WmHYcjk8T1EYwBaEASxXm05P2L3110RKkE8CPHrJzcDAN6xvZrdaBuv1WpKaIsTQsR4pVJRa0M2aqSaLZsweuq4ZVlqPciYOHkuPXRvNFBoE0IIIYSQHSLzh4HhQjsIAiyYnMGbFrSqKpVYeKvVqgoamrfdtvvc5vpYHhFYrCSOX3YUgqbPrBYBJQ6Gu1duRm/ZxZR8Cqcs6IgJbd02LkJJBLRuGRfbsVjGZayXiGYAsT5tEXuJRALzJ9XtxCu7i+o++mxnsvvQA9DExi3VbdnkEOt2Y0K4XglPJlP4/JkHYcnCSThlQXusEg7UN+0cx4Hv+zHBLp9BskbleGzbRjqdVlZzPUhN36SRNSzrUe6fzWZH/R5wvBchhBBCCNkhum1ct3WGYaREilyYSs+s67qqyhQEgbKOv7S1AscPGIg2AdCr2Y0haABGFOEyBu68w7uQSlgq+VtGe0k127ZtOI6jRLTYxqWiaFkWcrkcoihCpVIBUF+fUumW1xVHhYilfzhyMj70hpk49qDpCJyqspfTWbH70UW1VJ1lMy6dTqNSqahqdiaTiX22yOaIaZrIZtO48OgZOHvxJNWrryeUy9oJw1C9lmVZqFarsc0/WRuZTAbAUMhaNptFf38/oihCJpNR66hWq6m+cUlIN00T7e3to34PWNEmhBBCCCE7ZCTbeBRFOOuaB/C5O57G5oFKTGiJPVSEk+d5mJJPosk24YcRXuwpUWiPc/QQtJFs4/pYL6lar91Wxl9f7IUB4PzDu4bZxuU5JW18cHBQVTszmQwcx1GV63Q6jVQqpSqiYjkXUW1ZVsw1IRbhgyansagzg2wqoarmTB7f/cgGBzBkEZeNGQlEK5fLAOrCV7eMy4YKUHctyNgtfb3powL1EDTpz9ZfX6rXjuMglUohm82qTUDpGZe/5/N5FcAGQLU/lMtlmKaJXC43plnaFNqEEEIIIWRE9DFMutB+ZE0fVnYX8MfntsFOGLHqped5SmCL+DFNU6U+P7txkMnj45wdhaDJehEbr54qLtXsk+a3Y1pLOia0xaYbBIESV4VCAUEQIJfLKQuy7/sxsSNiTZ7LMIwRxzFJ4JW4LuT4RMTpqfrk1aELVZmZrQeiJRIJlMtlZdtutGLrGzU3L9+In/51DXoLQ64FcSHIv0U0S7q9Phs9k8mojT/P82DbtnLcSNW8Uqmn32cyGZUtoQc5ipBPJBJoaWmJjQzbFbSOE0IIIYSQEdH7IHVBdet20XTmQR3I20PpvnIRLMnClUpF2crfc0QH8ifncezCKaoXUkTOWC5eyd5FrziOVM2W+5imGducydsJtGaSuODwofFMInClAmmaJlKpFCqVihLXqVQKvu+rtGjTNGHbthJYURSpf+uvLWtMf27LsnDnql68+FAPPnTKfNX3LfbxxgwCMnYcx1HnIJlMquRwObcyagsYCrPTkfMOM4Ef3PMCessuJmVMLFnQrtabCGHZ1JENmjAM1cZdOp2GaZqoVquoVqsq1VzWr1S45bHNzc0qUwKAsozLhkAqlVK29dHC1UQIIYQQQkZkJNt4f9nF75+ppwCfc3CH6o0Mw1BdVHuep77E9rlocgrt7Xlkk0NJ1HKRTKE9fhCrdmP/NTBUjRT02z/+pgV43wkz4bqOEsIiakQMy/zjLVu2IIoiJJNJVa0UgS3PKb3Z+ogoEVpyf0mQ1nu7f/XkVjy7pYLj5k3GMV2JmNAmrw4ZzwYMWcblMySdTsMwDBVwJy0BjY8XZ8Gfnu9Fb9lFV7ONE+e1Aaifa70/W1830o8tPf7JZFJVpyU5PJ1Oo1qtqiRyOY5UKgXLslAsFmFZFoIgUK0KjuMgk8kgnU7Dtu2hjYBRQOs4IYQQQggZht4XqQumXz++Ea4f4sApOSycnI5VEHW7uFzEyvfEViwXyezTHp+I0GgMQZP1IhsnInp0LCNCwhz6vsywlq9MJoMoilAqlWLBVxJwJZVFqWZLX64IKb3VoXGut/R7z+uQ5PECksmk2vBh8virRyzjeqo4UBfdlmWpkEQAalybjr62bt7umrngiGlImIay+st5MgxDpY0DUIJb7OFS7ZZNFtmoqVQqqFQqSCaTqsqeSCRiKeTSXqBXs7PZbKyXfDRQaBNCCCGEkGGIYNEFUxRFyjZ+3qGTlZjWZ8xKz61cwAJDYvr3K7fia79/DlsKNQrtcYg+6q3RNq73tUq/LABsHKjiwRe3xUSwnlKvVwiTySSKxWKsX1sXQyLgxTmhj2ESoSQCXNatvK6Ipnkd9ayAlZsKSrzL7cwLeOU0BqCJoBahGoYhyuWyGtdm23bs8XrA3sv9Dh5e3QfTAM47rBMAdmgbFzEt6eXyvCL6HcdRa0iq2YZhqPuJCBfxrW8YymeTbduq+i7POxootAkhhBBCyDBGqmaveLkfL/SUkEmaOH1hq7KNSwCSWHfFxinPI3bSWx7fip8v24inNgxSaI9DdhSCBmBYRVjWzc8eXIulP3oEX/z107E513J/qWqLqC4UCiq4CqiLHFlnqVRK9dHKMXieh0KhgHK5DMdx1MxkEebAUPJ4KpVSM91XdRfUfUSsU2i/MhoD0BpTvwGo5G9J725E1lZf1cdHb34cAHDqgZPR2ZSKtSnI8+piWK86A0MOhsYwx1KppNaWfu5lc0YcOLImxVWRzWZj9x0tFNqEEEIIIWQYIwntWR05fPaMhfj7o6cjvd0VbJpmTKjIRaqeLO66LgzDwNw2qSYyeXy80Th2qRFxMsh5tSwLjh/g9hUbAACnLugAANVmIGJI/kyn0/A8T9nGM5mMsveKCBI7srxOEASo1WpKHEmLgtwu60pPFZ/TbsMA0FN0MFgLY6F87NN+ZegBaGIRB4YCyTzPQ7VaVbOqG90Q+tr6zh/X4KWtZUxrSeMLp88DMFTNlvMofdcydsu2beRyOXXO9XnqUvXW+8dljJe0soiglvA2yRqQ6nsmk1Gv27jBtDMYhkYIIYQQQmLogVd6n+3kJhsfXTIPfX19KJfLqqdWn2Ur4VVSNRIxFYYh5rbXBdrK7oLqr5ULWCY+79tIa8BIvdeyXkSwiMX77me3oK/soqs5jRPntSEKg5id23Ec9e9UKoWtW7fCdV2kUilkMhklgqX3Vq9mi8VXBBwwJPaloq2P+JKvfDqJA1ptrB9w8MK2CuZmzWH5AWT0NAagiWU8kUioHns5b5L8rff2A/GRXleeewhqfogvveVATKoXw4fZxn3fR6lUUsJeH/kmG32yPjzPUy4HaXUBhqrwsp5lPrdU4+VxuVxOrU89lXw0sKJNCCGEEEJi6HNqR7oolgtj3WoJDPVpygV1JpNRYtrzPMxurYvplZsKABiINl4QUQxAzbnW0QOqdJuvzM6+8OgZMFAXw422cXlO13VRKNTXRS6XU/eT/lrTNFXQnmzgVKtVNRNbBLveuqALbRHhyWQS87cHoq3ZVomJdq7DsSPCWhLi5b0Xy7g4DoD6eR7JDVGsVNXtLdkkrn/PUZjeUne/6G0K8vxiAU8kEqqSLS0s+li4wcFBuK6rxnoBUH+X+doi1iVkT1wT4rKQsXIitvv7+0f93lBoE0IIIYSQGI228SiK8P9+8zT+96lulCpVeJ6nZmu7rqsEkV4hkotqEdq+72N2S/351vdXUax5FNrjgDAMUa3WhZD0STcy0livNdvKePClXhgGcOFRB6hzrI91E7eDbdtKFCWTSeTz+ViqeCaTgeM4cF1XJVqLzVyq64VCQVUixVUht+kW9UQigQ8d14m7PnIELnnDHGVJl/uQ0SM90vI7L4JaRnnJuZC+6JE2abYMVnDhj1bgpmUbY5bykWa1B0GgWgvEhi7OGZl7LRb2MAxRLBbV8UiPtXxu6RVxeQ4ZEyebLtlsVoltscSzR5sQQgghhLwi9H5WEdpPbhjEzY+sw6dvewIDpaoSR3pvtjxOn3csf0oFqcm2MCVfv3B+bnORQnsfJ4oiZc02TVNVKXXkvEtlWYSMpNMvWTgZndvPuV6ZrFarSCQSSuCIKGpuboZpmkos60nQvu+r6rfM0db7vfWZ2XIccoyyTk3TRGc+gRbbVK4MSR5v3DAgO0bvhU4mk7G/NwYk6lVjnd6Sg7//8TK8uLWCGx7egKIzNKqr8TNINnxkpFc2m1VOBpmjLdVsy7LQ39+PKIqUwJfqNVCvsosol9vlM0w2bEzTRDabVWI+iiIUCgUKbUIIIYQQ8sqQSpLe43rLI3XR9JaDO5E2h3odpQIk1WwZySQVIOnT1K3Hkvr8/BYK7X2darWqKpbSM92ILjx02/hj6+oW26XHzoolP4uYlR7YKIpQLpfh+34seEqEdiaTUQJaBJzneSgWi6oaLZZiEdt6IJp+zJIjAAzN/ZbKt97HTXaNWMaleqzPqpbb5T2W8Wx6kFhvycHSHz2CF3rKmJxP4RcfPBbN6XpPt25Hl/MlqfJ6yrhUu2UONjAUrFYul2FZFpqbm1VVXe5fLpdVG4GMGvN9H47joFqtwnVdZLNZNDc3I5vNKpt5rVYbk3WcqROEEEIIIUTRaBsv1jz895ObAADnHTYlFkalJ03rI3KkglSr1WLjkwDgQ8dOxr++bSEOnNmlXlMXRmTfQPpUAahe+5HY0Viv2z50PJat6cORs9rg1OrWc7EX62LbsixUKhVlEZd/6xs11Wq9XUFEt8xClnUnIVVi+dWDr3QhCECtsxuXd+OZLWvx2dPno237feSrMeyNxJGcBgA7tYzLe2kYRqya3Vd2cfGPHsHfNhcxOZ/CDe85AvOnNAGASpXXZ13LZ4nMQgegzq9Us+WY9LGCIvBlE1AyJcTynsvlkEqlkE6n0dfXh2KxiFqthkQigdbWVrS0tCCRSKBWq6FcLsPzPAwODo76feKnGSGEEEIIATCybfy/n9yEqhdg/pQ8Fk22lW0cgKoiiXCSKpP00OpjlsSa25k10JFNqJRhVrX3PaRPFYASvyMh51UEkH4+DcPAsXM7YBpD51aEca1Wg2EYyiIsj5c5yHryuAhoeX7HcVAoFGDbNkzTRKVSUeOl9BFfjdVrYCgd3bIsLF9XxAMv9WHl5pKqrMuGD9kxumVcF9m2batAOn28ljgGZA31bxfZz20uYlI+hR9dfCgOnNYKALEeaHFQyEaKHrgnlnEJQRMhLQ4F3akgayaVSqnKtPSMZzIZNDU1qc2bgYEB+L6PXC6Hzs5ONXJOHDnbtm2jdZwQQgghhIydkdLGVXL0kdPVBbSeJK6HW+lWcX0WrV7VbrToUmjvW4iwAaB67Hd2X2CoSmxZFgpVHzVvaB61VMVNrWosgkoCpqTimUgklFCW4DWpVIpLolwuA4CqZNZqNTUDWVKn9dnIjRs98tgF22dHPbelrCzmTB7fNfr4LNnA0PuvxTKuW/b1avZdz27Gqu4CJuVT+PHFh2Le5JxKkdfXnfTNV6vVWOuBngMhuK6LarWqWlZ0d42eOB8Egertz+VyyOfzSCQSqFQqKBaLKlyvra0N7e3taj3JZs5YbOMAhTYhhBCyX/HTv67BMV/7I17YUtzbh0L2QRpt409vGMQzGwtIWSbeuqhDpY2LIJLHSPVQBI9cbIuAEbEjoumnj2zEB3+2Aqu3lii09yFEuAJQLQA7Q68yAvV18//d9yKO+dofVRhaY3+2VJ0BqA0YvQdcrLvpdFqJIxnV5bouisUi0uk0EokESqWSsgTLrGQR8o3fb+wln7s9K+C57qK6n6xlMjJhGMaq1fI7KyF5YhkHEHM46Js17zpmJv7lrEX4yd8fhrmTskilUiMm24vIltcS4S2VcalqV6tVVKtV9dmjB7NZlqU+i2QDR9wS+XxepduXSiX09vYiCALk83nMnj07th6q1Sr6+vrU3PfRQqFNCCGE7CfUvABf/t1K9BQdXP/n1Xv7cMg+hlT9gCGh7QYBjpzVhjMXd8GGry509UqkWCvFNi7fA6CSn/VUZwB4YPUg7n1+G57eOEihvY+gJ4zLyKNd3V+fmwwAAQz8asUGFGo+JuXrj9eFl+/7KBQKahNGrMcyd1lsvRKoJ2F78vdisYgwDGHbNoIgUNXtxhFQelVVzxMQh4VhGCqUb2V3QdmQmTy+c0TAAoiJbNlI05PH5bMklUphsOKh5AxtdLznuBmY05EBANUDrSfbi/CWtSjnRgLNJKjR933Vr5/JZJDJZNQmi4h8CVAzDEOtl3Q6jfb2dgD1anhvby+KxSISiQSmTJmCpqYmdVutVkOlUlG92blcbtTvF4U2IYQQsp9w17Ob1d8vPm7WXjwSsi8igkgfi3TkrHbc8ZET8M3zF6sLX6lAyYWv2MHFZiyztMXmKWJHqkkAML9ju8jZVFCvxUri3kNE9q4SxnXkfEnglWVZuHtlD/rKLqa2pLHkwMmxEDIAajyTpIlLwJVt20gmk2p9ZDIZ1S8t1WzHcVAqldR9RXSL6JLXEteE/FufBa+P+ZrVlkbSMlByfGwpB8q+zOTxkZH3VTYrAKhWEQAxsSzC2zAMlL0IF//4YVzyk2VKbOszsuUzBBjqy9bnYafTaSWWgaEQNBHZURQhnU6r/v5KpRILtJPHyueVBJ2JoB8cHFS91y0tLejs7FTCXmZxFwoFNY4un8+P+j2j0CaEEEL2E365fD0A4NLTFuDwGa1792DIPkejbVwn8l01Nsm2bXUhLL2QpmmqecSSIJ1KpdRtctEr4md2W92SvLJ7SGjL7eS1R8KkACCbze5SZAMjp43f/MjLAIALj5qBhGWq57QsC47jqFnZkmIuoWi5XE5Vr6XfV8LNxEY8ODiIMAzV+K9CoYAwDIfN9hZBBSAm1PW+4TAMkUpamNNef+xLvXW7vD4PngyhV6vlfRQXAhBPIZcAMQCoBQbe/eNleGZjAWu2lbGlUIvZ+EVUA0NrQj5XgHqvttxf1gJQX0/lclltpDQ3N6twPWl9EFu5hPXJOc1ms2hpaQFQF+WSNp5IJNDR0aFuk2q2CO0gCJBOp7G2unOnhw6FNiGEELIf8HJvGQ++1AvDAN5x1Iy9fThkH0O/uBWh/ZvHN6C/XL8IlrmzMnJJH88ktnH9+yKWgiCIVcilsjS7uS68V24qAGAg2t6kMWF8tCPWGi3W6wYcPLy6D6YBvPPo+meMHoRWKBRURTGbzaokaekFl+q2WHN1m7dUs5PJJGzbRqFQgOu6qp9X1pjeV6uLM0k7l2q23Hd+Rxp520LRCWNhbVyHcSRgTk9yl1Fe+txr2SAJwxCFmo/3/exxPL1xEO25FG7+4HGYNzmv1pousuXzAxhKhhdXjD6PW2Zxy+eRaZpobW1Va1YfSWcYBkqlUqx3P5lMorm5Gel0WrUibN26FVEUIZfLoaOjIxagNjg4qOZ3y8zt/3mxOur3jUKbEEII2Q+47dF6NfvkBZMRBiHufKYb6/sqe/moyL6CfnFqWRZWbirgU798EiddfS9KtXrSs4ggGZEjPdpS6ZFRS9LfKxfnejVRLtanN5kwDaC37GJr0aHQ3kuMJWFcR8SQPif5tkc3AABOPXAKprVm1PMDdcu4rIempiYlzqIoitmF9Qq1Xs2Wvu5Mpv68AwMDMReFbhcHhiqwMopO1qBUNkWYf/Kkabjno0fgXcfMVFVaCu04Ei6nb3xInzQQt4xLMnyx5uPDtz6DpzYOoi2bxM0fPBYHdjWpzTk9D6IxD0C3lQOI9VjrYXrJZBL5fF7dT9aU5EjIbHV9tFcmk0Eul1MivFAooFQqAQDa29vR1NSkcgNc10V/f7/6+SzLwlY/jWe31Eb93lFoE0IIIfsBjhfCTpg4//AuXP7bp/Dhmx7Dn57r2duHRfYRGqvZty6vJ0afsnAyzNBX1UDpnRWxrV90y9gf+bcIOLlfIpFQlamkEWFG61AYFYX2a4+e6jyahHGdxgRvGCbuWFEX2hcdMxPAUJuAPuPYtm0lxlzXjfXgyggvAKqnX6rZg4ODSCaTyOVyGBwcRLVahWVZaGpqUmPm5DXldfUwLRHQUkGV47atoRnbsvb1nmECVa3WK8oijBst42EYYqDs4EO3PI2nNxa2i+zjcFBXs7q/ZDWIq0A2T4C4s0YC1VzXheM4sfwHoB5KprcNSOuBrAHp1ZZzn06nkclkkE6nUavV4DgOBgYGVEZAR0cH0um02gzo6elBtVpVIwwty8If149tXVBoE0IIIfsB/3zWIjzy/96Ek+a2YOGUepiL2HYJ0YV21Q3wm8c3AgDedcwMFItFJbKlr1afTStVRd1+LJVDEdf6XG4RMvM60sgmLWwruRTarzH6OCXLsob1Oe8KWS8iUtN2Cr/6yAn45JsWYMmBkwEM9UqLwJUKtGmaSsCk02k1jkmcEVK5lMArqWZLv+7AwAASiQQymYxyTui2cGBo1rNYnfU57vpxS5VW1rEegsXkccRs+JKzsCPLuEwi2FpysWGghtZsEr/4wHF43dRm9Xy6EwbAsNA9+QyRpHFZo3IM4qBpampSnztCrVaLtbQ4jqPCG6XaLsn2vu+jXC6jVCohDEO0tLSgqalJbRjKOC95zSiKUEMKf10/+mo2AIzOH0IIIYSQcU8+ZaLiG1gwuV5BWNlNoU2GqkxSdf7tig0o1nzMaM/g+DntWLfuZfi+j7a2NpimqSpM0tOayWTUBblUvHQhJoFopmnG5ux++qSpmPnOKWjeXpUEmDz+WqBXe03TjFUUR4NUDPWZxpZlYc6kHD51+kJ1P8dxVCVS7Nq2bSu7ugh8PRwrkUjE0upd10WhUEAymUQ2m0WhUFDPmc/nVdCV3kMsjxdxJhs+si71NPMoivCd+9Zj2fpVuOIt8zAra6rH6MnV+yMipOW9kH54Pc1bt4zLeZw7KYtffOAYRDCwaNqQyNZt37lcDrZtD3t/RWjLBp3kB8hYL/lKJBIxu7neKiAbPFKBl1BGcSzI+MFSqYRarYZUKoWWlhbVOlEul7Fly5ZYZb1Wq+EvPSb8MMBBU2ysH+V7yIo2IYQQMoHpLTl4bnNdUPu+j1KphM5U3T75ty1F+AEriPs7jbbxW5bVbePvOnomqtWKqkBls1l1sSyzj2VutvRwZrNZdWEuF6zSk6mHVUVRBNsMEWq94QKr2nsWEU+jHePVSKNtXHcrCFEUqZnF+ni3VCqlqteWZalqtogiXbh7nqeSxWX0VqFQUGtRxoGJHVy3iIvQFvEnYkuvjMpjNhccrOur4vmt1ZizYn9fh/I7Lf3Qei+1fA4A9Qp3yfGxYs02APX3dNG0Vhw8rWXY89VqNSWWG1sV9GRwcTOIIJaNulQqpULJ9NA+ccnIWpLXkdFv0setj4qT8XD5fB4tLS2qj7tYLGJgYEBtDnmeh9BI4L719XX/9oPiP9fOoNAmhBBCJjC3LFuHN3/vL/jn3z4Nz/MwODiIZstDJmnC9UOs3lbe24dI9jK60H5+SxErXu6HZRp4x5EHoFQqwfd9ZLNZlQCsz9OViqQIabmglU0dsWkCUEIbGLKC6mN+aB/f84gQAcaWMK7TONbr+/euxYd/vgJPbxgEMCSyRaiI+JUqpQh9Eb+ylmQms7ggPM9TY5ekqiiiT0Z86bkAenVUnBESwqYLbd1ODgDzO+q2+ed7KqrKvb8LbbH7S7K7Psqr0TJe9SNc8tPleM8NK7D85YERe/3DMESpVFItACO1KujVbD1pXjZlJNROqtQ64p6Q9S3nUarmIrDl78ViEZVKRa2lbDarRhNu27YNnuepCrfjOFjRZ6HoRpjanMLxs5qHHfuOoNAmhBBCJihhGOGX29PGDzugBZVKBZ7nwTQMzG2vVyZW0T6+X6P3tVqWhSfWDyBhGjjtdVPQnk2oi+N8vt7XL2JHeiilqggMzbyVCreIILFz6uJG7L7f+MMavOk79+HJ9QMU2nsYse0C9SrkK7FFSxCeiGHXD3Hbig2489nN6CnWxZfjOLHZyGLjlb+LQ0J6+fWRcLLhIiJbxsMlEglUKvUpCbZtK0Guj+vSe6xFLMvaE+eFni0g4mteR/2z8G9b4qOg9ud1KOndYsXXK8i6ZdyNTFzyk2VY8XI/EpaJpvRQGrmOLpgl9Vuncbyg67oYHBys/39lmsopAwyf8x6GIRzHQaVSURV4aRWQEDPpMc9ms6hWq2omezqdRi6XU33cfX19GBgYUJXzuvsixL31yApccEgHLHP0DhD2aBNCCCETlAdf6sX6viqa0gmcfuAk9PZ0q/7FOW1JPLulipWbCjjn8Ol7+1DJXkK/uDUMAxceNQNvPGgKyo6v5scmEgk0NTWpSqQEW8lakl5WqWYDUBUjSR7PZDLKPiwiKAgCvNxXxUtby3h2UwEHTekEQKG9JwiCIFaF1M/VWJD1Iuf8nue2or/iYWpLGqcsnKzaCiTYTESvCLNqtapSnqXHX+6jVx9d10WxWFQbOtJ3qwe36W4Jmb0tlnP9OEWsSZVTNgFEiM1pq1dHn+8pIUJ8Fvf+iLx/juMgnU4rRwEQt4wHRgLvv2E5Hn25H83pBK5feggOn9Ux4vPJJklTU9MwF4WsTckNAOpOBNmAyWazSqQ39mbLMVUqFbU5IDZzfe0YhqHWnIzskhaEfD4Py7JQKpUwMDAA13XR0tIC3/dRrVbxQimBTaUQuZSFMxc0wa+WRv1esqJNCCGETFBkRNO5h0+HEdaTVOUi59TZGfzb3y3Gu4+ftTcPkexlGvuzAWBS3sbM9qzqjxXbuOM4qFarSghbljXswhaA6s8Wm7lcmEsVFBjqqVwwqS6aVnYPxqrdZPehJ4yPJFTGgm71B4BfPd4NAHjn0TNgYMhSLKJIXA3S/yoCR2zkjW0HInKlZUEeK2tI+nSB+BguCbOSzRxdwMt9RCzq891N08SUnIVcyoQXRNhY8pVtfX9MHpdQMakK6xsbumXci0x84GePYfnafjSlE/jPiw7B4mnNw6rZYRiiWCzGLOMi4iuVitqQK5fL8H1fhS3K5oxU0qUNYaRqeKVSQbVaVQGNyWRS3V/+lNFwhUJBpdinUimkUilVIe/r60OhUEA2m0Umk1Hunb9sqa+bty+ehEzCUL9Lo4FCmxBCCJmA9JVd3P3sFgDAhUdNj/VMep6HuS0W3rSwDQe0ZffykZK9hW6PTSQS2DQwdAHpuq4KIWppaVH9mnIxLNUi/d9AXcwMDAyo9SaWUOmblC+pVkk1cVV3kdbxPUBjwvhYx3g1PpecNwBY01vBsrUDMA3gHUdOVwJEFzty7m3bVgJO7LwAYmFlItKq1aoKUhPnhMxIlvuJrVnsv/J88hy6bVyq2qlUSglvqXICgAFg/qR68vrqPlfZx0Ww7084jqM2MCR0TN4nsYzX/AgfueUpLFvbhyY7geuXHorF05pUH7wgvfrSsmQYBkqlkuqblw0QeY9TqRRyuZzqm5aebGAoUK9x/fq+j8HBQVQqFbV5ox+DHFM+n1eiXzYLxDKeSqWUAA+CAPl8Ho7joFarYZuXxDO9AUwDOG9xGwDEZrHvCgptQgghZALym8c3wg1CLJ7ejAOn5FAsFpV9Ti6Cx7IzTyYeUp20LAurt5Vxwjf+hIt/9DD8oH5BKiN1crmcsvzqlUWpOgFQ1chEIoFCoYBqtapsp4194BJKBQCzWuoCqZ4VwOTx3c2rTRjX0Ue2maaJOx7fDAA49aApaE0NfV/ErvRi6wF4EoqmW8TFZi69tJVKRW3qZLNZ9XMAdXGkb96EYYim7ePhRGTprydrzXEcZR3W+4FFwC3qzOKgzhxSCUtVQve3Pm3JTXAcRwlQOZe6MyWfzaAlk0STncBPLzkSi6fm1e++PEe1WkVvby8GBwdV+4lshsh9bdtW1eNMJqOCFQGoNSvnWER2o+1chLvMXZe0cnFCWJal/qzVahgcHFRuCxkZ5/s+BgYGUCwWkcvlkE6nlSB/oKdezT5lfhs6bKBcLqv3YTSwR5sQQgiZgPxhZf0i+J1Hz4z1yubzeXUhtHxNL9avKuHkhZOGjWIhEx/dNv7L5S8BADJJCwYiNUapqakJURTB87xYZdSyLIRhqOYiy0VupVJBX18fPM9DV1cXBgYGlLARm7mIoSAI0JU3kLIMVNwA6/oqmJwZEjmvJBGbDLE7EsZ19Eqe44f4r6fqjpkLDu+KiXn5rJGxbqlUaliCtQheqXDLLG+xEUv1WqzG8lgJs5IQNRFgIthFOOuJ5NI3LhZhqWhLAJtlWfjHYyYjl8shm81i69at+6XQliquiFNpMdAt48lkEmk7iWuXvh5rt5XQlYWaiS4uBADqPZf3Xb6kzURHnlvOqWzw6SJbPx79NfS56tKfX6vVkM/nY4+RDRxpn5LMiGw2i4GBAdVD3tzcDNd1US6XUQ5MPNRd3xB85+FTUKvVUCwWx/R7xE8wQgghZALys/cdi//4+9fj7YdOVQmrUqUQC+UdT2/DN+98Dvc/v3VvHy55jdF7VwMY+NWKDQDqs7NlY8ayLDQ3Nytho6cNi2DRZ9Qmk0n09PQoG+eUKVOU9VT6LqWSKa8fBj7mbbftruwu0D6+m9gdCeONzydiWvqgP/7GeThxXgdOmN2iXkfCp0QkSYiVCF5JgwagqtJScZSZydVqVdl90+k0BgcHlaVXxK/0WWezWTiOg0KhoISevJ6sIV2Uy7qVirmMBdM3d2QTQAT5/oAI1CAI1AaHbhmvuD5uWV6P3q5Wq3BrFUxJh6rCK+dUdxTYto2mpibk83k0NTXFzr0gLgdpFxDRLFVjsX6LE0sIwxCFQgGVSkWNHtMD/7LZrArIk9fp7+9X61dmbHuep/Ik8vk8bNtGX18ffN/H8j4bXggcNDmD2TlfbSCNJeOAFW1CCCFkApJKmHjz4qlwXRcbt/fL5vN5dZEZhiFmt9QvA1Zu4oiv/Q19tvUfV21FX9lFZ7ONUxZOQs+WzfB9X1WFBgYGYknOYtGVkKpcLqcq2z09PfB9H5MmTUJXVxe2bdsGwzBQq9XQ0tIybCyP53k4aEoWkWGp4wEYiPZq8H1/tySMCxKQBUCJk3TSwnuOm4kLD58CAGrmsFi49eBFcUQAUDZx0zRjifSmaaJQKKgxULZtI5fLqZ/Fsiy0tLQowe84DpLJpKqWS5iWPrZL+rRlFJhs9IRhqESlnkwdRREcP0CwPf9MROBER86X7iKQ/AXHcdA7UMCnfvMCVmwoYlPBwWfeNBcA1PQBsYDLRka5XEYymVR93vIej0S1WkWpVFLWfnE8iDNCwu8aRboI8yiK1GuUy2VUq1U0NzejpaVFjeeScDt5PmmhSCQSytouQWuSTRHAxH0b6+f+3EXNqjovlfDRQqFNCCGETCC8IIRlGDC3z/osFovqgiiXq/dqizVzZpMEUVFo72/otnFJp3/nUTPge65Khm5qalJVPbmoFSuw9M+K4Ekmk+ju7laW866uLgBDfbJSMZS/SyhfKpXCpSdOxdSpU9XzAqxov1JERAKvPmFcEAu4Xq00DEMJZRG8AFRYmohYy7LUTHUJqxJBJiIol8vB8zy1oRNFEZqbm5HNZrF582a4rovW1lbVO63bxE3TrKdaAxisBTC2P78EmYl1GahblEWYy3HqP9P/+9/V+MvqQXzzrLk4bEpC3acxYGuiIQngUs0WN0QURegrlPC5/3oRKzYUkU1ZOP11U1SVWd6XXC6nRLDMspZzA0CtDR2pPov1W9aQnigv87QzmUwszdxxHFX9ljaWarWqckiam5tj4wgty1KuLunTl9cQt042m0UymcSWLVsQhiGeGkhioOajI2vhpNl5BJ4b6+seLbSOE0IIIROIX63YgJOuvhc3P7IOURRhcHAQvu8jl8shDENVPQiCQAVRrd5WRsX19/KRk9cKPQxqU8HFX1/shWEAFx49Q23MyCge6cvWxZZc3OoVMNd1sWnTJlUJnzp1Kvr6+pTokR5tEWB6IJpYewHQOv4q0BPGR0pofqXPKRZ027YRBAFueXQjbl+xAWXHVxVNQQLzROiKDVs2WfRwLalcG4ahbMCe56GpqQmZTAZBECjx1NbWpiqTtVoNyWRSbdaEYYibn/PwhYeBNUVDCXx93cpx2batjkdfY4ZhwDIAP4zwUp+jfpaJnDwuqeA9PT0olUpq3UhwYbHi4Au/ewnL19dF9s/edwzecOBU2LYdO5/yOyv/rwCI9eLrIjkIAlSrVdWeIrPRm5qalPNCd0DIeZbnCIJA/R+mj3orFovwfR+ZTAaTJ09WzyGbLbL5JMF50gsum32ZTEa1LoRhhD9trL8Hbz+oBamEpTZkJLRttFBoE0IIIROIW5evx8aBKkqOpyoVksxbq9VQqVTURUZzykB7NoEoAv62ubi3D528Ruii9jePbwIAnLxgMqbkEmpOdj6fV2K6VqvFRv4AQ+nhYk3eunUrCoW6M2Ly5MkqMVhswXLxLr2ywJA1V2zpfhAi1MYWT1SBsycQkb27EsYFqWyK2Kk4Hq69fy2+/H8vYfm6wWGvI5VKvY9fxJfYuE3TVOFTIqh7e3tjs5Kz2Sz6+/tRq9VUa4IIOfkzlUqhVqthoBbiTy/XNwNWDVpqQ0g2eMQGrecLiNiSFPRkMom520fNvbC1qh4/kQPRfN9HoVBQQXPSE5/JZAAric/99wt45OUCsikLN77vGBw1ux1AXAjrTgY9E6Bxdrn0Ycv/P0B9rSQSCZU2LutIn3MuAWqyASAbgcBQr3SxWFSZEm1tbcjlcgiCAJVKBZZloVAoxKrZUgGX3nLZ7CkWi6hWq1hTtvDyYAA7YeDcQyartUKhTQghhOzHrOou4Mn1A0iYBs5//QEoFAqo1WqwbRupVEqNzdErNfM70tsfS6G9v6Dbxj966nx8752H46NL5qk+V7EcSzVQQtAAqCA9+Xcmk0GlUkF/fz8cx0FTUxPa2tpUBUm3aorVWO/ZlMyAS3/1LBb9611YtqaPVe1XgF5N3F0iW2zaAFQP/p3PdKNQC9DVbOOMxdNjfbN6arS8vp42r1cmJfRKwqfkc6m1tVWJs8HBQQD1JGgRR/paFMH8h5dd1VfdXTVjtmUR/npVXTYAZINHwthmt9WP7fmtldiIr4maFyAp3MlkEpMnT0Zra6v6ff3YzY/jwdX9yCYt3PDeY3D0dpENDKXPi3NAb1eQMX/yu5tIJFCr1dRni3xPF+NSGZfNOVk/uVwOiUQiNl9dzx6QY3EcB47jIJ/Po6OjQ31fzp3jOAjDEK2trfA8T23ySFuBBPH19vbCsizc113fCDxzYQtaMgk1pi6bzY4584BCmxBCCJkg/HL5egDA6Ys60ZGrh1gFQaBChaQPT3rXPM/D7NbtgWjdg3vz0MlrhJ42nkgkkE5aOPeI6ThqVquq8ki/olygiliSKraIGNu2Yds2tm7dqtJ/s9ksWltb1Yz2RCKhLoobU8uBITEXhiFcP2Ty+CtAeqABjDmsaVfPCwwJqmq1il89UR/pdeFRByCVjEc96bZx/fzKnyKmpMqdTCYRhiH6+/vV66TTaeTzeTWLPZPJKDdOFEUolUqqAu37Pqqujz+tG5prvLlmqdcScS3VyEY7u/Rqp1IpmKaJOa11AbWur4qaH6mfaSKuwzAM1cZrKpWK9R27rouzD+lEk23hJ+89GsfMGRLZjdXsxnYFfYMuDMPY3GkZp5XJZFDeHtDp+76qTOup4XpwovRqi73dtm01F9t1XVQqFSSTSRWCJmJaAtLESZHL5eA4Dkqlkkoyl6DGUqkE13XR7yfx+Jb68V5wSIf6vzKKIlXNHssmFoU2IYQQMgGoeQF+/Vh9RNM7j56h0lwty0I+n1czUmWXX77OmJvF7/7pBFx+1qK9/BOQ1wJxM+iCGQBKpVLMSgkM2UGl11EECQA1UmdwcFCNZMpkMsjn8+rCWgS7PJ8IN7kI18c+zdvurFjZXYhZy8nOkWRoYCj5e3cg50We1/M8rNzYjyc2lmAawEXHzhrxWCR4UVwPUhWOoihWzRYLuWwGRlGElpYW5Xbo7e1VwVa2baNUKimxLRXQarWKRzZHKLkRJmXrzz3omSg6Q0Fp8jmnj/oS0S1VdKm2t2eT6MgmEAFY2+8OjaCbgEJbxKi8H9J2IBXlNy+ajHs/czKOm9sx7HF6K4FsxsnngQh4qRoDUHPSpXos7Si1Wk3NNgegNueam5vVWhEHQrFYVO0Ctm2rdhYR+el0Wq2farWqqucS4tjc3ByrZsvnnIShlUolpNNp/HmziQjAcTPzmNlqq8A+cYWlUil1nKOBQpsQQgiZANz17GYUaj6mt2Zw0oLJ6O/vh+d5avSJXJBINVH6FzvSwPyONOzE7qmCkX0buQDdXPTwpu/ej+v//JKqJEk4lYxwEtu4BA9JkJT0ORqGgcHBQSXIpBopgrq5uRmpVAq5XE7ZSXXbuT5Wad72/tiVm1jRHi0SLAXEk793B/o4L9M0sbG3iM//9wsAgDceNAVTWzIjPkZaDxpnaOtrRqqWQRAoe7iImGw2q4LRkskkWlpa4DgOXNdFtVqFZVlIJIYSwe9cW19r5y5qxvZx7NhYNmJVR73nV8ZBydqWNSkCXzZ81vS7ysqsr9mJggTPyUZY1fHwxV89gb+t71Hv0aTm4ena8rudTCZVmBgw1Jc9MDCgNlsSiYQS2HqYmYzhktYB0zTV/09S8dYT7aUvW0LTpCotlnXJlBBruJxXfSOlvb1dtSjIsZXL5Vh6vWckcf/6+s933sGtKp8gDEOVNSGz30cLhTYhhBAyAbh1Wd02/o6jDkAU1i94ZESTBNFIVUn6D6VaIxc1ZOIjF4m/fmIzVm8t48/Pb1MVILnAFqEtVmC5IBfbr2EYSCaTqsdTBJVcWOuVJwAxoS19vCK6pFo+e7tt96WtJfjb9TWF9o4Ryy4AZdndXegp8DIO68r/ex7r+h10Ndv417MPHvExYsXWk+ZFoMr5ln+LU0LWk/TjmqaJvr6+WDW7WCzGeoCB+qiu5wsmNhYDZBIGTjkgienbdWF3zVRVajk2vddaHBN6xV3s8UcdkMNpC9sxvTUTSxyfSGtR31hLp9OwkjY+/etVuO2xbnziV6tQKldGbD9onDwg58SyLDiOo2Zxy/87ck4FWbPFYj0PRMSrfiwipGVDT0LNgHpiuCSly/mUTZLW1lak02klnhOJhApnzOfzalNQ1qc4HUToG4aBv2wM4fgR5nWkcdQBefW6Mr5QXk82F0YD52gTQgghE4DPvflA3LpsHd5x1AyUSiWUy+WYPU5sgVJdEFtkEAT4/VOb8NTWdXj7YdNwwvxJe/tHIXsIuVD0wwh3PL4RAPCuow9QQjuVSqlqoViH9Sqi9L5algXf99UFMjDUfymVxGw2i23btikLsFSDJOFYKmIiZjpSIZrTCRRqPl7aVsbMpqGqtm5xJ/ExXqZp7rbwM0GvJhqGAdd18blTZ6Lmhfjy2xdhRvvIlU5pPRCRLo/Vq9lSbRSxJ2tBNmZk7FMikUBzczMcx1HCTK9EAsBda+uC59TZacCrYmomxJMwsblqIYqGerFlw0hEtb6eJBBNnD/nHFQP8xNbux6Itrt63/c24lIxDANmIoVP/epZ3P9CL+yEiU8tmYFMesianU6n1fsl1WwJONNHtAGIbbBlMsMdDxKK5nkeMpkMUqmU+kwQN4y+yZNIJDAwMACg/nmSTqfR29ur1pRs7EgAo7RRyP9rsr46OjqwZcsWda6z2ay6LZPJoFAoIIiAP2xPrr9gcbv62eTncV0Xzc3NsRF1o4GfXIQQQsgE4PUz23D13x2Gqc31FN8oipRw0itHUm0Sy2QQBHho7QBuXb4eD77Uu7d/DLIHkQvYB9cMYEvBQUcuhZPmtarKowhqFU62PdFXNmxEbOiWcgmlEhuoXtHs7+9X43ykEimvJdVNqXR7noeFU+oCblV3kfbxnSAbHLtzjJcgAgMATCuhqosduST+c+mhmDuleafHJBs1cnxi3RVrtmRF6JMPJMDNsqxYgGMikUCpVFJrJp1OqwCsHsfEE1s8GADetiCHWq2GrnT9uDc7CbUJIT+T2IAFee1GoS2VeNkcmmgjvmSTxnVdJJJJ/PP/rcE9z/XATpi45sKD8abFM1Qwmti8Zd61vAcSQCZBagBUGre0ADTieZ4awyX/L8nGSzqdrlfWtwecyfMVi0WEYYhkMommpiZ1LGIjlw3klpYWZLNZVCoVdd4LhXoLSjabRRiG6OvrUwJfNltkdJjrunhsa4RtlQBtmQSWzMmpyrxU1S3LUjZ7hqERQggh+ymO48QuMiTcptEyJ3ZK3/cxY3v1cGV3YS8fPdmTiNC+/bFuAMAFr58O36mpBGg9KVoqQhIEJEJcbKJysSoiRCqTcqFbq9WwdetWFZamB6zpIkiEjOM4OHZWM958cBemNNkMRNsB0gcNIFZt3J3PDwBlHzjv3x/C7Ss2qGRo2ahrJIqimLtBepuBIZu2PgZKT7FPp9PKmisJ0ZZloaWlRc1dlg0gz/NQq9VgWRb++HL9+Y+cmkJnri7ip2frQrDHseB4vhL3sqnoeV7s+GX0k7ymiD/X87C+v4aKN7QZOVGEtj7u7PHNLu57oQ8py8QP3nEwTpjbjnQ6Ddu2kcvl1Hvlui4GBweVwBZ7tgSE5fN5tUkBDNn7hTAMMTg4GGs7EYErAl02UQCowDQZ89XaWu+Xlgp2MplUExJs20Z7e3tseoHYy6X9YPPmzcqZk8vl4Hmeel15nbvWbO/NXtwBy4hU9V7aCmzbRlNT05j6swEKbUII2SeQoBdeVJKxct/fevD/fvM0ntk4iCiK1AWRpMCKFU+EkVzk6hefM5vrF1QrN1FoT1REEG8u1PDnF7YBAM47rEvZt0VEy8WtVB718Cm5ABYhLtVvqfZI9SeRSKCvr09dWLuuqyqvjf2NegX0osM68B/vPhInL5zMivYIeJ6nBEA6nd5tCeP684dhiMGqh/f97Ak8213AtfetRc2vb4zsaH6wnjwtYkuEsb6BI6JW1lwQBCqJWpKvPc9DLpdTAkjElKxJ3/fhIom/bKi/D+cc1KRcF+1pAykzRBAZ6KkitgkhIVb6yChxZsg6FaH9yd+uxrk/egKPbqwox8VEWYfSJmIYBv74Yv3z/sLXT8UJc9tio6tkozadTsP3fZRKJWzbtk31R+dyOTQ3N6vHyLpMpVLDKr4DAwOxEV96oKLM1JbgMsMwkEqlVHtAc3NzzHkgzy1haNILLudRXBEA1OZNtVpVLRaJREJtLGYyGVQqFawuAC/0eUhZBs5eNBSoJs8ho8MAUGgTQsh4RMQQhTYZKz9/6GXc/Mg6/O7JTXBdV9ntJORFLlLkAkUCr3Tr+Ix8/bbNhRr6yu7e/HHIHkIuEH/7VA/CCDhubju6ckYsiV6Etj7WS2ygcmEsF8TpdD2dWb/Alh7darWqLKIiVOT+eqCQBFY19tHK6wEU2oI+Y1iqcbsTEZ2DVQ//eMszWNldQEcuieuXHoJ8uv5aOxL2UqWWqnVje4CIG2lFkHMq1WyxDEvFOZVKqf8TxSUhj7UsC/eu9+AGwJyWBA6flhuqOEchOlP1db6pYsbWkqxrfTyYCGhZd1IBP6BlezBfrxMLdRvvyePiPPB9H4lkEhsG6mLyzIPalOhtvL+8P/I7Ku+dLsr1oLnGdVkoFFT7gWxkiCU7kUiozwj5HLFtW43kEpeM7qCRbAjZ4Gtvr8/4lhYF13VRKBRUO4sI9qamJiQSCVQqFVWFl9+pu7e7I05f2Ip8IlLtLvJz5nI5lSkBIOaK2BUU2oQQsg/Ai0ryStg8WMO9f+sBAFx49Axl6xNLJgBVQZKLSt1ipwJfzAgHtNatvatoH5+QiNA+ecFkvP2waXjXUdPVhWMqlVJrQ6rOtVotJoRFrEjPpFz0No6Mky+pREpol1xgy21S+ZZjkwt6z/Owob+Cmj+U9jzeBc6rRaYGAFC98Lsbz/MwUHHxj7c8jZXdRbRnk/jxxYdiQWeTEkYjCQwR0Pp5kjWgz9MG4tVUoC5+5O/SQy2VcHlu6alVs5FNC/esq9+uj2AS4daZ3j6+rmap90t+Pvnsa8yqkFYaEXZzWuubS6v7nFjy+HjfCJfNsyiKkEomcePFi/CzpQdhfns9lKxcLquNNNd1US6XlTA3TROTJk1CPp9X47dkDrcekqa7CMrlshLNkvEAQG2uiEtCNpBEiEvat4SWCdKSIL3Z2WwWuVxObcokEgn09vaiWq3GsiMaQx5t21Zj5HrKAZZtqm84XLC4Xb0HMmpO3wySdTmWdg0KbUII2Qeg0CavhF+tWI8wAo6Z3Y6Zrba6MNIvxvULFVlfYpuUf/u+jwXbh9DSPj7x0CtOR8+dhO+/63CcOq9FVYFEpIgIkfAjqSzqzxNFkRI/srbEOQFAPY/0P+qVaqmO66nUeuCU67p414+W4cRv3ouHV/er192fhXZjwrhsoO3u19hWqODDtzyDld0ltGWT+NHFh2L+lHzMaj0SuniTyrKsE1kXcr71qnxTU5OyjItYlrUmGzMSrifBW2EY4oleA/21CK1pE6fMbYqNaQKALrv+HFucRMw1oY+Wk00f/fNPRFkikcDc9vo6fX5rJRYcOd7/fxZrvrgGoijCgsnZ2Oi+YrGIrVu3qnnYIrJlHnZHR4dqAwnDEOVyGaVSSTmlBEmLl+/rG3Zyv0wmE5txnk6nUSqVAAz9HwVAVdtls0WyI6RKLRSLRfT396tWFnmcBKfJ63d0dKBWq6FWq+HeDSHCCDh6ZhM604ES8fl8XoWlyWgv6ekfy3gvCm1CCNkHYPAPGSthGOGXj9ZnZ7/rmKFqNgC1i69XrwEo659UIPVQtDlt9YufTYPVvfMDkT2GHkylj8XRRYhUqKUPVirXUuGWID29B7NWq6mLZAlEk8qRvr7Eii5CWwQ4MCSqxB48vaUumFZ2F/i5iPh7vLsTxgXXdfE/T2/BM91FJbIXTMnFNlpGEtpyzvQQNN2uLeJWZnFLf28ikUA+n4+NGASgfk757JK1pydci833bQubYIT+sE2bycl6dXVzLRFbN9KyIPZzOVYR2fL7kEwmMbejvpmxteSh4Aylo49noa07D7zIhBsOfS7kcjnYth2bTS2bC5VKRbkppB0pmUwqO7U4pmSdAkPhaXIOpZotgltEtbhYAKhecP21RBjLOpR+a5moIf39cgw9PT2xDRPZIACg+rTz+byyp/eXqvjTy/WNn7cvzKv3R+zisgEp6feVSiW2xkcD52gTQsg+gG5F4txYMhoeWt2L9X1VNKUTOON1U1Ac6EW5XFYjVuQiVS5CpEKQyWRUpUcuplzXxZvnteDSt52B5vTu7f0kex/f99FTdPCzZd1YetwsTM+bak2I8Jbqtt4r21gRlAtkWTMiUCR9WC5qZYNHLsolTVrWpWzu6OFZctE9v6P+HKu6CzDNGRMq8Xms6AnjmUxmj/y/IOfyXUdORdUHTlnQjnkdaSVGgaH+/Ebk/Is4E+EsnzWSDZFMJlEoFNTnU1NTk9rYkXMr6eIAlIALggClUkmFna2vJrF6oIakCbztwGZlJZbjtCwLU7MhgAilwETJN5DV3jPZ9NFdHLIJ5LquqpBmkyamNyexseBhdZ+Ltmxq3Att+X0FgN+t7MOPH9mMfzi6Exe/foo6j5ZlIZvNKgu3jOOS8y82cqkWS4iZfJaInVxeK4oiNSpMPmckxE/vnxZrd29vr/q3nFMR4NKXLe6HTCajXDPyVSwWVXiZzMgWR4i4GNra2uA4DqrVKv66KUTFizCz1cbiSSbC7ZsBIuABqJA+cWKISB8tvJIjhJB9BNrHyVi4Zdk6AMC5h09H6NVUUqrs2ks1Qu/NFku5PjNWLlZtI0AuycuCiYaIn98+uQU3PrwOX/r1U7FwPOlXFVEnwkPCf1zXjV0siwCT+cYiWnK5HDKZjKps6f2MUikXe69uxdVTzcMwxKyWeg1oZXdhv/5MbEwYH0sA02gpOT4KpXo/bCKRwD+9cT7mba/mim1bbtvRMcp50zdMxP3gui5s20YikcDg4KBqR2htbY1toOh/z2QySqyLIJLnuWdD/TVOnZNHS9qKBavJBmM6YaI9Wa9kd1eG3BqJREIJRdlIklBIyQYAoNL357bX1+rqPld9Ro7XdShiU0TyXX/rR8ULkUtZsap/KpVCLpdTfcnSI9/U1BTL/KhWq8oyLgnkuVxOpZMPDg6iVqvBtm31PjcGqcmIMalYi5AGoF5Ln4RQKpVi2Q5iP5fPILGcA1BOnLa2NnWcUoWXeduVahV3ran3Zp9/cCsMQG0KiVCXtSIJ5FL5LxaLo37v+T8qIYTsA0iiKpPHyWhZ2NmEzmYb7zzqAFSrVXUxIdZLAOoCUipMkhQrAhsYusjVL+zJxMH3fYRRhF8/uRkAcMHhXbGxS7pVVKyTIpRknYjlUy58fd9HoVBQyb/ZbFZZT2XNmaaJLeUA92+24AWhel7dUg4Mtc2IjXdmc/3S9OXeCsruUCDa/sSeThgHgLLj45KfLMNHb3kSNa9u7xZBIU4HEdojvb6cL0mUlg0dfYSgZVloampCpVLBwMAATNNEa2urWgNiwxU7t4gy6dsWwZZMJlEMUyq06u0H5WGaphLa0hIB1MVSpz0UiCZCW3fwSI+vpKQ3jkBMJBI4aXYe7z5yCg6dNmRxH6/J47ptfN2gj+e3VpEwDZwyJ6/EsFiqG8dnJRIJdHR0KJEq50e3levtJrpbRWzcUuGWKrNs0ABQLhgRr5L/AEBZzn3fR7FYVBsker+3VL8ldE369Zubm+G6ruoft20bLS0tyrGzbGMNW8oBmm0LJ89Kq59L1ooe4gjUg9kymQwGBgZiuSe7gkKbEEL2AQYGC1jf0x8bb0PIzvjEmxbgwS++CbNbEyqURi5s5WJSLrDkolJEjZ4ILBdGvu/jZw+txbuufwi/e3LTXv7pyO7C9308vKYfGwdqaE4ncNrC9mEjjuRzR4LL9HFIuVxOiWsR3CKADMNANptFPp9XVSqpAgVBgP/v8Rp+9VKEJwvpmLDWxY30bAJ18ZYxQ3Q116uJL2wtq++PR4HzSpDqI7DnEsbLjo/3/nQ5Hn25H09tLGBTYSjlG4hXs0V4NCLCTT830ocr4WiZTAa2bWPTpk2o1WpIp9OYNGmSEiq6s0HvxU0mkygWi6qnO5vN4t6N9dCqw7vSmNOeVq8h75O8d4ZhYEqq/vNsdiwl8OT15NhFUOsbP7JRkEwmsWRuEz5wzBQsnppTz62/R+MJvc//zufq9uzjZjUhm6hv5DTOvhYnAVCfYy3nX+zijaIcqI/xklFeqVQKtm3Dtm3UajX09fWp8yhhi8BQz7eeRi+bOno1u1wuq88mEfTpdFq1q7iui0qlAs/z1GZAa2sr+vr6UK1WlcDP5XKo1WooFouq1//cQybBtgz1/ujuimQyCdu21fztWq2mRn+Nlt0utH3fxz//8z9jzpw5yGQymDt3Lr7yla/ELhyjKMIVV1yBadOmIZPJYMmSJXj22Wd396EQQsi44fv3r8c5NzyHFesGKLTJqDGNesiLXBQFQaBCXGRMiVwMiV0ciKc9y4VLGIZY3VPEw6v7sOLl/h2+Jhk/yPn91eP1avZZi6fAQjisQikCWSp2Yg9NJBJobm5W30+n03AcB/39/erfEookF8JS4XyhP8DqgfoFaXdtKLVXXlsfyyQVMhH9B3bmAQDPbS7Gfpb9AX1k2p5IGK+4Pt53w3IsW9uHvG3h+qWH4uAD2pT4SaVSsWr2jkLQZENFXzd6b34URWhtbUWpVEJfX189qGzy5Fivs5xvEbyyNiTYUTZ3kEzj3rX14zvndc0qnErWRKNLpyu9PXm8IRBNXltaJ+RLfg49EE3OhVTd9WMeT+i28ZRt467n+gAApy9oUZsNeluCpLyLmN3RGpTb8/m8Ot/6Boa4pwYGBtR7q4/u0pPPxfadzWbV+yu3eZ6n2g7EKWHbNpqamtDW1gbXdbFt2zZlRc9ms2hra1OCWp5XrO21Wg0ru0t4rteHZQLnHlyfw62vZQkTldRx+XmljWGvztH+5je/if/4j//Atddei1WrVuHqq6/Gt771LVxzzTXqPldffTW++93v4tprr8Xy5cvR1dWF008/fUyed0IImSgUah5+8Wi9gvjLx3v2q+oNGTvPbynijyu3wA9CJZDK5bK6uJGLHknrFRuoXDBL5UgXOED9AkvvjyXjnyAIsK3k4t7n61Ws8w/vUpZevXrTWNETEZzNZtHc3KyCqkzTxMDAAMrlsrrYlZ5GqWKLxfaP64cEyRZnqN9RHw2kV011ofamhe340Clzccj0lv0ueVwXuLs7YbzqBnj/DY/ikTV1kf2fFx2Cw2e2KSEpbScipIGRbeMiSPR51/L/lgjeXK6eWr5p0yY4joNkMon29nZVzRZRK8JG2lvEMeE4jvpM+8sGDxU/wvSmBI6clo6l2UtlVcQRAEzN1NfKVjcBL4yGrXlZ3/raku+LfR0AessuHl47iG1lL7aZMJ7Qg8me3lzFlqKLXMrEcTNyseBMoC4mxVqdSCRUBboROfe6K0VGYuXzebS0tKhAO8l8sCwLAwMDKBaLCIJACXipVusbHJLbEAT1cVuDg4OoVCrK3t3c3Iy2tjYV2DY4OKjcN9JPLo4I+TlkbnapVMIf19fXx5mvm4x0VFMVf9k8lOq3PuNdhLZsUo+W3Z46/tBDD+Gcc87B2972NgDA7Nmzccstt+DRRx8FUD853/ve93DZZZfh/PPPBwDceOON6OzsxM0334wPfehDu/uQCCFkn+Z/n+pWf6+4Q2NO9kT4DRn//Ogvq3HboxvwD8fPwidOnKp6YqMoUmm+Us2WC9FGsS0Xw41Ce0a+fmGxqrsQqxCR8Ynv+/ivp7bADyMcOr0Jc9ttJRjEHi7rRBchujCSC+FkMolarYbBwUEAddunuCfksXLBuqXk4dHNQ7NmN9cseH6gko11oS3HoqdQv/nAVkyZMgUAVAvEeBM4rwRd4O4ogOyVUvMCfOBny/HQ6l7kUhaue9chOHR6M1KpVGykklR4gR3bxuXzRnqkpadaBK9pmshms3AcB1u2bEEYhujs7IyddxFn8voyzqlUKqkk61QqhUw2iztX19fc2w9qgp1KYWBgQIWlSVuMfM5ZloW2VIi0GaIWmtjmWMhnQpUxIPkEshb14DY9Yds0TXzt3g14sruKz53chbNaMuMyeVx6jS3Lwu9X9gAAlsxrgWVEKhgTgGo3kt9JCUQbCRHZrusik8mgUCio9629vV29v+KKSafTsG0bhUIh9vmTTqdVgnc+n1drXzZMarUaenqGig8issW67jgOBgcHUSwWVQhoW1sbqtWqOiYJQRPn16aBCh7eVF/f5x/cilJpQPVwy3HI/5WyCSnH0uicGA27vaJ94okn4p577sHzzz8PAHjyySfxwAMP4K1vfSsAYM2aNdi8eTPOOOMM9RjbtnHKKafgwQcfHPE5HcdR3n/5IoSQicLt22chA8BLvbVx+Z85eW0o1jz87sn6xsyZr5sE13VRq9XUBXEqlYJlWfVU1e3VbLmYlJ34UqmEgYGB2Hglufidkg6RtAwUaz429HOe9njH930kLQNt2ST+7vCpSjDrFSyxicqGi1Qcs9ksOjo6UCwWEYZ1u7lUGqXqoyeG6xfqf9qwvZ92ahZJE3BDA/2uqdLM5dh0oS0iTKpYwv6UPK7Po97dG61re8t4av0gsikL/7H0UBx+QLMSRHIO5NyI0B5J7Ov99fqfepK3jGvauHGjCjrr6OhQ60M+k0zTVKFoMkbJcRyVLG0YBh7f4mNLOUQuaeC0eU2x0D4RQ5lMRo2Nqq9JC1NsaVsYapfRfzapTsrPqI+/AuqV/Hnbk8df6qvb1sdb8ri8V1JB/oeju/DhNxyAtx7YoqzbIphlQ8v3fSWyd1S5rdXqVWAZ0aWPzkomk+qzAKgL1/b2dliWpSYTSHjZunXr1MadrHd97FpfX5+qgMvj0uk0mpqaVDW7t7dXjQ2bMmWKal+pVCrq/0Q5njAMce+GEEEEHDYth87kULuE9HvLzy3XYVKNF6eOnikxGnZ7RfsLX/gCBgcHcdBBB6kD+9rXvoaLLroIALB5c71PqLOzM/a4zs5OvPzyyyM+59e//nV8+ctf3t2HSggh+wRfOWcxbnxwLf64ajOOPCCPquPGdpoJEX73ZDeqXoB5k3M4aFJKjViS3mxJeHUcJzZaBxi6kJH0VrkwlovLIAiA0MfcSTn8bUsJq7oLmNGe3Ws/K3l1yIXhe449AO86clo9cAph7HYRF2LhlQto27aVMNJnOeshV5IWnEqllGCPogglx8efN9Tv/3eLW1GoOlg9EGCzY2HGdkGfSCTUc+lp5FLRrdVq6Cs5WLW5iPmTs8ia+4fQ3lPVbAA4qKsZP//AsajUXBzSVT93yWRS9cxKRU8CEuX2RkSoyoQCsWEDUAJNNk16enoQBAGmTp2q7MYi3qTdQNwU8jkm7gURSf/7ZH3T5cz5eWRSlgp9lHA10zTV/5dSOfU8D122j3XVFDbXEgiCoZnxUlF1XRf5fF7NYpbPRN1CP69ju9DudWLJ43J8+zqyaQHU3+8ZbcB7j+lCqVRSgtZxHOVs0TdApKrciASPAYi9X62trbFKtAhVGQ0oGzC2bcN1XfT396s+e9lkSSaTajRluVyOuWlEwOfzeWQyGSXE+/r6VKJ4JpNRm8z66EDZQKg4Pu5ZW98AuPCwyXCc+ms2NzcrN4NsOMkGhTxe1rTuAhsNu32V/PKXv8RNN92Em2++GY899hhuvPFGfPvb38aNN94Yu1/jbsDOSvFf+tKXMDg4qL7Wr18/4v0IIWQ8snh6C771jsPwx48dhX8+bQaMiBVtMjK/XF6fnf13R0yLBfgYhqFEdbVaVRdCctErlSYR4HJBq1cRgbr4Wji5fhHOPu3xjYi2KIqQSpgwt4egibNBeg6lWi2jehKJhKpC9fX1oVarIZVKxdaaiBbdSlmpVBAEAR7qDlHx6v20x8zMY05b/eJ7cy2hBIrMLxYnhd7GIBsA77/xUVz8o0fw0Op6eNP+kF0hv4e7S2g7foAXe4byjw47oAWHTaunaKdSKSWWRZAAQ+tmJNu43pcttnHpvdfDoyzLwubNm1XVuKWlRYkdPUldn8EtrytiJgxDbKpaWNXrwzKAtx/UDMMwlIgT4ZXNZpU9WZKoLctCp10/zi2OpZ5TzwIQ+7OsY/k5ZDMgmUyqWdov9dZi/dnj5f9nPb1eqrESVii92UEQqO/pY0ZH0mRhGGJwcDA2rcIwDGXlDoJAfY5UKhX1uVAqlVS4nd4PLc4Hmb9dKpVQqVRQLBZVP7Ukk0tVXpw05XIZW7ZsURX4qVOnqpR62cQTS7ic5z++VETJjTCtOYmjpqbUWhH3hPwpbREAYp998rk5lt/P3S60P/e5z+GLX/wi3vWud+GQQw7Bu9/9bnzqU5/C17/+dQBAV1cXgKHKttDT0zOsyi3IPDT9ixBCJhpy8bq/9COSsbFyUwFPbhhE0jJw5kFt6uJIdvzl4lVGs0jfoqwlwzBQKBRis2/1i0ygfqE/uzWJjlwKE1zTTHi2Fap4cHU/fG0eduMIH+lxlQtkufhtbm5GEAQYGBiA53lobm6OzTuWarYId0n8dVwXf1xXX0vnHdyGbCaDeR310KMtTkIJM6lg6xXNxjaGAzvrgnDV5mLM6j5R0VuGdodt3PEDfOSmx3D+vz+IJ9cPAIhXIHU3i54sLUJ6ZyFoqkK4vXIYhiGam5vVefV9Hz09PfB9H62treqxkkTdmFIvt8voN8/zkE6ncefq+m0nzMhgUi6h2mFE7Mi4KRnfJBXtMAzRla6/l1ucJIJgaDNRDwGUqqdlWUrsS3J2MpnE7LY0EiZQckNsLg5V7sfDOpSNgzAMUQkMfOqOlfjDc9vUzycj3PRWEF1AijiWar/jOOjr60O5XEahUFCjrkTQlstllEol1V6iB6Hp5wsYsulns1lMnz4dLS0tyOfzyGazKiVdHiObPaZpoqmpSc3Z3rZtGwYGBpBMJjFp0iQAUJ9Rsokir+l5Hqq1Gu5aU99YuuioaUAUqg1q13WV6JeME6n4i7gWxppbstuFtnjideQXBwDmzJmDrq4u/OEPf1C3u66L+++/HyeccMLuPhxCCNln+euL2/CZ257EipfrFRvTNBFEwObB6rhMNyV7ltu29/K/8cDJyCeGLnYBKEue4zgoFovKnitCWqo/YjXX7aH65o7v+zhrYR6P/vNp+NTpC/faz0peHWEY4jdPdONDtzyNz/3mb/8/e/8ZZsd5XYnCq6pOzqETGhkECICZYlJOligqUFSwLFmWrHEaX0u+Ht8ZjceeGaexLV97PqfxtT1jybYcJAcqkookJSpSophJEJkkcqeTc+XvR/Xa560GSDYkEIGq/Tx8CDROn1On6q239tpr7bUl6VT/nQx0MplEu90WtpnSzKWlJYxGI2QyGeTzeUm2OSaO70fWynEcPLzoYGHgIxvX8KbLJ5HP57FtMpCOzg0NYQzVBJZsk+oAbds2tk4E4G/PXPeHok+b9zLB6g8SluPhAx97EF/duwjT8dA3HWEsgWC/IMBVe3HVfWEla0dHamBshtXr9aBpGtLptDhU+76PxcVFkeKWSiVhMCnxZoFlOByKKV8qlQr17fddA/ccD47x5u05mb/MtUygRpk3EOAJsrezWUCDj4Gro2uP1QJ8tqrnQ21bUCXEqUQMG0rBex+sDeX3LoR1qM7OvvtgG3cfaOJvvnNcigu8DryWQLiPnYC6Xq+j0WigVquh3++HwDVVDCoLzL0hlUrB931ks1lkMhmUSiVks1lx806lUigWi+IUPjExgcnJSaTTadi2LT3g3B+SyaSoF4bDIY4cOSJO48Vi8STQr0rANU3D/ccGONFzkU3oeOPOitxvajHaMAwpAhiGgVwuJ6BfHfN2Tl3Hb775Zvze7/0eNmzYgEsvvRQPPfQQ/viP/xg//dM/DSC4iL/8y7+MD33oQ9i2bRu2bduGD33oQ8hkMnj3u999pg8niiiiiOK8jY9/7wg+/+gc8qkYdk6mcO+TNbz/3/ZgtpDA7e+fumD6wKJ47sP3fexfCCSgb71iSiSZTApZje/1ejIqM5fLCaiJxWLSm02pIGWbTK6E0TFHkdv4BR6WZeETDwemeS+5KJgTq7LGlmWFDMfo/JvP58UgqdlsQtM0TE9Pw/M8dLtdSZAByLoia2WaJu46EiTsb9hexHSlBADYVAqY0Zatw/QDZ3GOlwPGo6FWGqJtKga/t/tE54dC6XOm+rNt18MvfvxB3LVnEcmYjr9533V48daJkIoFGBctqIRRj2GlbFw1tyIwpjTYdV2USiUh1dh/yx5oekXkcjn5flTdEGAT+PV6PYxGI8Tjcdx5xIbjATsmEtgxmRI2ezgcIpPJSMFH3fvoDWUYBlK6j2rCRc2KYW5kYKqgC8hUWxTUUYc0BWPRJzBES+HJhoWDtRFeue3CGPGlXq9YLIbP7wrcxl+zLVAEsw9b7eGmKoXFEBa8OE3AdV0Z6xeLxZDP50UyrrrOUy0xHA7FZIzTCfg5ZNUzmYwoKNLpNHRdF/PFZDKJZDIpI7rYTw8Ac3Nz6Ha7iMVimJmZCfX5D4dD6aXPZDJyHF86FBRV3nLFNDRnXLDhWld78HVdlz7wlUoIdXrHauKMA+0///M/x6//+q/j/e9/PxYXFzE7O4uf//mfx2/8xm/Ia37lV34Fw+EQ73//+9FsNnHDDTfgjjvuQD6fP9OHE0UUUURxXkZrYOHOxxcAAD96zTrouo4N1Sws18eRlomBaYcSoCh+uEPTNHz8516Ihw4tYTYDDPo9+bmasPT7fUkUEomE9LgBkFmjZBxUxoOJIxkd9lJGI74uzLj3yToO1YdIx3XctLMqwIFAmyZEsVgMjUagqKEqwvd9WSulUgnVahUnTpwQd3sCHCaqLOAcrA2xtwnoGvDu69ZJISifNFBJAY0RsDCKoZQJRs6RPeLaY38kk9212eC9aj0T9b6NQuL5y2g/E5N8OmG7Hv7vjz+EO3YvIBHT8eGfvBYv3TYRYm/J8gHjcV7y+08jG6evA0FUt9sNtaewN3owGGBxcVGAFPux4/E4MpmMKB8ItKlkSCQSAups24aRSOGuwwFQfNPFWSkCkkV1HEdMs3isrusKaCZbO510ULNi0rZAgKnud7wP+B15bngeXndxEZfPpHDlmqxcp/O9AK46qC/0XTx0rAMNwCs2ZaX1g5Jwyqt5bTneiuuCQLfVasm5z2azYj5HgMvzlkoFRRFK0tljDQT3L59RdBHnM4Z91zRjTCaTaDabiMViiMfjIm03TRPHjx+H7/soFovSg83nHpntbDYrgP1Ix8Uj8yZ0Dfixq6ZgWUFhkUVFFgxZ5GPBkUVrmu9xrZzT8V75fB5/+qd/isOHD2M4HOKJJ57A7/7u74bc6zRNw2/91m9hbm4Oo9EIX//613HZZZed6UOJIoooojhv4/ZHTsByPexcU8Bla4uwLAtZzUYxZcDzgf0LXUm8oogCCJLxrdUUzNFQEkM++Om0Swkw+86YpFiWJWY0TJZU6bkatm3jf31lP170+1/B399z6Ox/0Sh+oPA8D7c+eAIA8PpLp5BNxiSRZSJJ0yAAIv8tlUpiVkRzq4mJCWGzyf6xFYHgnXLSu48Hn//yzXlctKYM13XRbrfRbDaxbnk++4mBJowjWWrKhfl+AqocE5sngj7tfYt9+W7Px3gmA7LVhu16+A//8hC+9Pg8EoaOv37vNXj5xZMAIDJx1XWb15HxdGB/JYjqdrsyposu0Xyffr8vRRoCqVgshkqlAtM0xW1+OBzK7wOQtpfBYIBEIoH7lzR0TA+TGQPXr0mIcodjnih3V42yePxkxzVNw0wqOK+qEZ8a/B21Z50AlMd+1WwGN27NY00+bBZ3Pq9Fqhc0TcOX99YBANdtKKCYGBvf0TCM9zRl4GpfNGdwc662YRjIZDJy/1KBoJpvssea/c8q/iObrYJ9AFKkYX83ry1BbaFQkGs6NzeHXq+HWCyGcrksahq2w3Bdcf0lEgl8dk8wQuwVF5VQTngCrrmOVGZffZ6qbPb329pxfpdkoogiiiiep3HrA8cABGw2EDyAhsOhzO3cM987rx/kUZy9aA0sdEe2sBSUyTEJSKfT8H0fg8EgNAOZM4t1XUer1RKWmqwVQZdqQMSfDUYW5tqjyHn8AoxaZ4g79iwBAH70qhlJmpkcsoefruO6riObzUpLAQFJuVxGOp1Gt9uVWbmqYVIsFpM1V+uauC/4SPz4NWukX7NWq2E4HGJtJjCRmh/FJHFXR3qxt3OlrHfHTKB03LcQKDier87jZ0I27no+2kMbCUPH/3nvNXjl9ikAkHsbWB2brYJ9tS+bcuJutyvXSx31Zpom5ufnhSWmdLdUKgljSJCtsuuqqzNlvl9cNkF7w7Ys4Huh80PQR3M1Fma63S5arZYAPACYTgZ7JBltHhf3TnUutmqIxu+nyorV/3huzsdQr1ksFsPnVsjGucZYTOB3XFl4oVx8NBrJfZpKpVAul1EsFqUw1ul0xDQtHo9LEY8GdQwaLgIIXTfLstBqtbC0tIROpyPnl8U9MuexWAydTkdGxhUKBZnjzbXL4gKN8XzfR2vo4O6ngkLdT1w7I885fm/uNSwe0tWcrTX0M+B7q20vq4kzP6gviiiiiCKKZ4x98108eqyNmK7hLVfNAgiMJOv1OjYWDTx4IkgsmRhE0t0f7vjfX38Sf3/PIfyHV23Cmy7OiSwSgMjGLcsSAKUmAkwSu90uHMcJyfjIJqpsEA3RNhaCJGrPXPfUBxXFeRuffug4LNfH9qkMLl8bJNfqNacJmmo4lMlkpCebjFU2m0UikcD8/LywUEzGmaCT3fzmnA/H07BjMoUbLpqEbdvodDriADy7PI59bnSyAdpKuS6LSK7r4i1XTOOl2ybxwi1VaNq4P/ZMuHKfT3EmZOOpuIG/ed91eOx4G9dtqsjPyWarxsRkfdUgmF0JttRWlEajETIkozSYPdKcasCiSS6XQ6FQEA8AAi0ambG/u91uSzHnQEfH0Y6DVEzDqzYkQgyy2s/N46L5FYGxWrBZlw1AW80yYLk+6K2uuthT5cNiAMElP8swDByom9i7NMKLNpexdTohv3s+BiXwuq5jf22EQ/UhUjEdL1yXhqb5IbaWrSLqfQ1AFAfcHzidgCPUWMhQfR4Mw5AxzPF4HJVKJZS7cOwXr1mz2RSwTYUEn0WJREKAPdtM6DTe7/eRyWSQyWTQ6/VgWRbK5bLIwAnMuQ5vf7wF2/WxcyqNS6bS4jVBtpw9+Rz1pba0cJ9R2xbU6QCriQhoRxFFFFGc5bh12T36R3ZOoZoLHlhkk9bng4T4wFKQkDwfk8ooVh+26+ETDxzD0HYxmQ3YKErumCix+k4JMPsdKQHs9Xoi2wRwksOzmrDyZ+uLQYK0b6EL2/UQNyIB3IUQvu/j3qcCqejbr1ojTBRbDSgLp3GR4zgoFArCWum6LqO9+DtkjGhAxffs9/uBy/1ghG/OB+vlXS+YlvdtNpsyAmompQOIYWFkwIMmbBqBNuW7ZFzpSn3N5gwqlQA0skDwfNsTeQ/y/J/W73o+vrRrHm+4fCYAQnEjBLLV9hACJgAn+X+cSjauymnT6TRGoxFM05T+azLWLPTNzc0JWMpkMshmszLai32zAEJFFXpL0JwvlUrhy7uD4331pjSSugfHcaUPlzJkFg3ZPkMTLx4bGdpyykDa8DB0dSyOdBSCTgRhMmnsRmDH9TgYDAQoxmIxfOyRJu49OoBhxLBlMjB1O1+BNsGvruswXR+Xz+axJh9HUveFtVVHbjF4bgl6h8Oh3O+851QpOIsUVLn4vo96vR46r/QAGY1GaLVacF1X1DNsYeEao6Q9Ho+H5OvsISfI9jwP2WwWvV5ARuRyOXG2Zz85jw96DJ/bG6iy3nX1lNwL3Hv4HKWygt+T5zCZTKLX6530nGy326u+HtGTM4oooojiLMf6SgYbqxm845r18jOaiqwPnuE4WBvBPc3KaRTPv/jq3kXUeiYq2Tium00hHo9LgsNEl4khpeGpVEqkcJydTWDFcSmUTFI1oTLgjuOgYNjIJQ1Yjocnl/rn+CxEsdpwHAe//8Yt+Osf2443X7lGwA3BL4E2k+lUKhVilIvFovTBJhIJtFotSTqZjAIQIGyaJh6qAR0LmMjEcNMlU7BtW8yy6IKf10wkDcDxNdStIAknQ851uNJ5nNJ2xvN1xNf32/vpej7+862P4AMffxB/dMf+U76GwJpsLf+8slBBhYzaO6/2ZbNgQjmx53lIJBIyf7nZbEp7ClUzk5OTSCQSAqYcxxEARjCUyWQwGo3kfVteEg/OmdAAvHZjXIAa5eCqcRowZm/pSk0n/LH6IobpZPC954Z6aL9TJeCqeoyO3VxvhmHgokrAhR+ojXuWz0cPFUqxuddfu6GEf/7pF+DXXr1WihErXf55zmheSHk/f84iWCwWk9Fc7MMGILPMCUZ5Hinlb7VaaLfbIYO84XAoY7PYT839JZPJIJfLieGaYRgytpK92epYtjVr1iCfz0trAplt3/fx9cMDtEYuJrMx/MjF1ZCpn9o2kM1mpdCiGuTRRJDP1sFgIO73q40IaEcRRRRRnOV434s34WsffCVevWNKfsZq6lQaePmWAt551QRM+/k9ziaKZ49/vS9QP7z58im4jiWJj8owmKYp0kwmT/xvNBoJ080knmzCqf5Maa6t9Mfuifq0L5hgj/U1G8sopAMJsNofS1ADjPudCbqSyaSM4eE6ojSTCS+TXvb9mqaJry6boL39ykmkkoHUt1arhUCZbZlj+fhg7PpMBhGAACYm8uw13XW8jY/dexjHWuPjfj7F99Of7Xk+/ssnH8WnHjoOQ9dw6WzhlO+rsoX886mmWazsgSaIIrPY7/fRarXk2nueJ4DIcRzMzc2JcRbXUaFQCHpkWy05BvWzMpmMHGO320UikcBdh4N/u3Y2iemsLmuPveCqYzj7qGnIRmDI78CiJIH2vBmeosA9lK0M6nlSXbtjsRgungx6jZ+oB2vwfB01x0kSvFeBQK3gu+OZ0QSb6XRaPDqodqCygMyy2tOfz+dDI7r4eo4CZEE3nU6jWCxKC5NlWaF9hIB+OBzKbOxMJiMycXoHuK4rAL5er2MwGAgTT/XHzMwM8vm8XC+1YGIYBj61qwkAeNtlVWgIT9iIx+NSbGSrATAuOtF3gAobqjJ0XZdRdauJCGhHEUUUUZyDCB4UWujvvu/Dc2z85o/M4t9dO4WYdn5WzaM4OzHXHuJr+wIjm9dfXJSkl/21NHuhJFh1UFXdX9URLuzNI5BR2Q2yEQRR2yYDZBQZol0YMbQcNNpBTz2ZKyBIKJkwqgZDqhySfbb8M+ficiYtnXhVFsi2bexruDjaAxKGhrdePgnHcdDv99HtdjEYDJDNZqU4tG45N50b6uIMTOCkGlBxLyQD//9+cQ/+26d34d5DLQB4Xu2Jar/naoG25/n41U89ik88cAyGruF/vetqvP7yNSe9TmWzCR5OZeSkAk2O/aM5med5WFxcxNLSEgaDAWzblvFZZLNpZEVpNw3QPM9Dp9ORz0gmk9IfS9MpMpuO48A1UvjakQDI3rgpHmon4PrkCCiyozwOjqZjEYFFSE3TMJsOzu/8cAymVECmyusJwmkuyaLT1mWgfahpwfHGz+XzCWyTiQeC6/i9wy30LFeuZywWE5AKINSTzfnnKsjmmC5grHQYDofCUtMdnL9L8M4WE4594zOGRbRGoyF7QyqVkjFcPCY+f+gV0Ov10G630ev15DXJZBL5fF4M0Qj8E4mEFAZ2Ldl4smEiFdNwy+UTcg/QbZ3Hw2clzwN7sYHARZ+KDK7vcrmMcrm86usSAe0ooogiirMU9Z6Jzz86B9M5daJo27awRJQwnU8P8ijObnzi/mPwfOCa9QVMZ7SQlA2ASMTJHBIkEWi7rotOpyP/xmp+e+Tg0aYB1x3PkgVwEvjeOZXCNRvLmC2mnvYYozh/4p/vPYTX/5+H8Y/3L4T68ZkIs6danUnM+cY0HiKwiMfjaLfbIWaT4BuAAJ67jwcJ6k3by5goBN4BCwsLkvCzFSEwRAteSwmvCu4ItNXeTP7ejukAoe+dDxJt1fn5Qo+nk42rShM1PM/Hf/30Y/i3+49B14A/fedVeOMVJ4Ns9scC4zVA/4ZTvZbMcqfTkXYBtp0QYFMiTKM8ym2PHTsmgKxQKCCdTiOfzwuIpsGeaZpiqpXL5UKj5uLxOL49D5iOj82lOLaXAtaTwFltWSDYz2QywnLz/PGcUaLseZ6suwUrDmf52cu9buX/gXHRW53zvb6cRjqmwfaAI82RvPZ8ej6zOBL0ZgO/+K+P4+V/fA8OzrfFSE4dW0bwSwafc9EJtPv9vlx/KlmoigGCYh4nXnB/UK8Dn1WcYDA9PS3zqFlcY5+0+nxS2w9M08Ti4qIotrj2MpkMEomESMbJaPPzdV3Hp3cHfdQ3biugnE2KrwS/v+pVorarAAGb3W630e12pbCdzWZRLBZRLBaj8V5RRBFFFOdjfPqh4/jAxx/Ez3z0/pP+bWlpSRJby7Kw0LPxyLH28yqpjGL14fs+PrE8Au5Nl1SFUWDxhQwPEyS1Kk/5I0fGqUmM67r42FMpfHqxigNWQdgDgnEmSI7j4GXrU/jkL7wY/+4lm8/lqYhiFeH7Pv7lvqPoWx5y6TCbTcaw1WpJIsmktFqtyjXnWBsA0qdJUMPklO9pmibmuzYergWf/2NXT8HzgnnbnIWbz+cFwDiOg8l4ANLnRzEB1yog4tx3tcXBtm1snQjYxD1znRAD93yIU7mNe54nvaC9Xk+ug+d5+I3bduFf7jsKXQP+5J1X4eYrZ096T7UYp04oIMPLe340Gsnca843Vk2gCGDo+1AsFsWoKpFIIJvNot1uY25uDr7vI5/PiwkaCyfs5eYYJn5XjkxiK4MRT+DLTwUA7nWbE6KyIXvJ3m5V1kvwTbk4peuUThNwzWY16PAx8nS0rPE5IqBWwTZbbOh7IWOvYjFsrgSft2+hf14CbX7/WCyGr+yrYeR4mC2mMJmGFNXU5wfHRHJCAIE6vzsnVVAxQJk9WwOy2axIwPmcAcamZrzuiUQCuVwOiURCHL4p96cPAw076WzO59nCwoKYICaTSZmnzUJLMpkUxpmFQF3XMd/38N0jPWgA3nHlhPw7j7NYLIYMCNmzzb/z3lP3RjLop2tYGAHtKKKIIoqzECpwet1lMyf9OwG2ZVl4bH6It390N379i4cAPL+kklGsLjRNwz/+1DX4xZdvwEs3ZkQ2SYkeJXJkIwjEyQKpsl8mnZZl4VgPONgNwNSclQoZ+zAJp4yczEUU5388fKSJ/YuDQML9grUhNnM4HIqyge7iZBlTqZQkv5lM0CrAa0+zIgDCfFHa2ev18NVjHnwA16/PYUs1DcdxZBQYQVImkxFQTaDdtjV0LV9APIAQcCHYJuu+ZRng7JnrAM8joM2CFhAG2gST6msIirdNpGBoGv7w7ZfjzacA2fx9Mti+7wtAtW0bvV4P/X5fTPEIrFTDMbLSlO/qui5/5/Hm83m4rovjx48LQCqXy8Jy81lGl+rBYCBS42w2sP7mGovH43i0oaM+cFFK6bh2EmJqRak7GXWqdfi+XC8sTnDNkq3UdR2pRAwTy/O054Z6yPyRr6WCgJ4FLA7xPMZiMTFE2780kPV3vjybPc+TVoF4PI7PPx4MtX/9JRMAxr33PCeqs7xqlqmebwDI5XKoVCrI5/NSgGCf9HA4FCUDW0vy+Tzy+bz0f/Me9zxPiATDMMTAjIXAfr8vzyGe/1arhXq9Li7jbDfg9SgWi7KuVYMzwzBw+75A/XLD+gy2TAasN43UaOKnHhvl5NwLpZ1h+XjYDkE5O++D1UQ03iuKKKKI4izEruMd7J3vIhHT8eYrTk6QyDaYpom1M8tSt56N1sA6pXlNFM/v8H0flbSO914zJUmm2kuYTCalOAOMjaT4d9u2QwZpQJAcfLuWls+oOckQoAHGAIbmL57nwXR8OJ6HfCo8dzeK8yf+6TtPAQB+5OIKypmEgCT2LvZ6vZCcO5VKoVQqSdsB+yrZNkC2keN7yHaTeW71R/j2XLBmfuyqSWiahlqtJqZH1Wo1BNJ934fhO5hIAbURMD8yUEgGBSNVasrjVmdpz6R8JGI6+paLE20Ta/Lx5wXQJkhbOdaL9zil/Ez4XdfF266cwXUbilhfTqPX64npFQtx6sgkFt74Xioo5O9x3BJ75in/bbVaAkgJcCnPpXkVe7Nt20a5XBZZOYCQgZ7v+zIqjL3UbAugf8SXngr2rRu3pAHPEdDH4qLKXgPjWd+UANPpnsfIAgGB1EzKxaIZw9xQx1XL34tSYbL+BOwqw0mptaZpeMtlVbx4XRIXVZIn7ZfnOlTpdL1v47tPBSZgr9qchecFpmI0H+N9TpM7st2FQkGUBqpkn+OsCKoJxtkTzVncwHh6ChUNVK1YloV2uy0ycq7tTqcjrQTpdBqpVEoKQfPz83KcvJ4s9rG3u91uh+Zv+74P0zdwx4FANv7WS0vC2g+HQ6TTaZRKJdnneO/1er1QYUeVsWezWVQqFaRSqdD5Xm1EjHYUUUQRxVmITzwQuEe/7tIZFDMnAxb22g6HQyQ0D2vywWv2zvfOm4d5FGcnVrJQZCFYdU8kEsK2MNlRHaTJZNMAh4nGwNXxUGM81qfmJOG6XgjokBkgG/E7tz+OS3/zS/iH7xw+h2ckimeKztDCFx4PTPPedd16YaMo1+10OgKcVXdf9mEahoFSqSTri5JhMpUE2mQqTdPEPXMeRi6woZTADRsL6Pf7aDQacBxHABLZKjKstm2LIdr8yBBASQUF2bKVzuPWaIjt04ED/r6FoHh0vjCJP0icis1eaY6m6zo++t1jGHiGgJEtUwU5P3R0rtfrWFhYwNzcnBQ71PfnNadTOGW3PA51DFyn0xFZLZk/MnyxWAzlchmmaaJWq8moo2KxKGPAKO9XZxVzXBaBWL/fl+M7OozhQMNGXAdetT4mQFkFhOqoKY6DUhUWPD6VoVcd9dekxoy22l+rMv8rncRd15V7QNd1XDydwxVrMkjoYzb7fHk2U/KfSCTwxd1L8Hzg6vVFVJO+FBMAiPkXzz0LCYVCAdlsVmaaUzZNFYPal035trqPAAj1PHO/4XOo0+mI3LtYLELXdTSbTQH/k5OTmJyclGfV4uKirC0W49Q+cIJlsut8ZhqGgS8f7GPk+NhSTuD6jSVROaiO+Pw9jq3j+SgWi1JY6nQ6iMViKBQKMg8egMwYX21EQDuKKKKI4jkO03Hx2UdOAAB+9Jp1p3wNZ5QyqaFccu9893mRVEax+vi7bz+Fn/77+3HPE/VQgqGyQjS1IkAGIAkmDfUYZCG/W4vD9TVsKcVgaEHlv+0EaQBBllrJtywLxZQOz4+cx8/X8H0ff/jFPRjaHjaWU7h2YwnA2ISs3W6Lcy7Zp3Q6fVJfdKFQkKSYv8fElSO/2HM7Mk189WgAMH7sqklYyzNu+/2+yDy5jigXBoJi4pplB+i54XhuO4PSdjKrKjO2c3nU3N5loH2+AJwfJE4FtFVzNAD4nc/twe9/cS/e85F7YdphBlw1L+R/VCEQhBuGISCYBRC1z1013+Tvcx+hgZkKtMrlsjhyt1otWJaFXC6HXC4n10z1FOFeQqVCMpkUMMeiDNnsl21IIeYMQ6wiAGE6KW9mnzjXju/7AgwJoHgOBWgrhmiqdJznUz1W/q7a606wT9ZUnaN9rtciATEQMP23P7YAALhpZxXA2AxPZYZVuTTPdbvdln59PgvIVrPPulwuy30JjGes87MBSNsSix/cAzKZDKrVKnzfR6PRkHu9VCohl8vJuR4Oh7ImE4lESL1AGXc6nRaAzONxHAdGPIHP7mkBAN5ySRHA2LOAxSW2UXEdjkYjJJNJFItFAeHNZlP60aenp0PFGcuyxE1/NREB7SiiiCKK5zju2r2I1sDGmmIKL906ccrXMLngQ3NTaZnRXogY7R+m8H0fH7/3CL71RBNP1fqSBKkjuVTGmbJHlUkAIIkxf8eDju/UgjV1y/YsptNB4ll3UiGHYnW8jeu62FgI3jeapX1+RqNv4a69AZv9/pdvEJATi8XQarUEALO/UXUYp2w0n8+HTNI4l52STjUJtiwLDy86WBz6yCd0vGZrEYPBQMyU2KtJkE0HYzJOY+dxI7SeVVm6ymhTufGua9fg4z93A37u5VsAXPjO42qBjPcuMO7P1nUdv/u53fjbbwctAe96wRrY5lDaRcj00nm5Wq0in88LaCEoYYGk1+tJnzQBIg3RWJRRwTlVMiz8ci0QfDebTelnpdEVgJNMGdXeYT7j2JICAC1bx73Hg39//ZaUFHsoLVZHRPFYOX+bn0UjN64JrhmqKjRNw/pcsK817Rh6o2AtqwaR6oxvqgooeVbN1e49NsRHHmzh0eOd88YQjdc0Fothvmth30IPMV3DyzYGvfCckc3rykKKeh1c1xWWlmA2l8tJkS0WiyGdDtqO+GzhueV7qCMlaaTGPSCVSqFQCMw3CWJpSpbNZqXFpd1uo9VqIRaLYWJiQnqy1X58miyq/dlUF9x7wkat76CcMvDKLflQUYQGfvQpIFvPudhUatTrdfEOmJqaku/N86S24awmoh7tKKKIIornOB46EvRLve0Fa2HoTz8WglXZ4XCIjYUKAGDf4pjBOV23yyguvHjwcBMHl/pIxXTcuL0i1Xwy2MlkUhJcyv64NiibZPLAxMSyLOzqJNC1NZRTGm5Ym8S3ngRODIAlJ4mL/IGwOUzEyJitC3I1PFXrY2A5yCSitOF8iozh4S/ffjEeOdHDGy9fE1I3sGeaLCDZSADC6lCGqTKXvV5P5KbFYsAKsT/TdV3ccThgsN64sww4pphQEfhRLmxZFrLZbCghn4yZADJYGGnQY/EQS6lKcVX3c8dxsK2SlGPp9ayQu/SFGCqbrTKqlLj+wZf34e++E5hn/vrrt+LtVwcGmpTn8j/V1Iu9tZyb7bqugFSCDbK+mqZJTzOBBo3GAIiChmsim81Ke4G5rGBgKwKNqtTWFbLuqlkjpd8qSLnzkAXPBy6fSqAaM2Ga/klGesCYtc1ms6EZ8ZqmCZvNvY9/5rnRNA3FpIas4aLvGpgbaJgoGaHzzf0TQIjx5vrjGv7G4QG+/tQAM8UurtlUlXN/roLqAiBg/tMA7vq/b8DuxRFSmgXHDVzfaS5H9lf93mwPUNljAOISzj+rzu7qKElgvI7pYj8YDOD7PsrlshRHVrYz5HI5Oe9sm+t0OqKKSafTIXadRnqpVErWJhVc3K840uumrRkkjLH3AQvWatsCR6iqBYV2uy2tE6VS6aR52ZSUR+O9oogiiijOo/jvb7oEd/3Hl+N9L9r0tK9R+8RM08SGQrA9H2qYsN3xzNkont/x8XuDXugf2VZCLmlIgsCEj8kBkx0yOQBCfWfhJMTHNxaChPU1GxNIxmPYWAj+XnMDgxcV5DBJdRwHSViYzCfh+0EbQxTnRzy51JOxPGsKCbzlqllJ/gzDwOLioozzYm8uwZAKxJi4sleR87bJgJMNI4N0pONib8ODrgE37yjI76yUG6t94sBYWZGFibQBuL6GJVMPmU0R+JCdA8LFR8ZKp/ILMU411osg5OGjbQHZv3bjFrz7+g1Ip9MCCDj+SC28EvAQ3GqaJmCFv0cQThDd7XYF2BBcEITzunQ6HZENEyw1Gg3Zazj2iDJjginVgJGjmQjU5Di1GL5yKAByN21OyL/RE4DgjmwrGVkAIZUE+4F5TtQiDPdPwzAwvew8fqKvhQpSZKvVn6lsNQsVmqZh22TAbh6sDUOvP1ehzs6mtH0yn8QrLiqG1E8ExjxerhcWqljc4PlVTTJZQFNd52kMpsrGqXRot9twXVfcx9PptBR1AMhoMJ5zysyHwyFGoxFSqRTy+bysTRqycR0CY/M3TdOk3eFQ38D+2ghxXcPrLspIiwE/l+tFBe4sAOVyOfR6PXQ6HSkgVSqV0Nx5stlqQWo1EQHtKKKIIoqzEFun8pgqpJ7239PptCQJpmmiGHPxnqsn8F9/ZB1cz7+gk8ooVhedoYUv7JoHALz58klhbtReQEprmUQR0PD//DmTJMdxcHSUwPGBjrgOvHpjwGpsWJaE1+yEAB3VuZXma2p/bCQfPz/iz+7aj9f9yTfw+YePCKCgLBMI2OeFhQV4nodUKoVUKiXmUar6wfd9FAoF6ccnM0bHaI5hoiGU4zj4whMBGHrZxizKybExEL0EmLgzYeYM5PHIJBuzyyqJEwNdikdMugn26FhN5m00GuGu3Qv40Bf2XPB92mp/r8rIE7Tc9miwB7x+ZxXvvm6dXB+ChJWhTiPgeaRKgEGwxPYBspqUaJOJtm0b7XYbnueh0WhIoWZiYkLAUKfTQb/fl3FObBcgW62CI4IcHhcBMQB8/YiJge1jTc7AtlzwOvbKspeWveMExGpPMN2i+RmZTEYUOSsNwABgNhOslxNDPfRzVS3GYo9qxsd9VNd1bJ8KFu8TDTO0L5+rUGdne964bUSdOEFXcT43qA7g+eV3U53p+d0BiBGiaojG66L6ejQaDXS7XSnglUol6LouP+M+lclk5FmmTjfodruIxWLIZDKyjrg3UM5OFp33kDqCjSO9Xr4hialiRr4PFTpc91yvw+FQWi9c10W320W73YZhGDIzW2WuyWYDkL1xNREB7SiiiCKK5yh830d7YD/7CzEegUOpnWma+Jnrp/Dai8uIaRHQ/mGIzzx0DEPbw6ZKClfO5mQ8DSv2ZCJVF3ImRpyPrCa3TDa/tRiwZi9aY2AiHxR0qJhouXGMHD9krKSCMdu2JbncfSIC2uc6/vwr+/Endx2A7fk4VAsMzmhkBgRg7dixYzLDOJ8PiiRqbyZBcyqVEgaaySh7E+k4rSbTrZGL7xwPQM7bLqsIc815tJR0Uo7Mvk72aVOuvjbLPm09lKgDwZpVwRgwNkn7t/uP4q+/8STuP9KWn1+IoQJF1dCL5/qBo8F99tarZwWIk4Xs9XoCiFUlC9+P54RA9VTBHtVEIoFSqYRCoSD9zATWbCGwbVuua6vVwvHjxwUE5XI55PN5Mcxir7RqQkZATiAvzCuALy4XbV67MQYsg0GOmSPTr6p0+D4q+KbRXyqVQi6XQyqVCoFEAjVN06QNZtGKyb3AFhwWFwne1GKIuidevLwXnug66I/s0Ged7VD739PpNH7783vxsx97FA8caYVYXBZU+F14v3KPNwxDCmJqvzMA+TlBtqoqUIu79IMwTRO5XC4EstnSoJqNEWDz3A8GA2HduU9QJcEWCPpLUCXB4/J9Hw1Lw7cPB0D7TduyUujhvka3dBYWVGf/TCaDfr+PXq8n+2K5XA6x2Z7nSbuEuq+uJiKgHUUUUUTxHMVDR1u47vfuwn++9ZFnfS1ZIWA86osJGQFQFM/f8H0f/3ZfIBe95fJJMTlbmfwBY9dhukBTQsdkUO3dbpgaHmsGj/qbtoyloxnDQ85wAWiou+PklOwAmRzbtnHFmjTe9oK1eOGW6rk6PVEA+Mu7D+CP7jwAAPjlV23C+164Xma/sk9xbm5OZLaU9BJkq2DCdV3pkWy322JaxDWn9lQSmN/x5AiOD2yfSGBbJSYyc4JF9oDyvQjACGiAIDkfj1oyQowaP4czjVV3ZNM0sWM6ADlsYbhQi4/P5Dbu+z7+4d078Sdv2YpX7pyVHmgCHr6WQJjGTDzPAAQ0nyp6vR663a4Y4tEFnMdTLpdRKBRC87fj8Tjm5+dx6NAhcaXmHPZcLifgh0UWsn0ESwBC6wIAHpyzMN/3kIkBL5rRpVWBn0eFhLq/8Xf558FggF6vJ6Za5XJZzhPBlNrTPrtc4FmyErAsO9SWQ1YYGI+84mfx3tI0DVP5JEopA54PPFkfnlNWW52d7WkGvvD4Iu491IJlO1KE5bMinU7LvaTOgGYRgqP4qJ4AxutINdAjYOc1Z281zcU4Yz0Wi8lYQc6u5jH0+310u+M2JNWMk6O1HMdBOp0O7UdsTVCLIFxjX34y6PW/cjqBjeWEPD9t2xaQP1bVBG0yiURC9rnRaCSMOg0g1daM0WiEdrsNTdPEjG21EbmaRBFFFFE8R3Hr/cdguR7cVWzK7H/iA8y2bXT6I+xpeOiYXdxy9fpQMhXF8yssy8Jbr5iEofl4w85qyLGXgIOSTMMwQmwAHWUBSJJCNvue+Rh8aNhZ1rC5Mk6sfd/HmrSLAz0DNSeJta4p4BqA/NnzPFw1ncDN1151Ds9OFH9193784ZcDkP0fXrUZP//yzeMkezl5XFpakgR2enpaXKVzuZyYEzHoBEzpLeWlZIoIdoAAQLc6Pdx1KABfb72kdNIoKP6u6tKczWbRbrfR6wVMExPkyawNIIa54VgaDIzHEBF4q6yb53m4qBok+XuWgTal5hfSnsj9HQgDbZUdjBkaXra1ikQ8+HfKvlUncJ6TwWAgslyyxZlM5pSfPRgMxA06nU7LPGW2BnAEGKXhuq5jcnIStm3L+Enf96XHlqwlVQhUIpAJZH83gJCbuW3buG1Z5vuqDQnk0wmR9Kq/z+9Ioy4WCbm+ms1m0GZVLGJyclLGh3Etci3TZ2Amo0OHD9PXMdcxsb2Ql/UGjKXkXMcqy6u21GypJPDgiSH2Lw1w3UVjJcbZNitVjcq+tm8J3ZGDmUISl04l0e2YonBSvwcL+qrhm67rApZZDGFhod1uS+98KpXCYDAQxplFF5of8l6kQV2v1xPFDa8JfQFYAGABhudb7f3nOaVSga9VR6+5rouRC9zxRLAn3LQ5IU7lVH/Rp0Adfec4jqgnKC/nfVQqlU5iszudDizLCvWcrzYiRjuKKKKI4jmIoeXic8uzs99xzfpnfT17EtVetiMtE7/06YP4g68cOacStSie22DS8MadZfzNuy/FZCEtySUZBiYHlNZRvqky3WQDmPBYnobv1YJk/aYt4zE5TKhoDrRkJ0I9b/wsJrXs94vi7Ifv+/jrr+3HHyyD7F985Wb8h9fuEHAaj8eFjanXg7nr5XJZktGVjtZMuNPptIAsFnA40ksd0URg9M3DA3RtoJrW8YqLigK8uEbYx8mkPJfLicSZyTePo2KMoAHo2hr6niFrjf+ujmdSxzVtKQfJ78HFHhxvXBC6kEJ1y2ZxjPee7Xqwl0EfjatWBuW12Ww2NG+a6hPOMOZ1ZYxGI+kvJWgHILPPef673S6WlpbgOI4w0zTcomR2YmIC5XJZgK/rurIe8vm8sKB8X4IeFm/2LfSwp+FC14A3bc9LkYBAXH1fFvyocOB5IzNvGEZoBBOLBXxektnXdR2JmI7J5T3veH9sqqc6lKuGfPy7WnzUdR1bJ4LPOtwYM9pnW3HGYgAQyMY/+3CQa7zh0ik4drhdTTUuU3vmeY+x4KLKqbn+VFdxtb2t2WyKMoLPDFUF1e12RU0DBEWeer2OY8eOod/vi4S9VquJoqbT6Qi7zT2BbDzXFL87cyRd1/GVp4YY2j5mczqumR2rIrhm6KZOybra2kImn4WufD4fcrsHArUh2ezT6c1mREA7iiiiiOI5iC8/Po+u6WB9JY0bNlee9fV8KAAQpmImAxg60DVdLHTNs/4wj+LshCrnY3Kh9kwTPJPNJptIgyQmpkxSmEB9b0nD0NUwlQZesCYpvZZkQmZSQVJfc1IhMMTPpqv5cDiE7bjYv9DF8dbw1F8iijMeLHI8vtwb/4FXbMYHb7ok1Dft+z76/T4WF4NZ2tlsFuVyWdjmdDotjCWvKdcXGSKCF0rO1TVI1vtLTwXr85ZLSnAsMwTQ1OIPHaYTibGLtCr59X0fvm1iank07dxwzGir/cgcqaSOiConfRRSMdiuj6fqIzlHF1I8k9v453Yt4k3/5yHc+vDi0wJtNQh+OcdaletT1t/r9dBut9Fut2UPSSaTMvucLB9BVL/fh2VZMvdYLfYBgeGY6jTOvWgwGCAejyOXy8F1XXQ6nRCAI4geDAb43P6gcHf9mjim8wEQI+Ajc8k1TnUDiy5ct/V6HY7jIJ/PY2pqSvYugixKp7meGTREmxsZoaKHag6mXhPVHIx/ftdVk/i7W2bwU1eXQu1dZzPU2dk9y8PXDtQAAG+8bEq+u+/7wuiqRnUc40gVA1UJNCsrl8vSo0w2uFKpiIs9gSldwNmaQraXe0Imk0GxWJTnSLPZDB0TC0KqBD4Wi0mhxHXdUM8+9yeeb8uyYDsOvngw2GfesDWQqHNtqv3nfJaqExKy2awUBqjGoOcAw/M8tNttuSe4Pk9nrGAEtKOIIooonoO49YGjAIC3v2Ad9GeYnc1QZ1uK07RrY2Mp2PR3z3UvuKQyimcP3/dx1+Nz+Nh9xzFwNJHKciyJ2judSqVEpse+VbUvk3Jyz/MATce3lwI257Ub48ik07AsC51ORxioqURQxa85CQBaiE3ke5L1/I3P7sKNf/INGT8WxXMbvEa+7+N3bt6Ov/jxq/DBm3YCGMuM2afaarVgmiYymQwmJiZCMk4yOQTABCscm0QzKFUZwdfQJOiRuQGO9nwkDOANO0oCxgjeqZQg0M7n8+Jgro73IrtlmqYAngUz3MHIz+YIHdVZ3zRN7FxTAADsX+rLebqQ4pn6s29/bAGLPRtDx3/W8UFqXyvfr1AooFAoIJVKCXAeDAYyG5jMdKPRQKvVEjl3LpdDMpkUkynKz9lyMBgMRIZbqVQETPH6t9ttYcBZzFP7nD3Pk/2sOXTx3bngmr3t0pIAIoKzlbJxstgsEBmGgW63i16vh3g8jrVr1wroYc+2qhTgcVIqvTYTrPFFa9wmoc7QjsVicp5UcM3vAQCT+SSq2biwsuq/nY1QlSPJZBJfeGwOtuvj4qksNpcTIbM9glQWUcjyE2Tz2FlIodqB7WuapiGdTkuho9lsYjgcIhaLoVQqAYD05XPNUPlQrVaRy+VEas7+5+npadl/WCwqFAqYmJhAqVQSdR9bFNhHzXPMvcY0TXzrUA9LQw/5hIbXXVxCqVSSZ6HrulIs4LORex3Hx3FqAlU5BPaM4XAo7DxnbQPje3Y1EQHtKKKIIoozHMeaA9zzRB1AALRXE+ybVeVX/X4fF1UCoL13vhcB7edh2LaNv7nnMP74a0dx68MLwlgzESELwV47JllkuZkoEiQTpO9r61ga6UgbPl69OSMOsDR+GQ6HKOkmDM2H7etoOWNAxCSTQNt1XWypBElZ5Dz+3IdlWbh793HY7nKPYjaLN165Vpg+lWXrdrtotVqIx+Mi51UdgplAM+nk2iLQIytNGSYTcTKQrVYLX15ms19zUR4pzQ21EvC1VGXQ9RmAJPNcTwQ8nudhdhnwnBhood5Wrj8y2gRrZFV3zARzdJ9YGsjxXyjBghmAEBh0HAfzHRP3Hw7c1N985Rr5t1MFCxFAeJwXWcqVzPBgMJDPrtVqqNVqME0TiUQC1WoVlUqguOKIN0rTub5UoEFZrWq8SHBbrVZhmqbMYVcLgWQUv3igB8cHLirpuGQ6I/8ej8dlxCWlvWrvNEGx67qo1+vwPA/lclmO3fM8LC0tyexlVbXB9WUYBtblgs9btOLSX8z7hKBcla3zflOLUASwBIr8/NMxyPpBgvcHQfBnlmXjb7psKgRI2WZAhQNZ8EwmI99b0zQpitH1HQj3f9MksV6vS4Enn8/Dtu0Q4Cc7zs9lOwoLMRzPBgD1el36xTOZDMrlMnK5nID+dDothSP2kBPs05jMsizceSTYC1+/LY9SPntSuwl79rkuuRep5mr9fl+KALxvgOBasyBFYM77i20Yq4kIaEcRRRRRnOH41IPH4fvAi7ZUsb5yamOalUHXTiZEZC03lYLq6v7F/gWVVEbx7OH7PvbPtfDA0S50DXjLlTPCHJEtIaBmnxqNiZhok/EZDAaSLMbjcXxjIUjkXzprIKH7AlTYljAYDODYFqaSQaK45IzldSv7FG3bxuZyAMz2zK3eBCaK0wsWUf7l3sP42Y89hv92+z4kkqkQECWDZhgG+v0+lpaW4HmejNShFJhggGyNCiYACJtDgE1QtLJ3ca5r4+GlYN+5ZWdBijU8XsrG2XeZzWZlDVHCydYGFTRPJ4PvcWKgCYuoAhV1FBlZbdu28ZPXr8U9v/pq/JebtgO4sIA2QZkqZ+Y99sXdS/ABXLU2hw3VnJhJ0QlaDXW0F//P60Bjsnq9jk6ng+FwiEwmI+OIhsOhgC3238/NzeHEiRNoNBpyHWKxGI4cOSKGYzTPI8DjZxH0crwWpcDqtRYw6/piqPeWnQVpV+CeRcmu6nrNwiH/3u12Zf7xmjVr5HNarRZarZaYw3F9q9JzANhQCP7fcuJo90dSzFkJprn/EVirBQNd1/HF/V387jfquPdIL+QYfzaCxVe2Vrz1ymncsKmEmy6ZDK0NFlw8zxMTPDLWapsarxedtml6x/5mrieej2Jx7NFAJYPa959MJqXgpwJSSsKXlpbkfqbUO5fLSdFG13Vhs6mE4P40GAwwHA4xGo1wuAscaLqI6cAbt+fFDZyzxSkbZ/sVJe9k3klm8FzxezDYesGCBs83j2e1EbmORxFFFFGc4fjx6zcgkzCwZXL1xhlqFZVyutFohE2lYJvet9AP9c5GceGH4zi49YFgpNdLtpSxphi4uq40qlJlfkwymDCobDYNhxZGBvZ3DGjw8dpNCZmLy4SD7JBlWZhJupgbxbFkJ7At1ROQTYaGa24mFQCa+c4Ijb6FSjbxtN8ritMPzwtmWH/m4Tn85uf3AwCmChnEjDDbS6BtWRYWFhbQ7/dRKBSwZs0a+XfVUZjrIpPJCOhlHy3XDYEwE3GaU/X7fXz5KRM+gh7/mYyGen0oexT7KYfDIYbDofRC0hgNGHsO8PX8rhV9CCCF+QHgawY8b2x+pCb/LC6xSFRJaSiX0iFQdKE4jz+T2/jnHlsAANy0oyJO8qrBGc+fYRjCUANhUMhiGoEY9wMAwsIRZNO0rNPpiKMy+2xTqRSazabM0c5mswLa1NFbdJTXdR1TU1MhEzYa5RF06bqObxzqo2sDlZSGV20th3qkOW+dnhNqAYXAnzJe3/cxMTGBYrEIILgX5ufnpVjNYhG/Ew0DDcNANuYgb7jougaO93xsWjHLXJWSc/6z6joOBMXNA3ULD85b2DHdx42KAum5fjbz3AIQZ+5brpjBmy+fXmb7TWH+eX+apol2O1BL5HI5OTdUHRCQkuHlOk2lUqFRXFSv0LxMNSrjdebvEtjy98hEE5zbto1KpYJUKiXsONdnPp8XCTlVFizwUI0Vj8dx19EA7L5sQwYzxbTcH3zGpdNpefbxvdmHzdcNBgORqZOR53kmm80xeEBQLFhYWDitokqUrUURRRRRnOGYzCfxsy/bglfvmF7177CPikF54Pp8kEAea5vomc4FxeBE8fTh+z46vT5u37UEAHj71bOhsUbsQSNzQTap2+2KOzQTWNVMTdd1fGM+WDNXVIF15bQkkJy5y0TWdV0xRFuyk/L7lN2RVbQsC5prYVM1UGfsmYvk42cyONf1tkfn8N9v3wcfwHtfuBG/efMlIQCp9oPWajV0Oh0kk0lMTk6iUCiIm7zKvBCAkeGmBJJmeiqDxYIOAVB7YOIbR4PPvGVHQYCM+lquKwDi7ut5HgqFgvR4qgksJb1p30I2Bng+ULPHwJNSaEp2CUr5PVTJtMoynu+h9vuqfeuu62LfQg/7F/uIGxpuunRaVCemaQoYoAR3fn5eQDCNzghqhsOhjF9i73U2m0UulxN2LplMYnp6WsZhAcE1ISOdSqVg27YAs0qlgkKhgGKxKI7MZMebzSY8zwv1c3PNca3SQMp1XRnpddOWFLKZtLDr7KMlC0r5L/cfnjfuidlsFhMTE1IcWlxcDBUfuG5U9QcZeN/3MZMO3u/EcLwmgfH8bK5RAmwWpVQQdtFEUPh8om6eVUM09hiztUNl09nmoxpnapomI/w4J533r+runc1m4Xme3F+JREKc3QFI/zLXG0E8P4d9+/QFIMimERt/xsJQoVAQ8zTHcWTvSiaTmJiYkLVJDwoWOniNem4M3z0eHOubdwTrkt+Hr6VsnO0PBNR8bx4P2Xy1N7vf78tzlnsmVT6nUpk8U0RAO4oooojiPAh1niwZxdFohIRv49detRYffsc2JGP6BZFURvHs4TgOvrJnAY2Bg2o2jpdvLYcYKMrc2NdGFoISXfbZkqUmQzHyDTxQC+SRr9ucFAaq2+0KSFKlgxOxIFlZcgKGWjVfU02zhsOhGFFFfdpnLujq/sXHF/DfbgtA9rtv2IDffvOlJ7G0bC2hLNjzPExMTGBqaipUmKFUl2CNCXEymQz13bPvcSULzmLL3YdNjFxgbU7H5ZMxMbliMYjzZMleUnKey+UkEWUyTfBCCa9tW1i7LPiZG8XGjuTL/xFYq0CbrRQfu/cw/v0/3I/7jrTl3873UA2q1LFSvu/jC48HxbaXbCpiopA5qcBGgynKYjnzeDgcynXg9a1UKqhUKiiXyygWi6hUKqG+18nJSUxPTwv7res6KpUKqtUqCoXg/ibAV6XcvBY8Dkq4NU1DtVoV0MxeWBZY+B4PHe/jWM9HQgfedEklVDQiICKIUlVdwLjoTPlwsViUQk6320Wz2YRt2yiXy6FihspC87Pi8TjWLndzLZixUMsEn63c89QWGoJb7o8XTwZv8mTj7AJtlSV+ojbA3377EBa7wR5OkOx5wbi+VCoFy7JQr9dhGAaKxaLkGSywqeef781WEPZuZ7NZJJNJ6bUGIOPUdF0XdYRlWfKcAQKHesdx0Ol0pADEnmz2+tPQka7fNNsDgnXXaDRCrQDcQ+48bMP1gcumktg+lRGjUBYNuRfxPQCEvAfUoh1VHKrihmw2jQG5RpaWlkLu56uJCGhHEUUUUZyh6JkO3ve338MnHjgG1zu9fq1d8wPc3ZuBjfCIG9u2cePFRVwyk4WhXRhJZRTPHEyYP/NoMJLprVetgeaPkzxVKqsmt71eL1RlZwKtmg7dM6/B9jWsy/q4YfM4yW6325KAVatVSSarepBcdd04Rt54rBhZbR6PbduSXO6OGO0fOFRTuzv2LOFXP7MPng+889r1+N1bLjtpUgH7TTm/1jRNAVVMjFfKwMlAp1IpSZbZj82klbJkOpDTndz1fHzxiWBt3Lw9j+FwKGwlGSzP80JOxpxhTLkqTZHU0YUEK7ZtY006WPMnBuO2Gf5fBTcqwLFtG/c91cAduxfw0NFgHV4IxcdnGuv1+kun8fYrJvHmy6ohwEk5L0dfsYhB5pkjuPj+vAY8Z2SIee8XCgVht1mwSyQS0oLCkU22bSOfz8vMYMuy5Oc0aOR4rVwuh/TyRAMWArkeyuWyGFF9endQFHnFhgRmKoWQdwCdnqm2UUE2vUq4J9GLgK1VnU5HVByJREKKAqr5njprXNM0rA389MQQjetTVUtQfq32alMC7XkeLp4Kzs3SwEW9e3ZGzXE8FRCAw3/53hH8z7uexB/ccVCKEQSAZLxpGsbroZq7qWw2zzHZZz5Tcrmc9NKzsJPNZuWcc9wbrwXBKccKrrw+NEnjeubYOXo6sB2Aewtl4iwaeJ4HT4/hjieC3uo378hLqwrXjW3b8jk0XaOzOdc890BN05DP58XoDAiz2WTA4/E4lpaWpDhF07jVRAS0o4giiijOUHzhsTl8ff8S/vLug1jFRC8J3/fxt7tM7DYr2GdXpBLP0RNM0vjgj+LCDsdxMBiOkIrriOka3rZsgsYqPBMWYOwEOxwOxayIAIaJlyQg0HDP8kivN27LSAJDVkDTNJmPyp5v3TVRjAXrq+aE54fyd8jsXLsug//42ovxzuvWn+Uz9vwKSoMJJorZFAxDw49esw6//7bLTzkO0DRNkQqrySwASYzVucEE44lEAsViUZQSBLk0QVs5vx0I1ty9xwZYGnjIxoGXrI0Lm0w1BKWl7BdNJpMyc5cGfpRqUhZMSTMQNkQ73hv3f6oeAVR0sBBAEMWCz76FnpzP8z1UI7SVP9sxncEHX7UeL72oIj/nfc3rynNCcD0xMYFqtSoAmYUJejiwWNFoNMRMkSO8VAVCNpuVoozrBo7y7GMtlUrwfV+uYTKZlF5azs0ul8tSGOTaNAwDExMTAIJn1hOLXTy8FOwxb7mkJAUdjlliuwHBrCoBVlllFfjw/LBHnO0J6sxkFhMJwvid1y87jy/ZCQyGIylKqHJ1gjb+p64xTdOQTeiYyQVFkwO1gVyj59IQTb3HdSOGzz06BwB4w6WTsgYAhAzeWPjg2DcepyoRVw3HaCbH1gNgrLpRCw0E8uyvbjQaUrRg0YQtDQTY3GP47On3+7J+8/m8rAUgYO4pGefcd3pIfO3wCD3Lw0zOwPVr0wJ6OdaQn8FRdq7rolQqybOM7VAcLUbvAa7XZrMpgJpO6FRwsIf8dIB2ZIYWRRRRRHGG4hP3B8ZWb79m3WmZ8zx0tIUTveBB3vAy8P2aOO2ORiM0eibuf2KAgQP8/Ms3XzDmP1GcOkajEXzPxf98yw64RgoJBGNSmAhRNk5GS9d16dOks7PKZrMws7sdR8fRUYgDr76oCMsyhQUHIEwY+w2ZjM2kHLR7BpbsBDakzBCjyPe2LAvbigZedum2c3z2Luwg0OE9nE6n8ZpL8/jM+3PYPpM/CWTz3C8uLooDNACUSiVhO8lGkZnjvHTP81AsFsVhl0kt/+MxMKkku6NpGj79eAsA8OqNSRhw0V+WmVJKqZoUEZjlcjlh6slQZTIZYV9pPESZbtUYAUjiWM9HLBYX0K+eK4J/Jsm2bWPrRMDi7pm/MIC26mhNoK0CQEptVdNCghKCQBraqUwt2XEy0tw7AMgaoFSXoHNlQYXPGAI1MumVSgWLi4HiplQqYWpqSlQ1ZCEJvtkDTEaVoMn3g9nNt+8L+nyvnoph63RBijOO4wibzfXJn7OwQpadUnQWbNgLTBBM+Tz9BwiiuM5p1KXrOqYymow1XBy4WLvCPI1rVPUK4J/5c9u2saWSxHzPwcHaCK9cVl8QhJ7poJkYEPS9f/epJpZ6FkrpGF68uQRzNJR7hK0aat8z1Qnc18nm0gCNRmWcu00VFV8fj8cFGHueJ8oKFnJVBYu6x2QyGQH3ZIbVZwvZYTLlQFBQIBNNvwky7LF4HJ/dEyhZ3nRxDpl0Sgp4bLmgBwnBMUeFsU+bn8HCDZ+xANDr9TAYDKTAxPVHhjuXy8mYxNVGxGhHEUUUUZyBOFTr43uHGtC11c/OZnxi2XkaABpeWqr47CNq9Eb4w7uP4sP3HIPj+ed9YhnF0wdnjxJk5ZO6sNmJRCI0PonVdrrGinNuNiuJkdqz961lNvu1W1KA54ScXGlipI49YcI6rYz4AsZstupyT4AYxfcfZIZ838d3nmphYTDuWb5ktgBD10L9g4PBAN1uF8ePHxcJJlnIfD4vplSqNJsJ5mg0QiqVEmm52pvNhFQtpFBunE6nsW+hj901G7oGvHZTUgAPk3B+FxYMstksisUiUqmUgDbDMOSzCQ5V0AwARQyga0DfAbrueK60OhqKUnZgzOhtXh55eKQxQN8cf4fzNVS3cX4327Yxsl186MsHce+TdWHuVKYtmUzKzGOVLVUVT0AAtLPZbOi+Vp3EyTiTMaY7M5lNUcQsg5RisSj3eywWQ7VahaZpIre1LEvAG8HcSCnElEolAVO1zkAM9d68Iy/fkRJe9VjIRvPf+Z6qHJpsqNouQcWEarymtkLwe/P3DA2YTi4bovU1AZ3AeHwXASWLIDzfqrHatsk0UjENAys8T/u5WkNsKUin0/jUg0HOcOOOCSTjsVMqU9RRbirg5b2vuthzljQl3qp5nLou+fnqOuPoMIJzvo6jstjWwGPj9WWrCQE/2xPq9boUFHnv00X8vmMDnOg6yMQ1vG5bQdaDWhTh9282m9KbzutC2TjbIVig4Tnmc5bHygIMi15qIWK1EQHtKKKIIoozEATLL9s2iZliatW/N7Jd3P7ICfl7y0/D87VQT2I54SId12G6Po40hhHQvoBjOBziyVof8z031FPIB3i73Q6ZndFwqtPphFgsGiLx78dHcRwdxBDTgNddlBU5H5miYrGIRCIhyRPlka7rYjIeJGk1OyGfQbDNxIUyzYXOCHc8Po9dx9vn7BxeaKH2YwPAdw918Iv/ugs//uF7cbQxEFBDZ2j2Q6tGQkyYc7kcqtWqsJvA2C2Zf2bxpVgsiusvrzXBKsEwpb7slfU8D594rA4AuHZKRzWtCzBnbyVnuTNZL5VKKBQKoR7dXC6HYrEoLBcTc2DsLO45FmYC9TvmR0ZozBITdnXNk0nMxHzMFII9dv9SYNh0PntXnGqsl+M4+PrBBj5+33H81peeAhQQQtDJ13Pd8HqrngyqWzcAYbZV53F+HkEywSOLPnRRjsViokKggRTHLNGwanFxUYAT34NsIvcrgqfRaIQv7GvD8oANeR3XbSjInmKapjDtlPPG43EBlGQVKVFmoYfGVXS/9n1fHKNZmOBaV8dNcb+jUoj+AHNDXQA02WoAAv75+zx/lLYDwLuurOLjb1+Dd11efM6BtmqQZ3nAHY8H4+Bef8mEnAdg7PHBwggZY3WeNO8vqhwGg4G0g6hFO74fi2d8DfeewWAgBmlUG7DAQek2AS2vY7/fFzWE2k7CHuxmsylAl6PICNx1XZde/9dsTiOXigvQpnJB7dXm9yqXy3J/0DANgBQMWMjh/stjpkmcajDJ6Q3qvO1niwhoRxFFFFH8gOF6Pj65XGF+x7Wnx2Z/+fF5dEcOJjMGEpoLDzpafkoeGqZpwnUcXFQNHih75rsR0L5AgzLND39nDm/5yMP4u28fkgQmmUwKO0TJHSVqqglaJpMR1pvsSzwexzcXgqT8hWvjKCQgCYPjOJicnJSxPQDQarUk2fB9f3mmMVCzk/D8MatIBkQ1aPuruw/g3//jAyEVRhRPHyv7se872sUH/vVRWK6HK9fmkdVtaRXgfb1yDvCp2E0CLbIsBKFkFxOJBMrlsiS/6ogkMjRce2Sy4/E4GgMHXz8UtBrcuCkubs9UXBB8kG0sFArCeHL9JhIJTExMSAJL92nK09U+7dlMABCO9yH/TjaNx002jCDMtm3smAkA5P7FgZzn8zHIIAJjoE2W9XOPBdLsG7eXkVJYQxbZgDGrz/chsCWAUtcJ5dsctzYxMSGmZpSg8zWNRiNUGOEaoNEVDazK5TIGgwF6vR7q9bqsHQIgAjx+R9VwazAc4c5DQRHv5u05AdJciwQ5ZJz5HSj9Zq/tYDAQQ79sNivztDnjW+3dzufzUmwAIMw07xcCzLXZ4LhpiMbXUoqu9mmT+Sfw52sThobY8v2oXqMzHStl43fuXsTAdrGulMKVa/Pit6AWWQi2aSTGf1MBO9tOVPCtSssJwln4I0tNT4hmsynybq5XPqO4JsmIa5oWUl8RmLOAx+KK6qSvFg10XccTdRMPzw2ha4FBozqejqCeBRbK3LmvqQqHlUUh3meNRgPtdluc1Gk0yDXO/Uktcq4mIqAdRRRRRPEDxj1P1DDXHqGQiuE1O1c/OxsAbl3u637ttjwmYkFS0lTk43wQbqkED4S9873zmr2J4uljOByi1h3h60+0AABXr80KU5NIJNBoNATYMhFot9sCmgmKCJZSqaAg07F1PNYKEp03XJQWp2HK7Zhoq2wWZYO+7yPnDxHXPLjQ0LBjwiZyDarAZ2s1kMxFs7SfPRzHEVMyy7LwnScb+IWPPwLL8fDqi6v4g7fsQNzQpVhCMMFEleCbJk7D4VBki5Q9kk1kYkmWkvJyJpiqjFjtEQcgDKRhGPj0Y0twPGBLAdhajoUSfCbiZMU5l7dUKonrMACZc6z2HrMgwKSZ7zW1bIh2rIdQ/7bK1gNjhpFAYPtUFqm4jp45Hol4PoZqgqZK4psDG996ImCNb9pRkRYRsqa8pryPed4Jdlh0UY3TqGIhy0tPhpUjlciQEywRRBUKBXieh06nIz2zlmWhVqtJzyxd7AlaWPgjS6ky3d881EVj5KOQ0PDKLfnQPkLwxfNCRnM0GonBGUEt33tiYgKO46DVasm5oOu1OideNUFTC1NcU5qmYX0+gD9LdkIYUxas+B/XIp/DvGfI+vLeUhUYz8U6ZAGGrQFHG8HM9dfvrEpBVDVMJYAl00xfDu4BNBWjmoF7BgsnLKT1ej0p3PD9OZN6YWFBijQE5nxdp9NBu91Gq9WSAhzZYh4fFVk00RuNRjKmjUUcnnM+Iz/9eBMAcMPaJNZVstJqwDVFd3W1pzufz8uzk4oRnhcy1r7vo9FooF4PWjiKxSLK5bK4rTNUNvt02qgiM7Qooogiih8wkjEDL76oim1TOaTiqzdCOd4a4ttP1AAAr1ifxOMHLJyw02j4Gfh+Ux56w+EQW8oBg7N3oXfeJpVRPH0Q4HxpXxOO5+PytQVsLifEbIXMNQ2CKKsbDAaSPJNRVE2NPM/DPUsGPGjYXtaxsaBjcbEma6RarYoLLIEbk28CG9d1MJ10cWykY8lJYhojSaSZWBMYbVruj90914lM+U4RwuYtS22Z7O9aGOGXbt0N0/Hwym1V/Nk7r0Q6GQ8BMCAAFZSLk31jLyoBNsE4HXJpdkcFDOWSqqSYRlYqM8c+WSaQtgfctmdZmrkhPJOWIIkJsOM4qFarmJkJHPPb7bbIcmdnZ0MsEItGXIdsmfA8b3mOe2LZEG0MAgm22bpA9o1g4adeuBa/8oZL4bljdv18DAKUlbLxO/YswfF8XDyZxubqsppg+T5noY3fl0CG/dM0jyLTSRVMs9kUFq9arSKZTKLVakk/LAEh55zz88iOdzodpFIp9Ho9Od/Hjx8XBpQtASwEEOSxDYG9sPQY+MLBAKTcuCWFdGJs1EfDLq59gj6uI7Wnn/sh13OtVpP7gWOZuJ+xTzuZTErfMN3Eydrz/5zh3nbjaA96qFY1YSxZ7FCvlwpoCdp838fHH23ha0/28JPXTuGtV2dCrTlnKngfkjn+9y/diLdePoHRyJT7ndeBTDXvc7K2LNSo8+ypkOAa5YzpkEx9GbyyUEGjQz6LWHTgc4JTM+gnwnNPhQQl7IZhyL5F4EqFFr8LWyh830dz6OKrTwSFvJu3ZUTGTjNHMuFkx8nyFwoFYd1JWrAgw/fudDrSF57L5TA1NYVUKoVutyvHSmY9l8vJHrTaiIB2FFFEEcUPGNdvruDjP/dCeKc5O/tTDxyD7wMv3FLBdC6GyXiQZDa8dEjKZds2NpQCAL9/sR/qRYriwgjKh29/POh/fdtV45FeyWQS9XpdHt7sleOIE47SIdPJBNJxHPhGHN+rB2qHGzclxGmVrGYul4OmaWi1WsJik/VhohsYotk4Noovj/gahTwCmPTato11aR9xQ0N35OBYc4j1ldWPOXk+BpNv/ud5njhHA4FM8kDDxi/euhsjx8Ortk/if7/3GiRjJxfkVJBN6SpNrThDmUDLsiy0Wi3peUylUjI3m7JxIGxsxz5xMoWq9FLXddyxr4GO6aGcBK6qjscJZrPZkCTVNE0xWsvlclhaWpLWBjLc6ng627ZDbCfXnO/7y3Pc81gY+HAxZrQZZNlUublt24hrHgxdA/yxCdz5FqphGY+fDNzndgWy8Zt2VARUk7WknJXfiSCCoIZAkKO8hsOhsMDJZBIzMzNIJpPSRgDgJOku5dkc+0RQ1G63RYVRKBTEkJFAXf0+LN5wr6E0fDQaYc/iEE+0fcR04E07itL3u9JYikUe0zTR7XYxGAzke7I4wTU/GAykgBWPx2XsGAAB69zfCJL4XdljyzWdTxooxFx0HANHOi42KA73qvM4ANmnWUTg8eu6jp7l4XjXwb7FgVyvM+k8ToAMQL6r4zjIxjWkjWDEHotgBL5UsPDZQsMz7uUq40/Du0wmI3JxKgwouU6n0+JKz+cQ7+WVwHUwGMgaY8GY65r99QDkGqr93NzH1H5rFphve2wJtgdcXInj8tl8qHClSsbT6bQw09xz6EHA5xmPFQharPhfMpnExMSEgGkWJoBxwZDu66cTkXQ8iiiiiOIMxanm3z5d+L6PTyz3df/oNeuh6zrWpILkvOGNwQsTl5mUB10DGgMHtd7pVVSjOLdBcLJrfoCn6kOk4wZ+ZGtR+tcMw0Cr1QqZymiahnq9jmYzkMsxOaC8lIDkwbqBgaujmgKuqPoi40wkEqhUKkgmk2g2m5LI5HI5SdjUvkUaoi3ZyZBslwmZrutBcm6Z2DYVuF3/sMnHWfjiaCsCA14T1x2PVyLYrVaruGTdBLZO5fCybRP4q/c8O8hmos6eRcMwUCgUUCwWheGmUzAQrI18Po92uw3P81AqlZBIJAQU0cGZ4EpdYwAEOHxy2QTtlWs1OLYl30M1emJSm81msXbtWpE301eA/dosBNIwSZXc8s++7yPhjZCPAz6ARSt2knyciT8Ta4IddWYuz9/p9E2ejeAerfal27aNo80hHj7Wga4Br7m4LLJxKgxY0OD3pzy6UCgI49hsNtFoNNDpdGSKQSqVwuzsrEhq2autGkBlMhlxtCf7nc/npYe72WxKCwAdpguFgrCaKvvIIjABjiqh/tyBAHC9ZG0C5fR4ranGVqp7M6XDbInhd+Ba1nUd3W5XCjoE/+qoMvaWc38j064qgHiMyWRSnrfzI0NApLqe1D55vp/qSq7rOraUg+N/oj4SsHsmiz7qyLFEIoGj9bFcW92neb9xVrrq7cAii2qSRwk51xxZcBYz+Bme54lU37IsaUlhmwqvBYE6i31kr3m/p9PpULsDELSU5HI5WQMsDLMowmKh7fq4fXcLAPCmbRkp0rCoSfO0dDot7DYAUVjQGE5t06KCQjXeo3ICGDu2k/nn8fG92dKymoiAdhRRRBHFDxCfeOAYFrunP/boe081cLg+QDZh4A2XzyAWi2E65UGDjxHiGPgxqb5blgXdd/D/vXULvvzzV2IilzgvGZwoTh10jb59d9CT+frLppDQPOm5o9SOAJmOrmSnk8kk8vm89G2SJfA8H99eCtivV63VMFpmLClxK5fL6Pf76HQ6ktRmMhlUKhVhsZhIVI0ggViyEwL01J5KMtqmaWLnmgBo7/4hAtq+7wvAJSgCICCQDB8TylKpJJLWYiaOf/yZG/Dhn7z2lK0lvu8LiCATBUCYbZXFZvLLmbCJRAK5XE6OSx2rxWScyfJoNBI3awJtAp6HTwxwqOUgoQMvmhr35qsjkpicJhIJTE5OIhaLiRzdMIL5yeVyOTRqqN1uy/cgiAQQYgsp4z0x0EKyXNVQiQwaZaiO4+DP7tqPm/70m7hzb9B+c74VH5/ObXyubWJtKYVr1xcwmUuIESLvfxYo1B73iYkJYZg9z0Oz2USz2RSX+nQ6jampKZHDqgZ7BGL8XaokCoUCdD2Yt0ygS2n/9PQ01q5dKzJzfg6vJa8Diy5sUzBNE/NdC/fNB9/9LZeURGpMZpn90NyTbNtGrVZDp9MRdpQzlzlGrNfryftzrfFc8fySsSW45N95D7C4Q1C9JhM8QxfMmBQV1dFe6v4HQOTYqis3vVOebFohVcuZCDLOXANP1gZ42f/8Gt779w/Ddj3Z61l04p7Onnve67xOqiRfNdYjs6xK+QGgVqthaWlJ9hGqVbgXspUgl8vBdV30+31RU3Hv4+fxPfnvqgHjSqDMc8zCwJ0H2miNXExmDLxofVr2LxY92Q5F9potLHSgZ0GB5wCA7DE0q4zH4yiVSkin0+KBwj2S+w/Xg3pvryYioB1FFFFE8X3GgYUuPnjrI3jZH9yN7mj1FU4AuHXZtfmNV6xBJhHI0mKah4IWyMSaXkYe9jS72TmZQiE17nuK4vwP9ou5PnDv4eUes0uqklSTRWKyoFbpmdSSCWAyziTkqUEci6aBpOHjxTMQliqVSolknDI6JhKpVAqlUkmknkwkytoQgI++F8PAHY+5IbPBxMa2bWydCOR/u0/88ABtlUFSixa5XC5kjMQ517tOdPGP3z0sv19Mx58RZLfbbSmqZDKZEFvNZHGl/NZxHDG663Q68nfOSyfAUgs5BEUE7GScONLrhdNAzLMExKtGTEyS8/k8JiYmhP0i61ooFERiq4I9JrUETwRH7HudXjZEO9ods4X8N1X6TjaMifN8e4h9C13sng+Y2/NtT1wJtMl2Xr+phDt/6cX47Zs2SYGGoFA1ReOeoI7MoqJBPa9sBeFn0o+B4JHANp1Oi9s41wD3Gcuy0O12oWkapqensWXLFgH2BEuUbZP9pISdIIog9osH+vB84NLJOC6qJqUQxfVICS5bEvr9PpaWluB5nowhJPDi+aE8nvdeNpuV88y+XAByDtURhep4OP5nGAbW5YKiz6I99gzg2lv5jGVhga8BAhZ9fTEGQwO6poeFrnVGgTaBJM/FZx8+DgDIJXTE9LELP49XNT3jcyAWi8k9ShaYhQPKt1UAyVF9auGF7Hg+HxRYqb4iyAYghmacOsBnG6XlmqZJ0YCych4D319taaBXgOd5+OSu5QL11gxSyYQUClj4YNHGtm15RuZyOWHZ2VfOPVw9vl6vJ/3lNHBc6TDP+0dV9kQ92lFEEUUUZyHU2dn5VPxZXj2OvungC4/NAQDece16AOM+yaoxRNtJoe5lsM7vSmLJB9JKl9Eozu9g5T+dTOBrH3wl7to9h52TwVpJp9Mi1yOYYWLIBIA9bJS48fr7vo9vLQXvc8OkD9gjeQ/28tIpOB6Po1gsIplMolgsymeopkuaa6Ecd9G0Y1i0Eygkx7Jjfh6TlRdtyOPP3nUVrlhXOlen9awHkyzOVwUgygO1tz6ZTOKxY22892/uRWfkoJSO4+YrZ5/2fdvtNprNJlzXlcSVbK5qbkSZLxlKy7JEdum6LlqtVtDzXK2K6RQZMTLlKiADIIW8+Z6L7x0LFA0vmbJDDLJlWchkMgLaUqkUJicnASDE/KTTaVQqFflcJriqXJdzuGlURDXFRMIEEMex3lhmrfpPUJ6sjrJyHAfbJgKJ8N6Fvnyf8yVU9kztL+ffbdtCKR2MTKNMlRJp9oay55pg13VdLCwsYDAYiBqGcnw6zHOuMa8Dz3s2m8Xi4qK0luTzeemn5TXSdR3FYhGzs7PCCPNz1CIev4vneTICieBk5Pj4yqEAUN2yIy9mZmobA3t3k8kk2u02jh8/LkWmYrEoUl/29JLN5jEWCgUB4FxHqjs090y6XPP7AZDzqOs61i8D7Zodx2DYR6lUEnCo+gioXinqczeRSCAZM7CuEMPhtoP9SwOsq2TP2LNZnV8fi8Xw6YcCoH3TjoocE+9hdQQe/07DMiobEomEFEh4LahocRxH9ge2pbAYViwWkU6nZawaryGduWu1GmzbRq/XQzqdlv9arZasfZ4TSv5ZCGIRN5vNhpy8+efvHeniUNNCKqbhtVvGsnGy4Cw0qUqXVColRT/6UhDwswidSqXQ6XTQbDYRj8dRqVSk/5r7Lo+bRRvek6raZDURMdpRRBFFFN9HOK6HTy0/+E53dvYXHpvDwHKxqZrBtRuDniAmmBNG8IBp+mkBN+yxXGgP8effPIbf+sKB8yqpjOLUQfddIOjvyiRjeOVFxRC712630e/3JekBxv2Gaj8tnXYJxuuWgX3dgEl66bQjCRaTHMpL2eeYyWTE2Ii9m2SqCGpmlsF1zU7KdyBDQtnhaDTCRMrHLVetxeaJMav0fA7VBEqdhczrBoxnRT9+oo33LIPsazeW8aodU0/7nrVaDbVaTUB2uVxGJpNBs9kUaTiZnmKxKH2Rw+FQRjxpmoZGoyE/K5fLITabIJ4AhZ8NjAHWbXvb8AFcVgGqcUeYeSaTXI+u6yKfz8v6YvEvFoshn88jlUrJXkUlDvs0ee4o36Ws1PO8ZUM04FjPg67TCX/MDPL4mVgT8Fy0rKzYO98FcP4BbQChXnjHcXBwqQ/X10RerxpI0Ume7KrqCG9ZFhYXF+W1vJeTySSmp6dFwcIRWQRLBAe1Wk3GJxHUkGFn4Yhu5VQyABBvhtFohGw2i2q1GpLzs1jCNfWVJ7oYOMBM1sD16zLCtBK88nvl83nYto35+XkBdRMTE2LARXDJohJfwxF4DDKN/HyuR45tIpBTgRJfuyYfR1zz4Pg6loaQ1/A7qS00VHaoKgEy9ZzEcGBxIAD4B/ULIIsPBHvLg0daONYcIpMw8JJNBWF+qXrgfaXK51k04PdS3dN5b5O5JbDs9Xri2M4WgkKhgEwmg16vJ/3MHKlG1pvsOPcCFvfUdigCYHVyARVbBMX8GQsrn17uzX7tRTlkE+MRXVRGqOuP+1E6nUaxWITjOCEPA44jpNlZvV6X81etVqUPnaHKy1VHenW9ryYioB1FFFFE8X3ENw4sYalroppN4NVPk0w/XVA2/qPXrJMkjA9GmlLREE2tptu2jY89sIDbdy1haJ85iVoUz01Q+ubpMRmxstKUqFarwbIsMaTJZDLSCwlAHFn5dzIs99QCkL2z4KCaGMu7OTeb40oobyYAV3vBVaDt+/7yqCVgyUmGHHRVMyHTNEPs0Q9DrDS1Ug10mCjG43HsmevgPR+5F+2hjRdsKOHvfuo65JInCwcdx8H8/DxarRaAwLRnamoK8XgcrVZL5qnTqIoGQaPRCN1uVxigRCKBxcVFzM/Py0gv9ujSxZnsL0E5wYs4pLsavnwgAKovnbKFDWMPZzabDTFr+XxenMSZdJLdouySjGQqlRLApDpJk6HnuitoQ8Q0YOgAXS8eAkTqLHEm1WRsN5Xi0DSg1rNQ61nn1X54Krdx03bwMx97FC/7o29i/0JX7qmVPaq8NpS4DgYDGeNmGIa0fei6Liwsg+eZx2CaJpaWllCv1zEajUTqy/PIfYF7RzqdDhUJOO+YbDb7uQFI/zbBnef7YoJ28/YcfMV9m+7Z6mfRrd627ZBJI5UTXEeDwUDk6TRuI9DhWlS/L4DQe3Etqf3cvu8jlUxgKhl81xMDTQqZQJj5VtcqiyDqGt5WTWBzOY5ccuxa/oOuRd5fVDWQzX71tjKSMU0YWhZyVAYegOwDaouI6rfBNaf2O1Ohwu+njhOkyoKMcDwex8LCAmq1mrQTqAWUTqcjBmPcy1hIWmkayecSi7q8hodbNr57uAsNwJsuzkmxgNeHBRWuQfoL5PN5GQVHxRFbplgkHAwGMoljcnIy1KKnstkrXcdZ4FDHvz1bREA7iiiiiOL7iFvvD8DyW65ei7ix+q30cL2P7z3VgKYBb3vBmAkni1RZNqVq+yk4/nhsh2VZSGs2KpkYPB84uDhm06I4/4IPfgD4y2+fwGv/5Bv40qPHpJeXkjsmz0xqYrEYut2uyNco5WPS5TgORp6GB5tB4vmSSVsklOzDdBxH+i2LxaL08bK3koZWAFYYogXHW7MTkpiq7rPskR2NRth1rIUPf+NJfGP/0rk5wWcxVDZbHZlE0GMYBvbNd/ETH7kXzYGNK9eX8NGfvv6kdhKC18XFRXFPnpyclN7ATqcjhReyh2Q1h8Mh2u12SE48NzeHer0uLOXMzAyAYO0RIBE4k+FTR7oBwN2HRxg5PmazwJaMLckrATPNlVzXRblcFqdnAvhYLCb9kOzJ5mfpui5KCjKF/D48f5qmwbUtzCwPWpgb6vK5AIRJVPu6+fO45mNTNfjFfQu988a7gsVRYKyAcBwH332qiUbfhgZgQyklElgadZGtAyAss2ma6PV66Pf70ttKYEVDMLKfansRABnJpZooki0cDAbC/MViMZH1A+OCEu91gg8Wb6i0UdtYDMPA/ceHmO97yMQ1vOainBR4eC44WokzilutligxqNxQJfQsqLDQQgafobLWKihWGVeeD64Lrn0ytmvSwc/nR0aIKVUNz3g9Cfz5PtwT33JJCX/02gm8eWcJwJkB2vRDiMfjcHzgc48GrWY3XlwKKYx4zvhd1TFUBLVqYYLXS1UlqOcZgBQRuM9QuWMYBiYnJ0XV0G63pWWAzxRN06Tfnq0tNGljLz17ptnmpGmaFFxYWDvctvHBzz0FAHjxxhyms2PAC0AAPQABzlwjHO/G5yjl6plMRuTz9XpdiqTlcll8DfgsXHn+VHWAuj+tJiKgHUUUUURxmtHoW7hrzwKAgJU+nfjkMpv90q0TmC2l5ecEWsU4kIQNHxpainycCc9F1WW55EL/vEgqozh1cL6sr8dw26PzeGKpD88ZS3HpMs1+Nxr/sKeWLAAAMXhhsnR/PQHL0zCVdLG9NB5jQ5az3W6LGzB7s+kazgST640AyPfHI77qTgKO50vSqiayfI8vPHYCv3BX+i8AAQAASURBVPeFPbj9kRPn5PyezSDQJuMBICzd7lv4iY98F42+hcvXFvEPP309CgrIVsGOOhd9cnJSjM84lmYwGEjyR2aZ48RUMEGQ3e12kc1mMTs7KyOWVKdvJs0EfEyobduGpuu4bW9gaPfKNT50fQzAbdtGoVCQRJrME5Pm4XAoBYFCoSBstjp/mCytOuaHSSv/TsAykwrO8dGuL69TAQELTZRvMiHfMR0wtPsWAyb1fNgTuV54rfgzzs6+cXsFMSNwd6bpXSaTkXWivg9bBQhYAAiQ5P5ApQN7ki3LEjkwATEdvIfDIZrNpoCMYrEIAGKuJsUPdzzGjv2vLLgQQBEYsT/4M3uCtXTT1jwS+njcFN9LndveaDRkPRNk87Xcd8iCE8Bls1l5DRBms9V7g/+m9sbzz+q6isViArQXrHhIUq1OXVCLjgRbKiBjOw+vDYvj32/wfAEBM//1/TW0hzYmcwlcOpmQ68vCLBlrHgPZbFX+rvZ083uyOMvnB+9LFtDUUW4cMcjXdDqdUKGRRdy5uTlRs9AvggBYNfpkUVjtG+dzbtf8AL982yEs9Wxsqabx/huqITdyehaslPSzoMh7Qh0zxmee53kykjAWi2Fqakqeb/zeqmTc9335PN6bLPCsNiKgHUUUUURxmvHIsRY0TcNlawvYuaaw6t/zPB+ffJB93etD/8aHjmHoqCz3LDa8dOjhaFkWLqoEFf19C73zIqmM4uSg/E3TNHzrcB/dkYPZYgpXz6blYc2Eg1JKJkutVkuSoEQiIfJfIAARPjR8p77MZk+Y8LxxvyATCYKsSqUi4IusKFkxJiAqw5lyB0jpHjxoaLjBOlMlvAAkqbmoGvz7nvnnt/O4ygAxVjJrlWwCP/WSzbh0toB//JnrUUyPQTYTSMuyxNQpnU6L5JdSfrJKbB+gxJEyS7r6WpaFRqOBZrOJ4XCIYrGISqWCUqkk7DMdyHl9AUgvLgGq53l4cNHFYt9FNg5clh+GerNVkG/bNiqVioBtgi4y1tlsFt1uID9XGUyy33ROB8YAiMwhAcxUIlhfx3rjEURMZtUeeZXpdF0XO6ez2DaVQzY5dvY+17Gyn9/3fXSHFr66LxhDduP2cqgVgyCS4ICsGYtaKoBgTykdoHu9HpaWlsSRm6CXahiqDOjmzevGIhw9IlQFDc87XcZphEYWndeT7SyJRAJPNkzsWrKha8Atl5Rk/ZGlJ9BmsY5rkOdBBeEEOfwdFnqowgHGShy115f3C0E37yG1N1l9XSKRwPr8svO4FRflDgBZr+p6IhgTqbzS3+55HlzPx8C05f2/3+B3Iph+xcWT+NN3XIb3v2RW5tvTtVv1MSDg53OA55M97DwPLJ6pbRw0ROM5InDWNE2KiixkLCwsCFNcrVZlKgZ9AXzfR7FYlGIB5elsAwAg0xV8PzCUpGnZvUe6+K93zKEzcnHF2jz+4m0XIas7UmhjP7qqklBVBmzB4tri+lJBfa1WkyIBx2ZyrfF+4zmj2oxqEZ6viNGOIoooongO41Xbp3Dff30N/ugdV53W793zRB3HW0PkUzHceMl06N9UFoISXvZp88FtmiY2lYLkbe9CL5KOn4fh+35oJu4nHwokfzdfWoW5XMlX+59XMgndblf6XtmbrVbPdzU1tGwDGcPD1ZWxpDuXy0lizd9nrxqBCRkmyuIIxHgMnudichnwLJpxYXKYvDLxME0TG/JB+rB/vgfbPffg5rkKdV4qE/hT9ed94FVb8clfeDFKmQAMUCZOCSjN7MisqAwU349MdzKZhOM40q+9tLQkTt0suNE5ulKpYM2aNchms7BtG41GQ5JFAmuVPQaCIk8sFsPt+wJTvJdO+0jGxiPKKA0m+002lf29vV5P3MgJEJm4Ux5KNhuAJL8sCBEwqcZTJQTM7tGeJ2tSNRFTWy7INDmOg/dcO4M7/+Mr8N4XbpDzfi7j6WTjX9lXw9D2sKGSxs6ptIBE13Wl+KACIPV78HyRQaULfLvdxtLSkng8FIvFkCszQTKd7LlXTE5OYu3atYjH4xgMBtJPq5o8jUYjNBoNdDod6dMtlUoC4gjgOQuZ4+FesjGLUsKTPYjrVb13VIUMACnYsCBIIz9gLGOmmoL3owqGyMgSKBOU0XWbEmm+H/c0z/OwsRj8vOvG0Braco7U3nIWIqmmUI3i+H4ffbSHm//+ID6/JxhFpZpqnW6wf5n7czKm49Xbynj5hpSsK/Y+s1dbNXLjsXIt8XwSfLLfmkVYMsNcu1Ss8F5V+/objYYoV8rlshREmKMkk0lMTU1B13WZq81j4r7B8WwsDI5GI7TbbXzz8BC/87UljBwPL9lSxv9512VIaq4UiKmmSSaTsqboKM59iuuR01oIvtlGQSUZFUX83qpsnt8JgNxrzM94b0ZAO4oooojiOY5iJo7tM/nT+p1bHzgKAHjzlbMnzdRlcqDrOibjy7O0/QBoE+hYljUGOIt9uKfpfhnFcx98KGuahsUhcO9TDega8KqNKTGHYXWf7A2ZhU6nI8wxx/7woU8G5Tv1INm6vmrBgCdVfiYzTJBKpVKof880Tangq4yJKunVNA1Ty/LxmpMMMYqqpNKyLFSSPnLJGCzXwxNLvXNwps9OqKNwOCfWcRwcrvfxix9/ED1zDMRTcSMkE1cl50zsmSgCAVigoRQZagKDZrMp86+BwLVenaecz+dRLpelj5vjddTefErEyXTS1ddxHBzu+thTs2FowA1VU/qE1b5NMo+VSkUMrCgZBwIzLLKkmqaJ1Fx1fgYgAEudoa3KfH3fFxXP4sCHAyPEaBMo8He5F/K78DOAcw+0WZBS+zgdx8Hnl2Xjb7hkQhhnAioCHlU2TsCYSCQEQPL7s82AI90ymQzWrFkjDubNZlMKEel0Wu5d7gFTU1MolUohtpOglMB7fn5eWPLJyUmRDfN9WBRKp9NY6gzxrSPBOn3H5VW5/mQCu93uSZJfAjOeJ/aaq27YXC8EzStNzbgGuL9xH+VrVLaZoYJQz/NQzqVQigVraG4wnlevKkHUwqjqvcG9MxaLIR03YHs+DtaCf1OLBacTKmPOVgGqWlQ1gurZobYnsBDC86ZKxXlc3IdYuKBvB1/b6/VEvVKpVGT9UVWj6zqmpqbg+z46nY6oGxKJBKampuTfAEgBiW0uAELeAlyvt+/t4I+/04DrA6+/ZBL/6x2XIK55Mo6OYJnXkMCd7VfswS4UCqIoUw1C+TzlyDF1zvap2GweO/c3FiC4DlQDwmeLCGhHEUUUUZxGNPrfX6W6PbTxpV3zAE6WjQNjdtMwDEwuuz83vDR8P8xoVxMuEoaGuKFhqXt+Oe3+sAcTB88LHIM//UhwvV+4sYCJbOAUzYc7jar48GZvLTA2Mer1egKIHcfBiaGBQ4M4dPi4rjR2bWWvMJkiMgZMRmmWRUDOxGIly6P2aS8tG6Lx2MgaMal1bBs7lgtNe+aen/JxJtlqsh2LxXBgroF3/fV38blH5/Dbtz0ur1dl4sCYHRkMBjBNU+SSfB/P84S1brVaAkbIupC5mpiYELdvld0pFouSfNL8h8yOOpKLfYYqG/6lJ4M95uqqh2JiDGxWMlzZbBbZbBa5XE6YTMqX+Xr2DHNtARAzKgbXHhlX/hvZ2rhnorisDF60xgCLa081ISJQo5zTdV1A02E5P5hk90zESjbb930sdYb4zlNNAMBrt5UAjAtW7JWmfFXtrWUBZSW48zwPvV5P5K90TSYDrUpcVTO5TCYjo/6AYIa77/vSc82e3Lm5OTQaDdi2LeZXmqYJsBkMBjKXPZ1O41OP1WB7wPaJJC4q6QJ8AAi44lQNtSdYXSsEOBzFxP5jvhdHxwHjHlmuZ7K5KkAmOGfxSAWfas9yIpHATCp437nhWNauAn2+P5lwdaY3FQlspTlQG3sFfD/PZt6zvE/+862P4E/u3IfjteBasW2FagiuB9XITi2e8trznFMOzqIHgTbPfb1el2ItXeb7/b6oajQtMHD0PE/2GypkkskkJiYm5LwSzHKf4zOPxULLstBut/F39y3gbx/pwQfw7uvW4vdv2Q7XtmQvVUE2R92NRiN0Oh1h5guFgjDvZLmlCLLcQsD1m0wmUa1WQwZwPIdq+0Amk5G2BxZ6CLIj1/EooogiiucgLMfDa/7467jlL76NufbpjTj6/KNzMB0P26ZyuHJd8aR/58Nd13VU4zZ0eLAQQ99PSFJg2zYc28In/90l+MoHrsF0IXnOE8soxsFKuq7rMOIJfGLZ+O6miwtIJpMolUriusrryT7WXq8nrANnXatMhOu6MtLr0oKJnOGe1LfIPkuaorESTxlvoVCQxJeJnOpG7fs+qsuu90tOEq47Nv1R5ef8ntuXjah2n3h+Am1VNs5ke6Fr42f+6VHMtUfYMpHBr9y04ySZONkox3FQr9cxGAwEZPJ+JRtL8zsmoEzyuF6KxaIkgHQd5zxaJntMhjlmJ5/PS2GO/ZFURgyHQ/RdA985FgDtl0wGhRgm3izOkJUsFAoCwnjdXdcNeQuQ/SKoO1UiyuSaQGDluC/P87AmHZybYz3/JMabYEkF70yUf+u2x3HFb9+J2x5bkGt1rmLlWC/HcVDOxPHJn7sW//0N27G2mBDZOM8dCygrmUhKv5noE5ASNMXjcZmbTgUEnb5prKhK/FmsoZO0OvqI0wrIEOq6Ln35i4uLaDQaIv0le1koFNDpD/Clg4Hs/8eunJDvlUqlRJFhGIYUYgCIfJmghcCfJpAcC8frTcCsysapymGhhWBMlfSqLuRk7rkGuZ7i8Timl4H2/CgmRW0Wp3gNVXZaHb3F77BtMvgOT9VNeEpx/HTC930pqKRSKcx1TNz6wDH8xdcPoTc0xQWcx68azHHt8Hg4TpIqCe43K0EkQTUQLryUSiUB0/V6Xa49wXetVpPxlXzmsXWBzyx6TZB5J5NMv4p6o4E/uOspfGJv8Mx5/8s24j++Yh16y4VGAmnVayIWi6HT6UhRmuot7lFq4YDPPY7I63Q6MhqRzD+fmWorA4vV/LPqJ0HWW92Hni0ioB1FFFFEscr46t4FNPoW5lpDTOaSz/4LSlA2/o5rx7Oz1eDmrWkaDA0oast92v7YEI2ysnwc8uCPGO3zI1ay2Yau4f+9ZQfecvkkXrG1KkkgZzADY0ktECQ5lJQyyVbHl/RdHY91gjV3baEnDAJfr8p+s9msJLNksigZJyPT6/Xk88l++b6PkjaEBh9Dz0DPHfdQMikhi2PbNrZNBCzDnrnu2T7dZyWY2DMpX+o7+Ol/egQn2iY2VdL48LsvR8IbhWTi8XgciUQC9XodR44cCc0+JqtHQKv2ILP/j0n91NQU8vm8tAMQjBM0cd1QUqr2ddKwjAkwe/cJSr5xwofjA1vyPmaX3b7VucUEcmRAmVRyffM9pYdUcbVXwaMaTLj5PVWmEQjWONUUR7vB3qa+hv8RiKpAy9B8DG0X+xf78l7nIlYqH4DxGrpkbQnvvHpaknYWM9QRXPxdtU2BwLNUKiGfz4tCBQjmrzuOg16vF1JNGIYhbGA6nUa1WpXjYd90s9kMqQTa7bYA9UQigWq1KuB7NBqh1WrBdd3QmLF8Po8v7FpE2/QxkTHwko1ZAS7AeL1ks1k5JyzoEVCygMDxZHxvgjP6AxC0UtFAlp8gm3uhWrhRmVvKrgGEwHcymcTabLDeFqz4SW0yBK8Et6oZH/dFwzCwvpRC0gBM18fRVgBu+T6rDaoXWEy77eFgosPVs1lMZAxpOyJg5npRJfWqWRfB+EoTNBYuWNhQmflisYjNmzfLM4QAOx6PI5/PQ9O00H5HsM3ry9nVzFX6/T4ajQZ0XUe5XJae54WlGj74yV344sEBNAD/8RVr8b5rJ0XNw2cXlTP8Puz7prM5C5HcT3kOVbNG13XFcI0j7VQlBL/fyt57FifVYjZVDWqbx7NFBLSjiOKZ4qF/Av7iBqDx5Lk+kijOgyBD+dYXrEXsNGZnH1zs4qEjLRi6hrdcvfaUr6G5DB+WqiEaGR0+vPhA+H7laVGc+SBAYZLkex5u2FTCf3n1eiTihjB+av9YNpuV/jsmnhzBoxoGua6LB9oZuL6GtUkLG7KesFtkbbgO6MrKJJ1MNllyMhtMvlTnWcMwANdGJR4kUUt2MlTQUXtFLcvCizbm8NkPvAQf/slrz81Jfw5DNbVyHAcDy8X7b92Lo80hNlYz+LufvBo5wxU2mffuYDDA8ePHsbi4KCBjampKpPuUYdMBt9FoSKGE17tarSKXy8nMbhri0RCKkmJKZ/v9vqwBghoCazJCTE496LjzUJAkvngiACqcZUvARzmmaq7FtUsWkOCaAEft+6fkFoDMXibAVuXjKjDwPE/8AY52w8wuEO4tJdjhz7ZOBKZr+xbOLdBW2WyeT/VnanKu9uGq84MByOt830ehUBDQS0ANQEAwJb9UILAwQ9OpmZkZ6YdVWxO4ByUSCSwsLGA4HKLX6wmgogEa1THJZDK0x1UqFfR6Pdy2Lyiyvf2KCbi2Jd+X64FjnVRHdMrkgcB7QNd16TdXR4dR5aGO8VLnPlOyrN4TVHEQRKkO3GRFyWBSobOpGBQhalYMpu3IZ6mgnfslwRzvExbHk4k4NhSC9z9QG8o5OJ2gJJ3A8lMPBsX5V27JSgGF+wTfW1V+8P6gGoDXgn3VzCOoTlELpwTak5OTItNut9tS6JmamhIVDVtguK4SiQQmJiZkHXNvYq//4uKirLler4dWb4D/9JkDuOeYBV0D/sMNRdy8oyiqLn4GW610XZfnIxUe6jFwHyG7zv54KgCoGmJRh8CZqgRV3UA2m0w214EK4vkMXG1EQDuKKJ4uPA+4+0PA0l5g1yfP9dFEcY5jsTvC3fuWAADvuObkHutniluXAforL57EVD51ytcwgWRCovZpAxBWezQaYb49wq/cdhA/+Q+PRNLx8yDUftFvPtXFl3cHxkeqURMTJNVMSnVCZSKsaZrIkFlI8TUD312WjV9f6kmfHpMLAnYmpuyjZrKSTqfl+MgU8LjVZJEJG5nFRTsux0UpJH9nNBoho7u4cn0J6cTqHVgvlFjJZn/lQBNHmiPMFJL4yLsvQz7mCshh8aTX66HZbApgmZ6exqZNm1AoFEJGZpZloV6vC0vIRJEy2lKpJIx0r9eT65rL5WAYhoxbUteI53mSeNKtnhJSsqf9fh8PNePoWj4qSWBbZiTJJ1samHDmcjlks1lhyggCTNMUSSi/D1k2AjcymmTUuHZU1Q6l48CYkSshMNU71vOgG7GQDJiFJwAiwafK4qJKcG/sW+zBU1jysx1cM2SPXdfFh799BL/6mb145GgrxB6qvfQsrAGQfwcCszkWZSj1JpjiuSHgInNJJQyNqYrFooAUMsdsMxgOh5ibmxPQWS6XhSEkY81zyfNP1rNUKuGb+xZwuO0iaWh4w/aSAH460XNNUzmjFo9YGEin0zJGjMy9yiRyj1RN0GzbDhmsqfPEgXEBmp+r7nfA2DuB7VqzxSQSmgcXOub747nZqlkkrwnvBYJXtR+aDub7lws+pwO0CRJ5nXaf6ODAYh8JQ8NLN2SlTUgteKrMK4tqzB+415OhV9cmiz68njw/xWJRlE/NZlNaCzhKjueB490oxWZLAosjLMLRNI/McjKZRMd08YFb9+HhBQsJHfiVF+bx+ksmMRwO0el0MBwOZT/gGldnebM4Qp+KlddJVfKoPdacRc+2Gq4/uonz/Kl/ZksN72WuuahHO4oozlQcuw/oBDOPsbD73B5LFOc8PvPQcbiej6s3lLB1Krfq33NcD5+W2dnrnvZ1lIPy4c1e2YbiPM7+I92z8LWDTTxyvIvmwD5niWUUQZCh+fahDn71tv34T5/YhYePtSVxYr8uARlZACYO7OFl0snkgLLFx7tJ9F0decPFpcXxfGQCMLKvZLOZPKiMFKWkauJF2aUKmABgIhYkrHQeZxJDWTPldqqZzPMt1P5s13UxmUvi2vUFvO3yKnK6I0lYsVgUAErFQKFQwOzsLKanp0O9fJRSUo5J9o2sH0c0USJJkG0YBgqFgiTjBOt00mWRhIw32SNKtPl5gIY7DwfJ/w3lIQwtcABmUsl1w8IA9yKuXX4m2U4CmZVmZVxHTHC73a70d5IdIlhk4ur7PnL+EHEdMF2g5YyBNgs9qsSebLFpmlhXSCAR09E3XRxvjc5J8VFVQPD727aNTz40h88/vohDta6YXJHxoz8DgbZqEMb7l9eYcloqZngOed0I/nh+OFud7CcLRr1eD7VaDe12G+12WxjQmZkZVCoV+Ux+bq/Xk37YZDKJtWvXYv369ej3+/js3sCb4abtJRjuSHq31SIA1zUBDiXuQFBIIJutaYGTPplz7m1kt4GxCVq32xXmk+uX78l9UTU+U92iVxZ3XNdFLpvFVHLZeXzZEA2AAFF+F/V9VDMyIAChV65J44XrUthcGTOmq90fWSih2uMT9x8GALxoYx7FzHiPVgtO6t6iFi4IiFlgU00t+b3VsX+8tmrht9PpyHXg84IMN0e/cbRYPp+XIgdbl5jLkA3fuHEjtEwZ7//EfuxZGiEb1/Cbryjjpis3hOadU33DCQr0vUgmk1JwAcatKCzk8DuxwKD29Xe7XaTTaWnd4blQi0hsMeA9pRZR2FPOz+NEh9XG6v3Jo4jihy0e/7T80Z57HKuvX0XxfAvf93Hr/QErfbps9jcP1LDYNVHJJvDqHdNP+zoyRExeJ+MB0O76Sdi+jtjyw922bcR8B+uKSRxrm9i30MNstXBa5hxRnLlgQvPNgw386ueehOP5eMOlk9gxmYZtjRNGJsRMHHK5nCTHNJACEOqfDiSXcXx7KaiqX1PoIZcZS8aZJKs9hUwUyEjS+IhsumpCNRwOTzKp8n0fU/Hg/ZbssexSdaxWE/xv7l/EHXuW8IINZbz9mqcvJF1IoUp++f1fuDGPF27MS48t5/66rotisYhGoyGSxmKxiGJxbHhIQEgGjQlhOp0W2TcZ61QqhVarhcFgIGCebrqUexJQs0DDwg3ZKXWOOxPlfr+PI2YKRzo2ErqPK/J9ZLMFFItF1Go1YehyuRwKhYL8LkEMQX65XEapVJIEnbOYaRJEIE3X/JXjebhGV7Ys6LoO+B5m0h6O9nXMDXRsS49VFgQtVADwOlmWhZihYdtkFo/PdbFvoY/15fRZWysMFfzwPrrvUAPH2yaySQMv2pgH3LGjNQBhKLmv0ymevfich03JuCqXjcfjAnbo/sxzWigU5N6v1WqhPl063Nu2LSPipqampCjT7wdsLN+Xva40xiMYfvSpOTwwFxQF3ryzIB4CZMHV70k5ONlGAjSOIxuNRkin02IWyXPBgoLqNk4Qxu9JjwpVSs39jH/nPaKCS8rLKW+fSTo4NkpgwYzJ+9GHgCoD1RCN+zaLVJqm4dVbi3jR2gRKpUzI14Ks6DOF6rFg2eNxcK/ZVgz5IDzdSDvuISxGsLVCbUNQTeAILnleUqmUqBxUozyqaLheeawcFTc5OSnfj/sH2W5ViXOi6+B9f3cfjrdGqKQN/PrLSrh221oBw6lUChMTEwCAWq0m+wn321KphMXFRVFr0ECP19kwDClY0Z2d65BTN9hWo6qyVhb96KnBwgWvM/dr+macTjEvysyiiOJU4Xnwd39G/qo3DgLO6s0Ponh+xSPH2jiw2EMqruNNV645rd+lCdotV80iEXv6LZcPST5cMoaHNAIWqumlQ72KpmnKOJF9C/1IPn4Ow7IsfGP/En7t8wHIvumSKfzOmy6GZY6kB5NqBIJTsphMosliEHgzcdM0DU/1dcyZMcQ0H9dWTGF5+DsABKgzkaJMkxV8GsEwgVDNtFjcUaXjZS1ItptOHJYHAedqQst1+MjRJj527xF8de/iOTj7z02o95MqIQcCMyk6PavmSEzKydoymeW5V/v6VFM8nluO6mKSS2MounsToKgO0aoUlsCl1+sJkFHZGAD46rJA6+riCPmkgWq1KjO/2ZtIhpAAhmw9gUculxOpruoEzcSUbHOn0xGHewBShFB7StX/S592IlhfxwaQe4DHoYI3fiZZ04ungiR670LwXc+20mKl27jruvjcsgv6TZdMI6758l14rgkOCK5VMJfNZmFZFjqdjowkIligo3e/30er1ZJjYFGG0tZms4l2uy0GZp1OB41GQ3q/16xZg4mJCXk9QVev15PxXtxLKCWPx+Not9v4zOMt+ACuW5vGRMKVAhDlupyzTaAFQIys2O5iGIbIj8vlsihlAMg+x7+zEMkZ4el0WoCTymYDY3DN/ZB748piCK9FLBbD7LIh2twweA8WJ7jWVX8KHicVBrxm3Ov5c2B18nE+Gwj6Gt0BXryljDWFBK5bmwnJwdl2ACB0zahoIeutGl+q95x6Hhh8Tx47GexsNotCoYByuSxzqvkdOcqLqgm1GMDnGMHpwbqJd/71vTjeGmE2H8Mf3jiNyzdMhFR6aqGQ65gFo1wuJy06dBJXlQrq96JUndep1+uJoZpqaqYWUlUPAqoKPM8Tbwy1uMpWnNOJCGhHEcWp4ui90Lpz6PgZdPwMDLhAbf+5PqoozlHsXJPHX/3EC/DBG7ejkFq9tqHZt3DXcr/ujz4L28feJCYIsVgMFX0sH+eDkMzi5nLw0Ni70DvrSWUUQbiui2/uX8R/+sx+WK6P1+6cwu++aStGgwCoEmir0mKyVWrPNJko9qkxedM0Dd9tBIne5fkBypmEADMa1qiuuJS/kc0iY8pkhoCMPd5qrywr+rquI2d4SOsufGioWeM+bRXk0Dl4a5XO48+fEV9Mwpi0fn53HY3lFg3P80JjvFh8iMfjqFarKJVKcBxHxt8wqSWjq2maSF8J0MkaMVEky63OHSbIJpNOhlK9bvF4HL1eT0yiyG5bloWGbeChhSDpv7bYl/7fer0eAlSU8xLkMvG2LEuSX64DHhvBCgBhhbjuuE75Xfmd1L2O59r3ffGmONrxpBdTNeSjXFeVtLquixesy+G1l0zjoskxa3U2Y2V/9mBk4Uu7A0+PN10+LeuAoIYFGbaKsOVD0zTpZea1TKVSyOfzKBaLwjq3Wi20Wi05PyrzqgIFnnfTNNHpdOD7PvL5PNavXy+ARV07i4uLwmoTaHGONdfkk0fn8NVDwbPprZeWZP1ks1kpLhGcVCoVAOOpDJS3c+QSvQXy+bzsU5RAG4YRcvOnnNkwDJTLZQFXKsNLllLdQ6nO4JpQzbPoOL0uF6zDRWs84ovXk0UnfjYl/jxWBq/FibaJej8AY6sB2uyXJvgvpuP4/bdcgn99707EdIhXAtlsVfJNBpf7OteYOpedewvl7/wsdR/hHsLzQhO+mZkZeU5omnaSAkEdm0Z/CLqZx2IxPLYwwr/7x4dR71vYWkniD183gw3VrBwHX0upN9sPqtWqmPJRlUXmnaPL1NGUqj8BzcxYuOIEBe4xLEDyPdh+RfWGapQHjJ3xuSeqbUWriQhoRxHFqWJZNn6Hdy16xYuDn0V92j+0kYwZeP3la/CzL9tyWr932yMnYLkeLllTwKWzJ8/OVoMJkSpjYq8sDdGYAFiWhU2l4AG/LwLa5yz2HG/gl27dDcv18aqLq/j/vf0SONZ4PBJ7uZj4qD25ZDrV/mf2+PKB3jA17O0GBZXrin1hTFUXYUrbVEUEE2Ma91AyrhowqaN22Fc5Bo+uGKIt2XGR2qlOz5RMblx22n2q3kffPL0E5HwNle04sNjH7955GD/60d1odgeSWDN5V12gC4WCgFNK9Qmc6DKu9tvSIIgyR7LPLJywd3E0GolsmOedyTKT83Q6LYmraiTU7XahaRq+tRgUCC/OWViTMzA9PS1zjgEIW0pwq47vAQIQw5nawNhQSnXsJZgiOOe8byavZMK49laao3meJ8XFIx1X9kIVpBJI0lyQa/J128v48E9ei5uvWCPX7myFykTzvH9t3yI6IwfT+SSuXJOR88R7m+BNNUcke0Yncs7ALhQKsrZGoxEWFhYENKt9pmpfM48LgDDjtm0jk8lg7dq1Ihs2DEP6+k+cOCF7V6VSEXUD1xeLKJ95bAmmC2woxnDl9FhdQ6mtqsYg+FPVOplMRvr+k8kkyuWyFExUt2gVxKlrmwAMGLPZvC+AsTRYNUTj+VV/RjZY0zRsKiUA+Oi5MXRtSF87MFb0qMUtrjueQzLGf/lgHz932xxu3xUUWdT3OVWwYAmMFRy8r23LFKaYr1ON2lTPDHom8DNZnOOxkfXmuiPQpvpFlYVThUAncZXx7nQ6YoinjsTidWbLi67r+M6RPn7hX3ahb7q4ajaDD71mCrOV8YgwysupTuC15/0BQPZNPju5NlQ5P/cC+p/w96mq4O/xHBNkc+2zhYHFCK4jdW/ms1X1UFhtREA7iihWhufCfiwA2l/2X4Ty5quCny8+fu6OKYoLMtTZ2c8WZAvUnqGx83jYEM2yLKxfrsA/VR9iZDnP+DCP4syH4zhYV0zgDTsreMmWMv78XVfBHPTFUCqTyQgY4fguAl3KEFWGhCygGt9rZeBDw5aMiXV5Qx78TJLYP0vZMJMBsqdky5j4MKlQ1xnZKCY2PGYB2k6QoDCBUceOmaaJbMzDVD4J3wf2zl/487RV0OQ4Dr68rwkAuG59DqVcWkyqmHQCkMIGJdg03lHZZ7KvtVpNmBQaT1Fq2mq1pB+aPYhcM5SQ8/6nzJLglWCJjBBBr+M4MH0d3zy2bIJW6qNSqcAwDJmlTDk6Jb6qQz4T2nw+L6wQgFDSCYx7Vvl9yUqSmWRSz/XLpF9lz33fR0kLChf1kQ/TH7sJr2T0CMzVnnfV7OpsAm2VzeY1uX1ZNn7zlWvge66AaLKPTPiHw6EUNqhKUV3aKZ3lOT5x4gRarZbMBAYghQrKfGmcR+abLG8+nxeQTRadTPHRo0dFwjs9PS1KHH4vyqUPHT6CLxwI9qm3XzZmqwlc2+22yJhpgEZDPhX4ca2USiUxPOO65h6lzjUmk5pIJKTooIJztY2C64mgVQWvfB33UKpUyvkMyrHgOp4YaLKeyLbyeql7gwrseB7WF5cd8Bd6wqI/01rkmqZkefdcFwfrZsjbgKCa35Xfh+uf9xqPgetKZcnJMKusLj+TxSyyuJlMBpOTk3LPct2yCEg2mwUCKlVYSNQ0DV/Y28QHP7MPluvjZZsL+O1XT6GcH0836Pf7UmicmpqS8Zdso+B+wuck1TG877kX8npz/QAIFbT43FPbULiv8TlJk0C2VwGQZyXvL/V5CSAkQ3+2iIB2FFGsjCPfRXy4iLafQfnyGzGq7AAAdA8/co4PLIpzEb/2qUfxZ3cdQL13ej36e+Y62HW8g7ih4ZarTj07Ww2VoaKEa2IZaDf9NHx/PMvYtm3kdBtTuQS2T2XQGDx/3Z/P1zBNE45t49du3II//7HL4NqmJEP5fF5YKSYrBMQEKGpyZVmWGA8JU+0CD7cDluC6Qk9mMKtSW5XNZjJOUEYGhPNDyQKqCYoKtFUJOQBMLM9xV2dpM9lkIkPmcsdM8NnPB/m42mtrWhbu2NcAALxma0FUA6PRCO12W9gsNQGLxWLIZrMol8uSjA0GA/R6PdTrdZHO0lCMSaPqRs7+1ZWzqsl6q0Y/7B30PA/dbjfUU86k995FA6YLTCcdXFINXHPp6EtWh4CYvaBk0plksh1B7eUnyGUirCpyePws9DCRVws96n5H8Bn3bVSSy/2yg7F0XJX+8rzTlIispm3bWOrbaA3ss+pbsVI27jgOrl5fwNbJLG5WZOO8ZjSFI/uvFhI4XomAJpPJwHVdtFotHDlyBLVaDaZpyoxzXj/OXmeP9Pz8vJhKpVIpFItFVKvVUN+zruvodDqo1+swTRPpdBozMzOhOcIEMq1WC4uLi/jnBxdQH/koJHXctKMSYojJZtI9XwWgVPCoLvUsIqjyb4IfFeiy6MMCJouCqtEXg4VC/plAUx25xmNWWz+yivP4iYEur1X3R3VN8f7iXsrYNhkA3gNLQ3ndM0mNyfITMP/Vt47ilr/8Dj76nSMAIOeH14xrhcUKrieeEx6zarLINcapFnzdSmNBz/OkPYTGfHwtgXYikUCpVAoZgnG9EIj/88M1/PYXn4DnA2/cWcGvvXwSmufKdRyNRshkMshms5idnZViT71elz2LewmZZj6/uB+wUMJ9g206/BkLPPzeDLb9cN80DEP2ZX5mJpMR1QVN2Vhw5H1zOvlWBLSjiGJFOI99CgBwh3st3vuSbfi3owUAgL8QMdo/bHGiNcS/3HcUf3LXfvROUxZLl/LX7JxGJfvs1U91NjL/K8dsGPDgwEDHHzMdTF4//VOX4B/eezlmCqkIaJ+lePRYC//p3x7CyLLlIWxovoAN1WiMYIVAgwmA2ovIXkqyo0wkHutmMPJ0VOIOthcC91cmFUyK6EScz+clqSDQ5ixuBoEUk0yuNf5ZBT4AMBkPkqyanYDrepKUqqZUNNvZvjzubvfzCGh7nocHj3aw2LORS+i4fl1G1AitVkuKIuqoJc6XJjhJp9OSsNZqNSwtLSEejwuLx+TZcRxxkGYfNt2b1TnCXG9q4s59o9frodfrndSDCE3HV48FCeKLJ0wUCsFMXLU3krJxJrTD4VDMz+gzwPUCQAyByJwB47E+BN9q4k93bdUQDUAItPMcAkFBAABODMf/5nmerN+VPfRMgP/TrY/ipX/4ddy+a+Gs7YcqY6mO9Xrv9evwxV96CbZUkieBO57XTqcTYilZCFOB4mAwQL1eR61WkzaASqUi5nmUilMd4TgOjh07hsXFRbhu4Ig/MTGBQqEgYJH70nA4FNVLNpvFxMSEADOyqNxH+v0+/s+3j+Ff9gb7wnuvmQY8R8Ca4wRjlNjrz2IQpxsQMKnmUtVqNdRrz7YagnGuebKaXKv8HT4PCRYpbwcQKuLwXHL/5bUieGJf72w6OO/zo7HTveM40rLBv/M6qTJjgq8d04FHwNG2BdP1ZT083dph60AymUTX8vHNg3UAwLWzwXdhoYUAVL2XuJ5UpQlNFimJp2yc35fqJtU7YuV+xWKPqiChUoGj2gjC+ezgOvqLb5/An30tGE32zisq+MB1RTi2FSrgEayzGN1sNlGr1aRIk8/nxeiOa0H1E6CaSi1y8jyqKhnf9+Xa8XUE1CzY0CwQgJi9qd4R3Hd4vbl2+P1XExc00I6kklGc8fBcxPbeBgDY/Ir34PJ1RUxddDUAoGAvAcPmuTy6KM5yfOrBY/B94PrNFWysZlf9e5bj4TMPBxa/z2aCxiDbScbH933oGlDWgkS26Wck6WDioW72Z5PB+WGNXcfbeM9H7sUnHzyBv/rGIWGjgXGPPXvI+FBWe9YYZOEIiCjxlQq9buC7jYDNvqE8QDabkQSTbDIr85lMBsViEaZpilyZQJ6u1mrf20o5KH/OpIxJRtkwoSOQ77adAACpyRITmdFoJCzOYufCnsyggibP8/ClvQGb/cqLisimg2taq9Wk5z2fz8MwDGEeT9W3RwlsvV4XGXgulxO3ec/zZJzXyt5Ygh6CVtXAiIm2rusy8mgwGITMeizLwoOLLuojIGt4uHYSUoShDDcej0vSyeNRZbwsxFDyzTVIkzXKuOlHoLLgXGsqOOB6pNs916HqVUAlz/H+WBZNgAaM1T/8M1UW60rjSQy8hs91cN/lfaO2HqgSaQJtgmyCWK4ZsokEkPy+VEOQDS6VSiEjMMqG+RnHjh3D/Pw8LMtCqVTC+vXrxaQMCBg9OpWrbtX0EaBiioZmo9EI3V4P/+tbJ/Cp/YHK5edeNIsfu7IamjesehUUi0X5N8MwpKWB64syd7rncy+kvwSLNWzD4VpVvyslzdyLVFUO7xMVMPFY1OvDogaLnmuXncfnR+MRX47jhOYv08Wbx8VjBAJMMplLoJDU4fnAE0t9Oc+nChaqWCC9c18DrufjkukM1pcS0nrCosPKdUVwrMqYVdNNrhEgKMipzyp+fyplCGI5nostLDwPPEccwUZWmQqtTq+PD911BP90/zwA4GevreI9l+ekeMcCoXqvE0R3Oh1Z/zMzMzIaUVVBcB/ifcTnLU38VBDP7w4g1MKlsvyJRELatTzPExUaixn8jirjr/oFnE5c0ED7b7/91Lk+hCieb3H4HqC/CKRKuPZVbwUAXLZlPY75wXw/Z27XuTy6KM5i+L6PTzzA2dmnNx/47n2LaPQtTOaTeMXFk6v6HVZNWdHnw6liLDuPLxuisQJP2a7v+7DdZ+4Di+IHj73zHbz3b+5FZ+TgyrV5vOuqCUl0V0rbgDGbrZr+UK5HtoH/Rhkyk7kDvTjqloGk7uHaqisghqwfJYvpdBrlclmSD/YKM9liQqOOfWEySlZG7T9jb6+madB8D9VYkJgtLjuPM7FlwQcIErsb1mfw0K+/Bh9537Xn5uKcoVBBU3cwwlcPBIXVH9kaGHpxVjZNvmjiozoPq+H74zFXBOS5XE5GJ5GJabVa0DQNU1NTyOfzYoJGpoXrhK9lLzhZNDpKE0RQNRGPx/HV40FyfsOEjWwqYK9o1kbQrybbam8oAa4qTdU0De12W9a82j/OPYmvAyCeAaoMmL2WAEKmfEyIq8ttCzREIyBSVRXAGHDwvy2Vsw+01VYDADje6OPzuxZheWNHbJUUIhCg8aHcb8vMJNUvVA2ortuZTEbGKRHokJF0XReLi4tYWFiAbdsol8vYsGGD9L76vo9ut4t2uy2fx/VLkGrbNtrttpzj4XAI03bwR99axBcOBs+hD75qA/6vl26Q9yQoIxCjURmBNlsaWBRmMZmtEwTUZOZVpphrnP8ny8nP5mcShPE6rOz75/7G9cX347oi47shH1zDmhWD7Y7BPJ/FAEJFUx4DMFZnGIaBTaXgtQeWhnI/ngqc9Xq9kOP/px8+AQB41ZZAIZTL5cRNm8fLvZfnVi0CUN6tst8swPK+VxVJXIsAQh4eBNksIhCgspDLe5xFkUa7i1+9/SA+t7sOXQM++PIZvGnrWNHAZxaffdzjuGdwj6hUKlIoZjGIz1jeXwS63Bf4nWnAp7aUcIKCrgemoepnmaYpvilkstXryOcc35PX74cOaO+bu/CNV6I4v2L48CeCP+x8ExALqoQXTebwBDYAAJaeeOhcHVoUZznuP9zEofoAmYSBN1x+mrOzl2Xjb7t6LWLG6rZZPqTViqyu68LuqIZofGCdaA3wzo8+ih/5s+9GjPZzGAcWuviJD9+L5sDGZbN5/OlbtyG1TF4y0fM8T5JIJjR0ySXIJdNCpoRJKJM3MhP31IKk8ZrSCMVsKiQZp2RX0zSRj5LxoeSPcnWCO4J4VTbOhIOJLIEVk1LHcTCZGBuiqckrWTcgSHp1z0EhdWqweSGFKsl+7HgbpuNjKhfHZdMp+TfOjyVAfabgPOLRaIRCoYDZ2VlRMDDJrtfr0HUdpVJJWgA6nQ5qtZqMP1INjngNyaKTKWLxhgB6NBrhYMPGU10dhubjxVOuJMkqW01DImAMYJh8EoBQtkkGj4kuP191/VXZskQigWPtMbNJ4KmCA1VNQQDDOe7Huh58bTyKSe0LBcKMsWma2FoNvscTS/2zUnxU+2/5fT790HH86mf34pdv3SWydsqbyc4DkMIIMDa8AxD6mXqv04dBZbtTqZQwwpTfkp1bu3YtCoVCqEDDGcPs2WZBh9JkAjSC0nZvgN/56hy+dmgIXQN+7ZVr8N4XbpBjAyDrSdM0Mczj3qOqLVhsSCaTKBQKAsbVudksCKrAneeOa5X3Aj+DrQ0rmWsWItSCIvcwvo4KHxYuZktpJDUPHjTU7ZhcX0qaCVZZsGT7Dt+P771lefTmvsW+3E8rn8+cMMDzdqQ5wiNHWzA04JWb8yJv5n7Oa6K2Sqh7OK8FTeNUBpjHutJMkN+fyha6m6t7hPp9uZ742YZhYK7Wwi/8y2P45pNtJAwNv/O6DXjJGl3OmVoY0zQtZNin9uEXi0X5/G63G5L0q0UBqsCYK5H1Vtts1PVCxp3FTh6H2kKgGv+prTkqo60qnbiOVxsXNNDevxgB7SjOXPiuDfPRzwAAnpp+nfxc1zW08tsAAL0jj56LQ4viHMSt9weO4W+8fA2yydWDiKWuibv3rW52thpMqvng5MNwkiO+/LGhBx+Ead3F4cYIzaGD461RxGo/B3FwsYcf//C9qPctXLomj7/8sUugOaYkMuy1ZcLHxIoJCoEFZbZM3FzXFemamtwe63p4apiEBh+vXKtLskLWkdLcbDYrrr4EXkwS2MvJZA2AgKZYLIYv717Cez/6EFqWJgySKrtk0sgiz5KdCEnnAEjCRvbpQl97KmhyXRdXzubwqZ+8GP/jdRsQX5Z/67qOfD4vUvxnCtM0sbS0FHJKZqtBu90WB2kmtJyRTNBE8JXNZkM9u6lUCpVKBRMTE0gmk2i32/J+Khj1PA9fORr83hUlB+WULsCFfgGZTCYkO+Vsd/Y1et54rBNBmMrAMXjcPAYWbY62bbz2T7+Bn/34LrjQpadf9QfguieYNAwDBc1CQgdsD6iNxm7R6vXh5/J+sywLM/kE8qkYbM/Hk7XBc158VFkuFhJufyyQzr7h8jUhN3T1e64smvD+VcdTqeOPVDBJyXAmk5G+1G63K+CkUChgZmZGQDmLNrxfaXbF46UbuLpXeZ6HI3OL+O93zuG+EybiOvDfXjGJW66aFTaea5JMJdcq1wKvbbvdlj7+RCIh/gMr2WyCPcdxBLxSBQRA+pDJtnIdqt4BAOD6GjqmF7pnWODknsjijCrjD4pLaSkuqoZoNJxk64xqxsW9X90br1+XwY9eWsBLN+Xleq5ci51ORwBsLpfDZ5bZ7Os25FHOxMQETZ0Lzv1WVSCp9y/bR1TvCLVPm8fOvYUKET4XaPSotjvwz5SoU1kSi8Xw5IklvO/vH8TDJwbIxHX88S0X4bKyJ9ear2O7SCaTQbValeIwCwL0GmALguovwmefKoVni5VhGDKikIU9AuZcLidFLapHAISc+vkeAKRYoZr1qcoF9X5Xi+KriQsaaD9VG2BkRyxOFGcmDtx3B0p+C00/h8LOV4f+TZ+5FAAQr+85F4cWxVmOgeXg84/OAQDece360/rdzzx0HK7n48r1JWybzq/697h5k2niw6W6DHb6fhKmP5YwWZYFz7awpRpInqJ52mc+HNfDz/79faj1TOyYyeHPf3Q7vFFPwEoymUSn00G/3xeWutFooNvtivSNiTWTMLI17KFeKU+7txkkApcWHczk4yHJI5PMeDwemtlMAxvLskRWTMaRiREleDYMfODjD+KBIy18dnfrJGaRiRkABWiPDZ2A8WxYJqGj0QhfePQE3vORe/FXX3vibF6iMxYqaGJSVkzHsX0iYC54HlWA+XRh2zaOHz8eSG+XTZxGoxHq9Tra7TaAMUChKRT7stmTmM/nMTMzI2BAHS3k+z7q9TqefPJJzM/Py1ojUBoOh2iOfDzcCK7jy6cdYWBUdoy90ryGBBQ0KWJyz2vPZJzgRpU9q+OX2MLwl3cfhO8H5zGXTgpAoqJCTXJ5fwSgxcNMKrge86MxQOV35/Xiz3jvaZqG7VOBvHjfQv853w9Xstm7jrdwcGmAuKHhdZdMCftIwMHvS98GypIJRlQwxutEIEozJxb4CEgIlH3fR7lcRrFYFCBbq9VQq9WEEczn8/LevV4P7XZbpMZ0z3ZdFwePzuNX75jD3oaLdEzDb76iildsrQiIZuGAoM4wDOTz+VDbDIFos9mUPY59sARELOwQhGmahm63Gyo4k7nmXmZZlqwzgk0AaPYt/Nt9R3HF/7gTH/ryE6G9TGW4+R25R3IfM00zuOfEeXx8jenIzkIpi2NUUrCIQeB69dosfvqaKq6cSYUAK4N7PwCUSiUYhoFvHQjmbr96S05Ybt6X/J4sZPF7cN0A4zaVXq8XmkPOIgCPk+/FIhVl8Sxq8BxTccBrR3adBZndhxfwno8+hIN1E6WUgb9+505sL49H65Gh5ix1gn+uY7UlgsUdqn263a7cV2Tt1QIvWWjLstBqtYTNZkGObDYZb7ZDkOFWXcTVdinVLI97M78PrzEQSOY//+iJVe8TFzTQdj0fBxd75/owoniexOJ3/hkAsK/8SlSL4WSqsuUqAMDk4AkgMuF73kfPdPCGy9fg0tkCrttUXvXv/SB93a4PLPRdSaTE8Vf3kdPG8nE+6PhgUvsSI6B96mCyQ2aBrDLndqoOvGSZe70ehoM+fuP1W3HFbB5/9patgNmXBIlghEwSExuyEPzclUCbsm4mjAQRmqahObCxqxcw0D+y3pCElgkuE6VCoSAjcMh2qQwVizZ0/lWN2v7p3iNyXvq2L8kDkxkV9Ewtz9Juu3GYbhgQqVI60zSx2BniWwdruPep+nN9OZ+TUEFTZzAKSXhV0yi1H5vnlgwl5xYfOnRIAAx7Dj3PE1DEftN8Pi8gG4CAVTJOvV4PrVYLnU5HDL9c10W73Uaj0UC/3xene64TgoG7jzrwoGFzzsX6HGQtkMljIqpKW5mgqsBedbPnvsQkneeLwI2tCul0GkcaA3z2kSAZvXF7Bd872pc9i2uRa1+9B1gUIrN4rD82GuOa4zGr147AddtkcP/sW3zuC48rgfZnHgoMMF+9fRKZ+JgpBcas90qHZJ5j9TrwPuf9SPM6AkPP89But4XxJitKtcVgMMDS0hLq9Tr6/b6sDTrTk92kdJnvORwOsefwPH71rkUc7vgoJDX8/mun8eJtUyiXy1KsofqDMuJcLidFG65vXdeFaQcgI+ToTE+5utqCwL0YALLZrPxZ7TEmo0vjNABoD2284n/ejV//7C7Yro/9i70Q0OZ3VPv9+Xfum+xlXpNZHi03GoNwKjt4nXjcLATQzI1Aj69TixdcC1QyOY4jEwYA4N9+/kX4/96xEy/akBOmmgUQri9KpnnN1WIV70HLsuQeVMefrTQwY/GWxX3e8yxikMmmp4JpmrLmdh1t4Kc+tgsnOjamczH83Xsuw0XVscqnVCpJMYDnhOeazxuCY14bmgOy/YHHqfbe85hYhOl0OtJiwOcx1yM9Dui+n06nQwZ8wNhcksHiAu9XnjveH6rqpj08tcHdqeKCb6raM9fBZWuL5/oworjAY6HVwyWtrwEaMP2id53075defg28O+PI+kOgdQQobzz7BxnFWYupfAr/8x1XhuRgq4nHjrexb6GLZEzHzVfOntZn/o/P78O/3n8Mf3DTWqxdfqgzYanoQ/TcJBp+Gmv8riT4pmliczl4UO9d6P1Q9mmrPWt8KK7873RDve7XbSzho++5DO12G/YyY5jL5ZDL5UJziEulkkjhVEdlPugzmQz6/b70uZIZYuLhOA4e6mTg+BrWZTxsyfvQNF0SDCB4+KfTaQE8g8FAEgjHcUTSyb5aIDy71/Z1fOSbgYnof3/jTrzjiiqOHDkiIIDJGwsDSdjI6Q56XgwLpoEtyXFSrpo8jUYjbK0GBakLdZY2z7HnefilT+6D7Xj4f14+iy3l8UzWVColkt9TgTjP89BsNiXBpXyX8nyOpOEa4Tgw9tByPWSzWQFY6txyMlQEo5z3ynVIKevAdPCdpSC9e/n0eA6s6phMpog/U3s1uT4pv2RfrTrKiyBI04IZy67rSvFA0zT85d1PwPV8XL2ugP9y234AwD+/Yx2yyyCPrQ7q2iNr5LruspoijWNdH5gZO0QDY1ZbZbcJZl60KY9cJoXr1ufkmvAeO5Oh9p4ahgHbcfH5xxYAAG97wbpQ/7HqiK3KYgkY1eKNruvCoLIQoipIisWijPri+SBDSYUMpa8ct8VrBIxdmIGx5J+S4CMtE7/+1TrqQx8TGQO//7pZbJ3Ky7xrTdNkrakSZXUkksq4zs3NSZtCsVgMuYpz/6PXAAtRwFjeq/pMEAxbliW+Aryuf3/PIXRGDkrpOEzHw+HGEJYHpHSEwB0lx+wZJ5gjgDcMAxsKOjAfKCk8z5fPpDSZkndeKyAokNEJngC+NbRxpGvhIi+JNTkj1O+tzrXmtdc14MqpOEzTE9k41wlBJMf/8ZqSzVfZbBZdCJxjy20v/H6qF4fasqQWTvjso/KCBR0AeKLt4YO3PYmu6WJzOYn//e5gvGi/38dwOJQ9hPsJgFDRTt1ruKY5+q3VaomUnLO8OUkBGO/RZN/r9boY//FzuJ40TcPi4qL8bHJyUvZv5gWxWDB6buUcctVokqoxPtP5nd59w0b8wir3igua0QaAPZEhWhRnIL55x6dR0broaAVsvvb1J/17KZ+DPnlx8JfF3Wf56KI4V3E6IBsYm6C97tIZFNPPbJSkRmtg4V+Xf/dze9uyqfNBOLHswttUDNH44F2fD7bxvT+E0nEmIzQNoiSNLMRKkK1KCVVgScfbVCqFlqXhff/0GI51g4SHSSATyomJCZmDTMOXYrEoTCITTbIAKhOl9kOy51cSMNfDA51A9vqaDQY8b2ygxMSZoJ7JE9kgghSO0CG7pDKV6XQaH//eETT61v+fvfcOk+Qqr8ZPVXXO3dMTdzbnIK2yhCSUQAIhggjCZDAmmfRhHPgIv8/Y2BiwTTDB2OSMiQIkECggoZxX0mpz3tmZnp7pnENV/f6oOW/fnl1pZzZIu+u5z7PP7s50qLp169Z73nPe82JhTwBvuXBRV6mCKq1Ua06T7o58nIGkqhAgo70w5oamAePFBibLJ1ebL9b9aZqGPRMlPDZaweZ0DVFfh/EgyCCLMj2Jw3pY1lSS6WUQT8k43eKZIFFbOhGsxmKxLjduBvsE2GQi6c5brVaFSWy1WnggbaNqakh4bKyJmtLeicdLkEv5LOWhVEkUCgVZW5T7MplFkMb5IgvvcrlEBjuSq+Lnjzj72QeftwRDUYeV2p1rdZVdMNjmfkeQAgA9ugMy9hVNAUTq/UWQo+u6GLS1Wi2cOxzCR160Ghct7ZHrcjyG6jauaRru3p5GutxExOfCc5cnZR9SjZwItFRfBgItqlOYTKGKgte/WCyiVqthfHwcmUwGtVpNAn96N2SzWRQKBdkPgW7393A4jMHBQWEcVQC6NV3Fh29OI1OzMD/qxldftRyrhuIIh8Oy31FNRRUPXcapwuLvyZ4zGUDjNV5v27bFyZogR+3d7vf7u+r9mdjhOmPpAeCoz9iB6CMvWIZEwA3LBvbmGl2JCD5PVYk31xuVFpqmYX7EBQ02qqaBGtyiaGFZBe8X1ogDkH2X823bNr75SB4f/v0obtqcOci3g10ofD4fLNtR5/IeNwwDwWCwC+BzLyE4ZPKAa6fRaCCfz0u/6VAoJIkw/p6v55phUks14eMzqVKpIJ1OSwKNgHNjxsL/+eVOlBom1g0G8Y3Xn4ahWEDUPCrjO937QVVekb0ul8vI5XLI5/PSp9vv92NwcFCSLUwMMdnERAGd7Gmix72B65H7otvtRn9/v7xGvW95Xjxu3jNApy861wnnarYxIXCSA+1186IYivme7cOYGyf5aLRNaJt/BQDILXwhYDyF0KN/jfP3+JPP0JHNjWdj/HFLGk+MFGbNhNZbJn411Tv7unNmJxv/9WOdep96u/MwYSDWcR7vtPhiADAcdDb+0UID+Wpz1sd9Mg9VAqaCZcoUA4GAsDHhcBihUAjBYFCYQNaPMejP1ky86VsP4dF9eXz4lxvFlIhSS7YLoaxPrQdjPa7KaNNRnAyQKlvnw5sP+60VP0ptA2G3jdPjnXphlYVUa8wY6NEQjQ7nZIAYrDM4sTQD//2nXQCA91y+DC5Dl6CVSQIGYgxIbdtGn8dhbyZaHSMcoGPwI9J0mFiYcBJBJxurrQZfN0yZWZ05L4gev9FVm1ev16VFkgpwG40GJicnxZQMgEjH1WQHGUn2Q2YSh/JRBtT5fB5jY2PYt28fUqlUV2sc1lKrQEy9fvV6A3eOO0H/JYMWPG6XAHTKQBkEc11PNxWz7U5/doJcsniqvLLVagk7SEAOAF+9fSfalo3zF8Vw5vwoVvY77PK+YrvLTVg1CCPw4/qLwXEezzVs1KxOna3KYjP5xICYx6Ves+Ol8pkuG39kn9MK7kXr+mHA6urDSwaRa4XrgUCNDCXPgfcUDdF4nYrFosjBbdsW53uWqxCkUpJL6W0wGEQikcDQ0JDIZ5lI0zQND+7J4WO3TaLQsLCy148vv3I5+sOeLlBLhpyA17IsBINBOT+gO6mRSqXEM4DKCJYv8DxdLpdIxCkJ52sIOpnkIYPOEgaO7927F/lqC4t7ArhqdRLLp2r0d0x29mfV54L/Z0KD4J+JqEQkhITbubbjU/JxGj5SScQ1rP6b643rdEnCuce2T3T3tldNKb1eL/64JY2LPnUbvnzbNjk/t9st/Z1Zv0wvDs41P4PXhcwvFSU0V+VaYj2yusczvuCew4QOk4lqK7aHJoC/+dUO1NsWLlgYwZdftRI9YZ8899TWWfwOt9stNfrcYyqVitwDpVIJxaLzrGASe2hoSOaV9wTLBqigUA0lWTtP0M1ryzZ28XgcoVBIElacO6p/OI/qNeJa5nuY7HG5XPjqHTvx68dGYVozj7NOaun4j99xASKRyLN9GHPjJB+3PTmKy617AQ2Yd/HrnvJ1+fByxABs3/gAll/yjB3e3HgGh2XZ+Nj1G3EgX8N/v/FsXLV2YMbvvXnTOIr1NgajPly4NDmr72VdNwDsyja6Wt4YhiF9ZfO2H5YNkVw1m034DQvnLYggEXSj1uwwc/8bBoNoPgiPZkyUGnjd1+7D7skKhuN+fPG1Z0htJGtUCXIBSI9j9jrl/xkIZbPZrmCHzLvaLoVZeMMw8GDBASOXDxuAWYM5xeYwYGZdHWXIZINomKSa5pDlYuDgBOQGvvL6s/HjB/bh5WfOw48f2IebNqbw/CUBrA57JCgmw81Mv2qIZlkFWZcEbjyeWq2GVf0h7MlUsXmsiOcun1n/+BNhqNL8G590TImevywqwIGAtlqtCjjm/UeJpgogS6WSBPKq7FNlj1kvC3RKHlgOkk6nu1q0dSkfpn5GCS6VFT6fD4VCAZtzFlI1F7y6jXMSLfj9QakV5TVWzaH4/WTkKE8NBoNdTLOqeCD7yD9+v18C/LZp4d5dkwCAv7xkEQKBAFb0BfHHbRnsybcENDDhoAJssm6apsGtWejxWsg0dIzVDMxzdYA27xkmGHgNyUhNFivYOVlHwq9jce+xD3O5/wKdoP3tF87H1WuSCE7V5DNhQRaM14/MH9U0TF4xsKcyx+VyIZfLCahU1QYul0taJPGcuTeoLdzo8kxAyf2CPhS5XA4PjdbxxUeqaJrAWcNh/OtLlsKtmQLyCNoLhQJKpRKy2WxXzb5ai8t9jQaRtm1LbTeBHWucgU6LKCYgqdZhYoHKC95PbrdbwD3gmJZ+/U4nefi2ixbA0DWs6Avi/j15bEtXcPXKmNy/BGuq8Ryl5CqY9vv96PMUkGm5MVIBlgQ0uden14rzmnBPV+u0l02ZlG6frMkezQ4CBKEulwu/3HAAqWId6WIdmhaS5wmBpd/vF2UAE6gAZE6r1aok/Hw+n7yfiR6uD14rJjK4dgl4uZfz85loMwwDP398Ep+6eSds2/Fb+NiVCxDyew/yGwAgzLBhGMhkMiiXy8Ky87mh67ooYSgT516jKtE4R0xeMmFSKpVEJs/9r91uS0kB91X2nScQ571GRZiaeGSiZTqw5+u9Xi9ShTo++4dtaJoWvv36tTPeL05qoD035saxGC8MboemldHwJuBd/NynfF3KtwQxAPrEnHT8VB337crgQL6GsM+FS1bMDigQLL/yrGEY+uyA7n+85kx8666d+OOWNM4c8sNGB9gBQERvwgUTbRgo2D54rQ6TWKvV8LmXLe2Sgx6PmsQTbajBLkHCkY5M2QHZOycqGIr68IO/OA9xjy1AmJlyAMJmq5LsbDYrARRNYxjscPD/DPAY3GmahtGmFyN1N1yajef0ml01qGr9GINzZvLD4bCw7gwa1fpGAF3r6LzFCZy3OAEA2JIq4fZtExgM9WNdzCVASpUYAkDvFNCebHtgmhZcLkMkxwQQlPAv7w3gJgCbRk8eRlutt954oIC9uQY8hobnLg6LfJ+Bsq7roopoNpvCnKjgSGWXYrGYSM4JXFSgqzJtDProJs02WJFIRGoOW60WYrGYMNKUk5bLZQn4/zTuhHUX9NvwGXYXe6PuEUCHneY6Y5KIbsFM8qi9jim/pGO0YRhdPcXNdgs/e9vZuGdnFpesGoSu68Jo7841u9jK6XPBIJ8Beb+nhUzDi9GqhvkxXSSknA/VaIzBtm3b+OffbsONT07gfZcuwrsuCR7zNaMqaSjXB4AFiaAAIxXgkM2mxFut9eR9ppaIUPodCoVkfmk0RtChumDz/5THUmIciUQEqBMw2LaNfD6PdDqN23aW8I0nW7Bs4PIVPfjUS1egVi7ChtZVa5vP5zEyMoJCoSAMMA38VGaV66pQKAgQpQqHzCzngjXPqjKBQIvJJCopmOzkfHD88P59yFSamB/34+o1TnJ7xRSjvS1dkWQhE4dqXTaBMZVjTJSFQiEM+k1srgCjVa0r+RGLxWSd1+t1IfqYSFVVFDQpTZVaKDdNBN1G13PZ7/ejWG/h5k1OXf/zloalfIO19gTHXDsE9nwOECTXajX5mc/nExk5kztAJ6nBmnQmS6hQoPM7wT33gq/fN4qv3uW0Ov2zswbw/osH4ZqaL6q9eO+FQiGRa1Pa7XK5kEwmJSnk8/mQy+VEbh8Oh2UPJMGg9genMohzpnbr4H6WzWYBAOFwWM7ZMAxxPuc9xftRTVjyD9luoGP2p3oQaJqG//rTTjRNC+ctSuCshYmZbhcnP9Cut0y0LRuhWfS5nRtzQx3apl8CALynXfvUsnEAC1adC9wGLLBGMZ4toD8xZ8J3qo2fToHll6wfgs89c/CWKtRx51R7jtn0zuZYlAzi/75gOd64rsOWqWZBLpeBhF5F2gojawXQY+a7DNGYiQeOX03iiTamB7tHOnKVJl7/9fuxPV1Gf8SL77/tPPT40AVOVBYCgDiPBwIBlMvlLvdnAi+aYKk145SPkwUFnAD4gZwjHT63X4dPa6DZast3EUzTVEhlSmlmxKBBlXmqbLZp2Qclf1YPOoHyrmwdhhGVAEf9W9M0RPUGXLDQsnVkWzoGPHpXokBlQpf3hhHzu2d17zzbQ5WNs5fthQtD8LuAZrOTUOA1VRMu/BkAMRujAVUikUA0Gu0K+liTTXaK7B1bsjEJw+SK1+uVGlmyowQL1WoVLpcLk5OT0tJrvAZszuvQYOPCZIdx47ESOPEzVLMugh41YCfwVZkdsmcAxJCNryWT6tI1XHXaPLkvVw04a213toG22ZFVs+8yP5v3C0FRr7sJwIuRMnBBvGMCx3uL7Bdln7zXliUdNvF4+VZMl43nKzX4DE3uT84P7yVV9q/KVVmrzsSCyozyHFnfzGuutjoaHx+XEhlVBUXAyHVEplnTNFQqFYyOjuKXT+bwkx1OQu/a9YP4p5euQrVSlsQTE4q1Wk1aFjLRFAgEukz6yBAy8cv9Ue05T5CvspPqvq22BlPVNYVCQcCfKhm3bRvXT5Vqve2iBXAbTvLi9HkRvHBNL86cH+2Si5PpVI2ueG/ydTShmxfUgElgrNap51aTA6rMmOdFQzQyobGAB31BA+mKie0TNZw1HO5SAXk8Hvz64QNoti0s7vFhacIjezoTuZTVqyCU19jlcqFQKIgaQC0DohpmuveGunYAZw+jdwTLrVj+BE3Dv966Fz97LA0AeM+li/C602Mw221YU1J+fofK9qvu4ATZPT09kjBIp9Oy3plAYqKNnRC4LpjAYEKPAJ5rkRJ7flY0GpVnLFl0Jjq55riHMWYiEGeSiPuYaoDpcrkwUWrgh1MdO973vGWz2i9OatrjX3+/BWv//vf47r17nu1DmRsn6Wg3G8Dm3zj/Wfvyp31toHchygjCrZnYufnRZ+Do5sYzOYr1Fn630emdPVuw/PNHRmDZwHmLEliUPDIGhQ9EPlSm11NRPp61O2CcgUutVoNp2TiQr/+vA9qqY++RjM/8fgu2pEroDXvxg784D33+jrM2Azs++MkqkcFqNBrifBoIBFAsFiVQZoDLBAhr2fjZ4nqq+fBk0WG3ntvfkZySkSKg4FpgEEoJM5lFgiXODWuzbd3AlZ+7A5/87WaU6h2GffWgw8ZsS1e72GlVNm4YBmBb6Jlq8zXR6vSU5t9ktBuNBs5fEMZDH70Cn3rl6Ud1TZ7JIXV5mo7fTcnGn7c00sV48RwZIANO6QBZGRo9MXgjqKbLrc/nQzgcRiQSEeBL2WU2m5WaSLVuNBKJCJtNkM15ZwkCTbHIeN0xZfWwNm4j4TEFALN1kcrAErTqui5gjkE2a3jVemyWI1DGyvNQQfoDO9NomR0DK46FPUH43Dqapo3RYqcXL4NYrjXVH0DXddnz9pVMCZLVJJK6blVzvqVTst2t446E9FjviapsPFNu4JJ/vxvv+8lGtG2tC2iroIwgVDWM4n3La0rQpCZACAa43rinUEHB9afuBywt4HrjZzWbTWzbtg3ffXhCQPabn7MA//7qM9BuOT2JK5WKlKJQqcLe7n19fQKaCLJ5rQhGeYxc86rTNEEM0GHYp5uysb7eMAzxI9B1XUoTODRNw8/edSE+8bI1ePHaXjnH5f1h/OvLV+ON588XAK1eCxW0MumpGqK5XC4xGJ1oGLC0DtvNBISqoFB7gjORxeNbHHf2ih2TDtAj4OO9+MupdnBXLosKqKOagckBlh/R0FA17uL88DpQacNnlJoI0TStq7UVj5XPG5/PJ+fTtmx87IYd+NljaWgAPvbCZXj1mpDUVzOxzHuW15q1+ABEicFkWi6XQyqVEhl+KBSC3++XZ108Hpde2PQcIJvNc6bcnGta9SYYGBiQsgSuFz6D+XqeI/c/tT+9OtTvpO/E1+/chUbbwhnzY7h42exKA09qoB31u2FaNrbMOY/PjSMYqUIdH/jUfwC1HOxgL7Dwoqd/g6ZhIrAUAJDZNQe0T7Xx28fHUG9ZWNobxJnzYzN+n213emfPFqD/cUsa7/juQ7hz+4RkbOttG6lyWzK7lBlON0RjwNlut5Eq1PHcLzyAl3z1QdSbM+/veDIPNdg9mvHRa9bghWsH8P23nouBYIcBUANAMggEGmq9NQEH2QomSijHo6MuTV9Up1MAeLgQgAUNyyI2BrztrkRLPB4XBo9MNYMign4VZPM1DCCDwSB++tAIdk1U8OsNo/C4Oo/8Ff1h6BqQq7ZQNo2u+jnWhJP97HM7ayrddEvAzGNRDXeajcYxBzXHc6jlB5Zl4a8uG8blS0I4f2FE5oIMDaWbZOiY/OD/2+02otEoenp6kEgk4PV6kcvlBLiosnD2Mi4UCmIiRDk0XYfj8bh8TrvdlvfU63VMTEwIKCLIyVebeGDCub4X97a6Ej08FzKPvHZut1uYT4J1fj/XqFrPWSqV5JpTikojt9FMEW/7weN40VceRKbWvQbcLgMfvGIJPnH1IiSCri7n8elAG+gAaBqiHShZsNC5B1Uww795Xs1mU+pj9+fqqDTax3RNMsHJY/7NhhHUWhbSpSb8Hpew+mpyhME9JfO8t3ivMRnCcyBDGY1GEQgExICvXC5LW7hQKIR4PI5oNArTdJzoWUrA9oNc4wSGO3ftwpfuTuE3e5z5e++li/DhFyxHqVTE5OSkOJvTVI1tlKisYAJGVXFw7+M6Z4snGkwy6Qh03K95fqrrOj+TnRzIvgMQefH04XMbeNUZA/C4dKn35+s4v2RL1cQP1xe/UzWUA4CBiA8+3YQNDZNNl8jZ1TVLoM19UzW/YxKFhmg7JutyjlQjjeZruG93BgBw+ZRsnMCa38N9h6CP/3a73fI8UROkTJaxKwGvEedZTRr6fD5hyzkn7XYbxWodf/XLrbh5Ww6GruFfXrYSVy8Pde0bAKR0iWuD3gAEtgTaBNmjo6PSGi4Wi4lKg50NuDcxocT7hfssATFVCbznDcNAPB6H3+/vYrfZr53XlPEUpe5MmlKZxblkwouJC03TkK008b379gIA3nfFsq6Ez0zGSQ20Vw04GfmTzeF0bpwY4wf378Vzm3cBALQ1LwP0w8sd28nVAAB7znn8lBuUjV93zvxZbaSP7Mth92QFfreBF50+OKvv/NED+/CHTeO4Y+sELMvCfXsKeMUPduMfbh2VbKsw2lPtbtjiiw/hZrOJsNuCoWlomTZ2T1blYXiqDga7QIdtns1omZ3AO+R14SuvPxPzwh2DKDX4YyBj2zZyuZy4LDNQ48OYrZwo3QMg0jU6pDLoI6CxDTceyDjB2KWDlryfpj+qOy6DN2bZ1eCPQJtBFF8H3YX/vH0nAOBdly6B19XZ43xuA4un1Bf7i6YEtyqrSNZHbfHFueD8kIUiq91hu0/8NaiWH9iWicuXRvHhywYBq+M+y/o9BrJ0f+Y1puMupfuUek831EmlUtJTXZVt0xGatcpAJ4ilsRETNfl8HtlsVmS6lJJbloV7xzU0LQ2DfgtLQqYEspT3c20QYPN7WItNKTrlxtOdxgkEgY5clsZ7tVoN371vP2otC71hLwaj3d1gDMPAa88ZwpUrexD1e4S1ZXJIlcSqtdphvQWfYcO0gYlGB0Qx+TT9/iSbHA+40Rf2wAawfaIiyZRjuWZ4LCw3eNn6wS42mjWwVJewrl2tPWbwz+BerfUPBp1674mJCUxMTKBUKiEQCCASiSAajUppAstH6O7s8XgQDoelnh5wwOvuvfvwTzfvw60jzv3515fNx9svHEa1WpX2SgDksxOJhOwlLHVgKQLXHIE2ARClxKyn5vXka3meZLIDgYBcGzV5wvXItcdkDsdIrgrLsrvUDWrNu2Xb2JutYk+mKp+nMtdqAk1NBPB8AwE/+qe6LRyodACY6pZPNphgnoy+qrK4aGEIf3VxP15/TsdUlaUZv35sFLYNnDkvhIGwRxJ2BJdqIlUF2bqui5xaVXMwsVEsFsWkUVUesE2WKqWndwQAx+iu0sC7f7oVD+wrw+fS8MVXrcZVKxMCnJlooVEi55R131znVKrQdXz37t2o1+sIhULo6+uTPYaMtmVZ0vpS9V3gPUSQTe8K1SPE7/cjFouJfwGTh/TV4P7L56OqKmCpiuqJUi6XRRHCNfWtu3ej2jSxdiiCK1b1zXrPOOZAe9GiRV0Lm3/e8573AHBO5OMf/ziGhobg9/tx2WWX4cknjwy0rJgy2Ng1WUG9dXxaOMyNU3PUWyZ+ct9OvMB40PnBYWTjHOGFjiQyVtoxK3v/uXFij0KthZFcFYau4RVnzpvVe9k7+0WnDc7KKyJTbuC2LU7903XnzIdpmhiOeWED2JdrwrQ7btq6riNh1AHYqMGNmu2Sh1qz2USz0TjudYkn0lBl47PNLlcabbzua/fhK7fvAACpnSbIpks0f0ezGAIqgmRm6ynfY90Yg81IJIJwOIxcLidyWzU7r2kaniwHUDU19HhtLPN3twuLRCJdLAoDEsqUKTWmMytrPtVA6voNoziQr6E37MVrzltw0FysmpKP7841Jfjl8THJYxgGegwnOJloewQoMpBj4E0g8dOHRnDxp2/DP95w4ptGquuIckuy0wQR6nXTdR25XE6khUx2kf0g400wXqvV5DUExrxOBO6RSAS23Wl7QzbQtm1ks9mu2kHWR5MBb7fbTmDdauPW/c7rLuptwufzSpCqskIAJHDnH4JBVQUBdAzJ+B6uRQJMHn+z2US2XMcPH3IA53uvWH7QPaky1QTpBCXsA8/roJYv2LaFfq9zjcZqRheIYcJA/S4eo2VZWDllirUlVTmm+6G6ZvZMlrFhpAhdA156xjwB+px7HpMq8VVBHZMh3GN4H3GtjY6OSpIuEomgt7cXAwMDct4q80uQyM8kkCyVStizfwT/7/f7cPeBFnQN+NClA3jl6UlR5qj9q5PJJKLRqJQksRyCLvecA+4xtm1LrbBafx4IBEQVpErGCVbVFmNce0w+8DpqmoZotNsLp21aeN3X7sdVn/8TNh/IybVQ1UffuncEL/ryA/jqXfsOUiWpiiVVrcFEQKPRQDgcxoDPWfujVV3OWW31BKArkcbEJ1VFuq5jedKPFywLYWkyIOuUia3nLk/itecM4cWrYwfJxlXmGYDsKQT13Kd4f/O5xfZc6nOGiVt+hppoU/09JittvPcXO7E5XUPYa+AbbzgDV542LPcTr50KsJlsU5MlPH+3241UKoXx8XFYloVIJIKFCxcKgKX6gdef14jt6Bjb8Hvof8HrxSQ3kzBMfNIzgusRQJeHhNqxg+fE71brwWn2BwDnL+7B2QvjR8RmA8cBaD/44IMYGxuTPzfffDMA4LrrrgMAfOYzn8FnP/tZfOlLX8KDDz6IgYEBXHnllTKBsxn9ER9iAUc+viNdPqbnMTdO7XHD42NYXX8UMa0CO9QPLHjOjN7Xu/QsAMBy7MNovnY8D3FuPIMj6nfj7g9dgV/85YXoi/gO/4apUW22ccPjTl33bHtnX79hFG3LxunDUawccKRj82I++N0aWpaN0VJbDJN0XYdHByIa5eOBLslurVYTueTW8WPL4JyI40hl47Wmib/4zoN4cE8O/3n7TqTy1S6QTcaS2XM+eFU3dzIsnHcGADR7Yf10PB5HrVYTh1WgUyfogFQDd084GfPnJJsw2y1xpaYxDbPvfLirrbsIvCmBYzBEVkszXPjyVDLhnZcs6TIoa7VaqFarWNUfQtjrgokOsGaQpwZqvVPS8ZLpRt3q1FOq9eas59RgYSRXO+GdxwlqAOCunVl87Z792JepdAFtlfGgdJoskAqY2aeVLBdZSAbNwWAQAwMDQjBQPksmkIylyqQQeFHmyb2ASYFsNouJiQnYto1bRmxk6zZCLhtn9XSSApTD0kyKcm8GxASDdEknQKLsnPPE2mE1WFfZ2B8+OIpK08SqgTCuXN1/0FxrmoamaeP+vUX8ZnNBQIlt2wLIVEab6862O33cD1Q7cmBeE/7he5kwME0Ty5JOic3W9LFLPHLPBZy955ePOEnWCxbHMRALCFCibJzHyXpaJsXI6vI10/trG4YhiRfLsjAwMCClBAQZvDaFQkHYRipdCCIzmQy27NyDj/5hFA+NNeHWgb+5IIKrVjjO9arhptfrRSKRkPrvSqXS1TKQr+Nexp+zbpY1u2RP1UQcGU/V5IxJGs7rdGYYgNT3quNXG0axL1tFttJEMuDsaWryotlsYlmvA762pStdLC6TBUxmcG3zvqBCzOv1YijgJBVGax1mmNdQTaJwTfLasyyATDJLeejAzveu6A3gby5fgOctix6kbFDd2FWzPH4Wf87zpXkha5pVJ23uKQTyLIGhbNw0TaQqFt7/6z3Yk2sgGXTjm69fh+esGJDWYaqChp8NoOuaqUmwUqmEdDotCeZEIoGlS5fC5XKhUqkgn893yfaZOAwGg2J4xmQmWX62eGPplPosVtcWlRRqz2yuIT7rp5dZcQ1WKhW4XK6D3O0vXp7Ez971HLxgFu1e1XHMgTYzbvxzww03YOnSpbj00kth2zY+//nP46Mf/She8YpXYN26dfjOd76DarWKH/7wh7P+Lk3TxM1yTj4+N2Y6bNvGt+7ejWv0+wDMXDYOAEb/GgDAoJbBfH/jMK+eGyfTcBk61s+iNhsAbtqYQrnRxoJEAOctmnm7B9u28dOHnJYZ103VdRuGAa/HIwYqe/ItCcwAZ79L6E6Qk7U6kisGrQujzuuOZWB5Ig4103+our2nGvWWibd/9yHctyuLkNeF7/z5uQi5rIOY7FwuJ/I0skYMSOk8q2kaSqWSmJ8x4CCjmUwmYZom0uk08vl8l1M4r9ueuhfjdR1e3caZ0ZoEBAzICG4IOljnS0moKmMkIAQgDMaNG9PYn60hGfLg9ecvlHkgw2aaJt5ywXw8/vGr8H+ev1wCT4J6tdbRgzYihgN4JpqdQHI62G40GgJwNo8VT+gSBpUp/u69e/Ff94zipm2Frt7VBG9Ax4W+1WohHA4LC6jrutSntttOuy8ygYFAQCS+kUhEgnRez0qlgomJCXFWplycIIbHQcBMieX4+DgmJydhmiZuHnXhBxudWtZL+xoI+jwCpqvValcdJNkaBqkM6MmKsQyC64lAAuiw0up90Wg0UG608f0HHVOn916xDPpTtDZsmjbe+7Mt+PxdYyg1On4GKthTpeP83uSUIdpIqQOoue/xGqnJACYCLlkSwSdeugavPWdeV23p0YzpsvFfPeYkWV92xpDMI4+LyQoyZjRtItPMntZUPXD9kH0jcBgYGBBjPHU9ut1uWQOGYSCZTErCrVwuY/v27di4fQ8+cVcBmybb8Ls0fPSiKK5Y2Su13+zrzJIW1pRzPfPnTIZUKhWZezKCqgEkk1M8B+4pPD/19zwXvpfgV+2xTXUFh2nZkjz88+csQMDTSQ62220xYuMetHuyCtPWuoA20FF1sDSG64hJVrfbjXlBZ72M1XToeseVHEAXG6rWgjMxwaFpGvbkmvjZhhQ2T9RlvwYgewnXCvcX1f8C6Eji1eQU55BJP4JVtplUy1BYasQ55nOIz4BS08Lf/G4UY8Um5se8+O9Xr8D6RX0CbrnvqG0ieW6cP1WWPTExIQown8+Hvr4+JJNJNJtNFItFUSvQ8DEcDst6aDYdQz6Cat4fZN553kxc8HnK5zKfv/wOAJLYUGvwyYKrbDZVIYdad+r5Hsk4rjXazWYT3//+9/HWt74VmqZh9+7dSKVSuOqqq+Q1Xq8Xl156Ke65556n/BzKIdQ/HHRO3TxniDY3Zjge3pvDttEsXmA85PxghrJxAIA/BkSmmMv05mN+bHPjmR/ZShNt88iAKWXjrzxr+CkDzEONJ0eL2JIqwePS8dL1jlSdATD7b+7KdoAVpVqJqTrtrB3oqlOs1WpYEHEe4FtT5VOa0VYB5Uzrs+stE+/83sO4a8ckAh4D33rLOVjR4+mqC6xWqyiXy12GM5Rwt9ttVCoddoQgm8wmg51QKCT9QgmIyuWyBHlqffa9WScYPDPWgFfvMITsnUy3WR6f6iquGt2obDulfYZh4Gt37gIAvP25S+D3GDJ3DDYAwNBsYbNUh3uCftX4q3fKeTzd8nQFcjwemtcMh11wGxpKjTZGcieu6ofrqNiwcNcOx5ToiqXhruCXQICBPN12acjDcyajx6DbNE0kEgkJ/ADIa1utlgSGBJUejwfRaFRAGFkfqiFKpZIwnJQ/apqO34358eMnHTXfixcClw3aAkTVY583r1vWzCCVcknAuYY0JSJgVZl9GvxxfXBt/s8jKRTrbSztDeLqdU/tUZEI+TAYceZiX6HTU17t3626UPNniamyhX3FTosfmi6ptbcEdPyzqi+A1543X/oqH0ug7XK58Nj+PPZkqvC7dVy9brBrflXVCQE055DHQoWC2o2AIIpAhPsJk2kqCON6ME0TsVhM1BPtdhupVAqPbd+HT9xTwe6ChZjPwCef34ez5jv13bFYTFQ5bAWl9mrvrDFN6mnJuqv7BYGtmpwi6COQdrvdYs5FBlKV/xNAkblk4iAYDB60v//2iTHsmqgg6nfjujMd5QSTRVzHtm2jN+hCxOdC27KxO+P8nGuK4FA1RCNLq4Ll4bALGmzUTB0V2yXJAqpB1DXH41Tngp/9u20l/NvtB3Dz5glHcWAD//ibjbhvVwaNaa3eVKk00HEGV5M4ZKgJ/Jk0IzAGOu7avFb8P9cu4OCzarWKew60ka+bWBD34avXrcCiXme9FQoF2e+4j/HZyPnk36ZpIp/PS1LZtjuGfJwH7pMsfWEShvtbJpNBJpMRA0nOJdedev+oNekEyypAZkKESU0AouyhAgzoAG2uH113OjDwPd+7dw8+d/M25KvNo9g1jjPQvv7665HP5/GWt7wFAJBKpQAA/f3d0qL+/n753aHGv/zLvyAajcqf+fPny+8uXJrEtWcM4cwFsWN+/HPj1BzfumcPLtafQESrAqEBYP4Fs/uAKVYbc4Zop8T4/361ERd9+jbcsml8Vu/bn63i3l0ZaBrwyrNnW9ftsNlXrelHNOBkiQmmliedbOvuXFMe6JQ69bo60nGgI2VsNBoY8NswNCBXa2PsFC5rmB4wHG402xbe84NHcMe2CfjdBr755nOwutcrzC7lYwyaKD9jMMmMOYPher2OXC4njDIz6X6/XxhB9qqldM7n8yEYDMqDPdtySb/jc2OVLhMqBqKqcRLljAy8yLqowIPBHdfLt//8PLz9uYvxhgsWyryp/USBbgdlFRQS7DDg0DRNXO8nWt1gn4EUA6xWs47lvY5/yqYTWGnGdXTTpgmYNrAy6cNwpJO0YFKEwWW9XhdgwZICgmKyMwzYWbtPFkplrcplBxgTkHDdqAHr5OSkrDFVjszrEQyFcP1oADfscK7nG9Z4cdU8E16vp0vpwrY5fr+/y8SPCTwa2PFnNDCisRBbDNKMSAVUgHPtd2edxM17r1h2UK92dei6LqB3T77T4ovMeqekohOWOiqeOjTYKDZtVMyOURpwsIO/CrQJctW1fjRDVdK4XC4Mx7z4yAuW4a3PmY9IwNvV9o/JLwJhOnmTteN1pyyXyTjuaQRzZCJVNQHPq1QqiQSd14Y1+0/sGcenH24jVbXRF3Lj8y9diFX9QUQiEcTjcdnXyFyrNc5cDwSj7Puugii1xpZgWmVWVVUE91fDMOQeYVKQrCX3DwJHltCow7JsfOk2h81+0wXzEfQYMjeUs1PyblmWrLVt6YqsJQJtdU4JXnkOvNfCQT963M4ewTptHjPBMe9vVSbOZCfXC53HuRfevyuDb969Fx/42Sa0LbtLwq5KzrmOyBTz3lXbvam+D/l8vus5QHaWzx7KpulMzp7ud+x39vXr1vciEXCSxaVSCfl8Xp47ZID5LHS73SIrbzQamJiYwOTkpNT8kz3n3KglHWpig3soP6dUKsnnsy0m1xSvofqMppyfzy6v1yvPaSYgOOhgzxp51QSNTu98jgNOWeDnb9mOL9y6HbdsTs9us5g2jivQ/sY3voGrr74aQ0NDXT+fTr+rcrVDjQ9/+MMoFAryZ//+/fK7K9f04/OvORMvWT/0lO+fG3NDHX9z1Ur8n4GNzn/WXgvMkBXjaPc6QPvGW25BrXnqMof/G0a+2sTNT45jvNjAQHTmtdmA0zsbAC5c2oPheOAwr+4ea+dFsXYoclA7MLfbjeVT9WW7sp1erGQaCXYKtk96toqkrN3Ay0/vxdsvHIahd1qXnGpjtrLx27emceuWNLwuHf/9xrOwMmFIgMm5JZgIBAJdD2cGFAx0isWigGcyTgzSGPxMTEzgwIEDmJiYkP6zar9OTdPwQN65xitCTfQHdJFmut1uhMPhLhMtgj4VjAAdNpvBFQMQvn4o5sdHr1mDoNfVxfjQ9Iif89k/bMVl//pH3LqzJIEog1BVxsuexummWySMXGNk2QhCV/Y7Qe6JWqfNoBYAfvWYY+J1+ZKQgCCCAQZjmqZJcEogR+klgTKBlSq3JHNMqSZVCqqpkWmaXcwlmSZ+L6XarAOHbuC/N5q4dXcNOoB3nRHAxX0OIFBZXtbKxuNxAUWWZckaZzKA95PKqJPdoeyUIAjoABPACVq/8Joz8ev3XoSXnP70Mdh0oE1FABk6fibvP/EM0Gwkvc46G290WhSpst3pYJsB/paxAn7+6BieHCsd9X6olhrouo6QR8drzxnC+65Y1mUWpyYKVCMplY1jPTVbchGMUArLe1jtM0wAVi6X5Q+TswTaY2Nj2DhaxKcfaiHXAIajbvznK5dhQcwrSTzOL5OHBNpca6yjpQqHEnXW+9LETDUsU68D91T+jEkE1t9yENSqsmneM/QxUMcfNo1j63gJIa8LrzlrQOaUIBtA13nwObp9onqQlFoFe7xnVF+DVquFYDCIfq+TOBmtagLOmIDicfO+4PVWDdFs28by3imvgJST6GLv7CuWx+Fzd9azKhtnwlRlg3nv8r7g/UwpdT6fl/PguqNxJtBJLFJyXq1WMVrVsDvXgkvXcPnSsKgUxsbG5DnH9cAWc5qmIZvNytopFArieG+aprDK3PdisZgkEllexR7a3Fd5j9BBPJFIIB6PS1s3tT4dgLDZnDPWVXP++f0cTHhxTwS62WwmeFieAQA/vH8fMpUm5if8eNkZR4cvj64B6dOMvXv34pZbbsEvfvEL+dnAgHNzpFIpDA52JEbpdPogllsdh8puzY25caRjccwFVO52/jMb2fjUMAbWAgD667uwcbSAc2dRmzs3Tqzx68dG0TQtrB6MYN286OHfMDUsq9M7+7qz5x/m1QePV58zH68+Z/5Bcka3242lST+evzSE5b1+2IAEoZqmIaS34UUbDbiQt/3wWx1mqNls4oOXLpfgiAH9qTRUgDRToH3V2gH8/YtXY37MgxVRh5FmEMkHNtDJeDPYYmBFU7RSqSQBLZkCBmmmaaJUKkmNWTab7QIrwWBQArK25pZ+x+fFqhKQtNttMaLK5/MAIEET2WwGuKozeL1eh9/vl2Np2d3XnKUFnDOyZAwyc5UG9mSq2JVt4uyeTm0yXy+mVFPS8cmWB6Zlw+PuBK8qi9poNCS4PFEZbQadI4UmHhspwtCASxcHYVkdF3eCbJoKqWZVKvMVj8dFTk7pK5knrjEVTDFIJ5ju6ekREM3axEgkIjJeFfwUK3V84eEqNow34dKBD14Qw3J/Fc2mKVJcJmAASB3u5OSk/I7u6AQNBGuUMufzeTHzItDj+TMppZZCAMDpw7HDzrmu61gxlYDZnWvKWqHMlJ+lysHJfPZ5WphoGBitapgfRRcgUtkuXluuxx88MIafP5bGX1w4H+vnx4/JmiHrrP6fElcy0WQo1fp3AlIG+2QqaWam1p+rII7vJZvK7yGgJaNbKBTwRKqGf72/jFrbxsq+AD73sqUIupx1xX2I30HJOocKeLnmIpEI0uk0qtWqlMawrzfvdwACAtUkAcEh1xcTPny9mhRSa3DVPVkdt21xFGdvPH8+Ij6XfAYAAdJqEmvplDnotnRZ9joqNpjw4rUj+0sTrXrdqace8Jl4suy0+NITuoAy+goAEMWKmjhTfVUWRN3Qp5RmeyYr+O1Gp67/BSvjctzc1zl/ai0/Jc+6rgubTfMvrhn6PXA9UMnh9/sRCoUkGcGEDZUU94w6wPWCBUH4dedajo6Oolgsyl7B8+KcUJ1AJQafp0wS09OEvayZSGCCIhAIiMKGa1n1xPD5fJJspikp7+l2uy37Kq8Vv49JAq5lNT7gz/k+tbSGf9jqEHBKzf77T07p1bsvWwa3cXRx1HGLwr71rW+hr68P11xzjfxs8eLFGBgYECdywKkTuOOOO3DhhRce8XfRdTxdrB/+xXNjbuy8DWgUgfAQMHzerN+u9TtAe4W2H4/tyx3ro5sbz+BgjfV0Zvlw477dGYzkagh7XUfsRAkcrO5xuVyIBLz464v7cO3qKLxTQXmnRg9iiJabMkQDHADKhyc/81Ss01aD26dTQZmWjXKjLUzuK07rwbqkS5gMmlOpJiwEKgQVrVYL4+PjyGQykuFnrRgf9mrbEDKWqkEae+ECnQz6owU/mpaGPm8bq+K6HANlmpQK8zyB7sCBwRWDRAZPhmHAsm28+msP4G3feRAH8jUJqhjMqEw2P48s447JmgSbap0sjyFqtODWLJjQkW13DNHI3FBZUa/XsaovgPXDUTErPdEG19Fvn3QkgWcPBxF2d9yPpzvSMvgmWOL6sCwLuVwOo6OjAkZoZhePx7skuIZhIBaLCYjm/wMBx606lUqhWCwKIGKbGrKcY5N5fPKeAjaMN+E1gL89P4wzezu9pSnBJmhjzaKu6ygWizBNU1yPVekuAITDYWHJeLzhcFiSTUwyEOC53W48OlKaVcylaR3z2t3ZOqypwFll6tTyB7UGlEqekQq6ZP38Pd8HQJJhlmUJ2NqSOnqDSHXv+Y9btuF/Hj6AUsOUZNf0mvHpdfuq7DUYDApI4V5ByTUTNWxxVKlUkMvl5I/a2omMbi6Xw337yvjUfQ7IPnt+BF951UoM98a65MjT2zrRr4Hsn2EYArLIuJORjsVi0nuZ+yUTUtwvuLbU2nTut9yneDxUFKmyYrU/8/Tx6Veeju++9Ty8/txBeT2Pmfcr/29ZFtYPBfGOixbgTRcsEHDFYyRoU83aVHM0lgUNT3lijVY7vgRqohbo9N5WPVM437Ztw+c2MBxx5v2Lt21HpWFiMOLB+nkhAdp8L0E7k1msn7dtW0Cr2+2W+5lO4gTjat24+oziM0B1Jrds4O4R5zlz+SKni0kmkxFjxmg0Kuw/u2kw0UJlBec+EAhgYGAAsVhMDB1VI1ey39xTM5mMHDOl7TxernsmL9VnDO/1cDgsRo8ul0vMKTnvKjFLEgLoNkHjPKltBrmX/vSh/UiXGhiM+vDKs2YXGx5qHBdG27IsfOtb38Kb3/zmrjo6TdPwgQ98AJ/85CexfPlyLF++HJ/85CcRCATwute97oi/729++hh++egBfOiFq/CXly09FqcwN07B8fOHR3DL5nH8s/0/SABHJBsHAPQsh6kZiKCGvbu3ApfMrbmTcWxJFfHEgQJcuoZrZykNIpv94vWDYjQ1k5Eu1nHbljSuOX0QYZ/7oN+r2WxmxmlmQtlWXKthDBFkrQBMMysPIvYATRXqOFBq4aJlvbM6p5NhqDWSTzXapoW//ekG7EiX8Z+vWYew1+hil0Mhp35YrR9j/arq3k2TFrYiYfDr8XjQ09ODWCwmAQQf5KyTYwDBwICAQjNc+FPK2XPOj1Xh9/uEjWbdLNkiBsUMrlhTqwILShw5btuWxbbxMsYKdYQ8hkjeyYaoAazL5epyCd86Xobb3QegY3Sj1m6aZhtJdxNjTR8mmh4MBppdtcCc02azibVL/PjpO847JDP1bA+ViWubNvxuHZctDgk7SmYP6ATRDMjYjkkNykulkrB/DOQIPNhqhvJeAF1ARdd1kWWyHpLsNpkcABjNlvCpB2rYV7IRcAH/50wPTu9zi5N1NBqVgJLrw+v1IhwOo1gsCnMUjUZlvU03QVN/pkooG42GHEsoFHKuqeHC+3/0KLLVJn74tvNxzgxVXYuSQXhdOuptC6lSG5FwWwAD551rjmDbsqypsoUo9hXNLjWGyq5Nr1W2LAvLZW1XJFh/ugTdUw1VSVNr2/jK7TtRb1s4fTiOgUS34ZmqUuK+AHQSbWT0UqmUtHQDOnsagSoTaioDyzVjWZaYMZbLZdxzoIX/fLQKywYuW96Df3jhQoQU93mai1Gm22q1ZM2RydN1HdlstsurIp1Ow+VyScKG5wmgSz5O5QOvGUsSmHii4/30uVTZbKp5VHm5OjRNw4VL4qhUKqjVagKMWOsOQGqjm80mhqMevPfShV2GWSzBIbjlnFM1xD2x1WohEomIwehkQ4cJA6bZbQin1nnzenH/V2uQlyQ82Fdo4RePOmUqV61MQFcSnir7T6UC72fWwFPZq6oauObZnk9NqlCCrzL/TKY1m01sKejI1U1EfTrOHHAAdalUkv3A5XKhWCyiWq1KTKLKxZlEoWpGrVvn93NuaHCmqqXcbjcikYiodTin9MNg0m96m0PuFZTKs9+1aoCm3uPTndl5L/LeZDcP7t3NtoX/vH0nAOBdly6Fx3X0fPRxAdq33HIL9u3bh7e+9a0H/e7v/u7vUKvV8O53vxu5XA7nn38+/vCHP3Q1B5/tWN7vBE5zLb7mxlMN27bxjbt2Y+fYJELBPzg/XHPtkX2Yy4N6dCmC+W2ojzwB4EXH6jDnxjM4fjbFZj9vdR96QjMvTSk32vjdE45546tmKRv/+SMH8OmbtuDXj43ih28/tAmf2+2GrRnYlamgrbmwONwxmHG73Ui66oAJZG1/l0FPo9FAuljDG3++AxqABz70XGFTT4WhnuuhZOOOPK2Bj/7qSfxyQwqGBjy6N4tzhoPy4NU0TcAEB8GoGpS2221xeiZAZ3umUCiEnp4e6LqO8fFxYQBYt8ZjVOtgKQHdWvYi19QQMCyc02vLdVUZLLX/J8+VQQuDOQZ0DMosy4Jl2/jqnXsAAH9+4SK47E6GfzrIBiAs27K+IHQNyFSaKLc1kSYy4He73ZKo6HU1HKDd9sCy6l0BM4En5ZUnqkeAuobef/liXLsygFq1jFa9JkGcWo+rBraUVLtcTr/pfD4vLDHNedrtNsLhsMhLWZ8NdOpiy+UyQqFQl4s43XDV+nxN0zCSreAf7ixirGIj6tXwofNDWNrjleOr1+uIx+NdkmLbtuW4UqmU1GuqpmsEHzxunp9qimdZTqunarUqknO/348f3L8PqWIdg1EfThueecmNx+XCp69dhbDRRq+7A4rVPs0E2Tw+27bFBHKsYsPWXV3ghOBTLffg75b0eKEBmKw0MVluIhCwDrl3HG6obPbvNo2j3rawKOHHGQviAoaYcOK9qQJKXisCw1bL6Z9erVYlwcZzZcKBwIBGaq1WSxyRCXhqtRpu2lnD9zc7oOFl6wfxfy+fB9iWmCiSKY5EIrAsS/ararUqKhoy4zTq6+npESabx06wwoQU5fKqAoSvp/qDDCUBLNcUQZpqXEdZ9PR9as9kBYmQBxGfW5I+BH6cSxWkqmZiqqqLP+O8MhGgSs7JhlMZlgi4ENBNVC0DE00X4oDMqeo8rpYwqCZ/XIdLE17cvrsix3L1mqTsr3xGUBnAe48Akfc0zQrJZqtrk6ys6opOllj15uC+rGka7tzvrJlLFwVRr1bQqHVk13TDJwBmgpolVNxPeB04t+VyuYso4LFls1m0223E4075BhU7TMoAnSQIATbLaPhM4fVhVw++JxKJyNoiw87BZxHQbYKmrjuuB96Dv3hkBKOFOnrDXvzZubMvCzzUOC5A+6qrrjqo9pBD0zR8/OMfx8c//vFj9n2rB5wWX1tSc0B7bhx6PLgnh01jRbzIvREeswJE5gHD5x7x53mG1gH5beit7sREqYHe8JyHwMk0WqaF6zc4piSzrbG+8fFR1FomlvQGcdYsuh3Yto2fPuwYOb70acwb3W43HjxQxcduGsWyHh8++4JeCUR1XRdTqqwVgG13GIJGowG/1kYy6MZkpYWt4yUkY+EjYnBOxKFm5dXacwacjUYDn7plD37x+AR0DfjHFy3BOVPav+kMBD+DgQ7rvCjDo+kZmQ6aygQCATGNSqVS0jNZ0zTpw6kGITRII4C/M+08cs+O1RAO+IQJ8ng8AnBVkzag41Gi1uAS1FI+alkWbt+exZZU2TELOntAAioGNIcahmHA77axsCeA3ZNV7C2YmO/uGKLR9I1sCSW86aZbfs/jUutSORf1lolq00QieOIw2ypoqlarcGsWamanX7nKlvL1DFAZRPp8PpRKJWlhE4vFkEqlkM/n4Xa7EY1Ghf0l6GKb0lqtJuyQpmkSHDMIJCAzDAM7x4v46C0TmKxZ6PHr+P8ujmJ+zCt1slQqqIwQAKmXpDMwAGGzWfdIYEppOsEBnfMBiLkbADExalu2MD7vvGQJvK6ZA1dd1/G8lUlUq1VxsVaVO/QkUJNM7XYbAa0Fv2GhZuqYaBiIicrC7GITVdbUsiz4dWBBwo+92Rq2pcsYTkaOGmj/csoE80Xr+oSNI3BUE3VUF6i1u6xbzefzXZ4QTFTxPuO6yeVysr+wFzoAUS9dv72Bn211QMfrzx3C+y4eQnlKYRGNRpHNZgE4pQHBYFBAWiaTETVMIBBArVaTOn6alpXLZXkNE0u8NrxuTPYRhFOhwYQUgTavCcGXWktNmbMqNVbH3/38cWweK+Jz152OdT2afLYwkFOgi/sU93bTNDFZqmPnvhJiAQ9W9BxsgsbEiAq0+SxlgrLfW8HumoEDVSAR0CTBwHIusqOcB54nP8u2bTx3UQiG4cKPHs9gXsSLxQmfXG/Vq4D7uVqXzO/h+ZZKJXkOcP6ml/AEg0GRb1OlwNc2m03UTA0PjDpxxMXz3KhWK129z4vForh5R6NRxOPxrjp93ptUM7CmmvsYrzMA5HI5NBqNrlIYJrw5lwC67otCodBVAsLrymchE0LhcLiLsVcN0ABILTsVAeq9w4SVOrcA8JylPXj1OcNYMxiBzz37veJQ45RwymEv7Z0TFdRbp15d4tw4+vHte3YDAN7R85jzgzXXHplsfGq4B9cBAFbp+/DY/vxRHt3ceKaHS9fwzbeci3dcsgSXrpydxJp13dedPX9WIPbR/XnsmqjA59ZxzelP3W/W4/GInHdvrgELmsiQdV1HwmhAg4UmXKjYbnnQ0jhFdTk9UVnFIxnTzYgARwKWyWRQqVTwr7c6IFsD8IkXL8eVK3tEQhuNRhEMBhEMBiXoVNuH0LmVAWcul0Oz2UQgEBCHVFUil8/nMT4+LqApl8t1BZ6qnJcB0FjdhV0lHTpsXNRnCsBXAZKaqeffBD6qNJMMitqv97/u2gcAeN258xD26BIoPhXIVr+Hddq7cx0HYgaBamKjZ6qncbrp6TKd4n2gljB87759WPv3v8e//Hbz0V/8YzQYbLZMC5tTJWGUaR7EdcBAneyVypi4XC5hbiKRCIaHhxV5fTdLRka4VCphYmJCgDZBuwo0XS6XgFmfz4et42V86OZxTNYsDIYM/P1FYQyGjK51q4IDMosAhCUtFouyVijTVM9nersjJvQ4CoWCmBgxwfTLRw7gQL6GZMiL15y3YFbzr65rykyZaGDPXZ4LoCbELPR7nft/rKZ3zbcKzHmNVZZ5xdR+uGVKPj7boZYaZKtt3L3T6bn+svXOHs5gHoAcP49NBT9Mini9XmSzWVQqla7SDBWYEWxVq1Vh/CgDzmQyGEul8L0na/jZVud377t8CT72olVoNjqdKsrlMorFopQk8BipqqA8vFarSXkMgVUul0O9Xpf6W8rdqc6h5FsFtqxL5zmHw+EuYzOuO7WWna7zTDROH/fvyuCB3Vk0WiYGA5YwkFwragkG1y3XFgD8bMM43vWjJ/CjBw9IQpKsJ68L7wnOMSXyBIf9Xud3B8qdZA6BNpl87oXqHwJhy7IwGPHgVeui+ON7z8HnX7Gy67tVdpW9zdV6b7V+mHsV9xkqB9TacDL9fr9fnknc37iO7xlpoG0Bi2JuxFHuMvmkKouJHZatqQkGAupAIIBEIiFlTTxWgmomsiORCPr7+xGLxbrMXVVJf7Vaxfj4ONLpNHK5HIrFoqxlAF1JGyZ2AoGA3B9qclpdb0xc8bi5/6olWKryb2FPEJ951Xq85aLFM9sgZjCOm+v4Mzn6I17EAm7kqy3sSJdn5R48N079cSBfw++fHIcXTZxeucf54RG4jXeNfgdon+Y+gC3mqQNm/rcMTdNw+nBsRm656tg1UcZDe3PQNeAVZ822dzaZkEPXZ3O4XC4Mx/0IuDVUWzZSFQtRpdesSwdiWh05O4CsHUDMqoj0tFqtYkkihnv3dALLI2FwTsRxKNk467e+dPcofvrYBDQN+NTL1+FFq52aUQa3hwKbKmupaRqKxSImJyclOE0kEvIwJ2AnYzM+Pi7BBt1TWSfq9XpFZk7m0OVy4a4DzjVfF20i7tPl4c7AsF6vS80tz5f9vBlMMehgUEyJ3592ZLFprISA28AbznXUEmzD83SDcsJ1gyEcyDcQC3rh8ZgSgDCAZZDX624BsFGxXKi0NYTc3b24edyNRgO9oRBMy8bmE0hpxut935483v3jjThrXgifuCIpATwDaTJeDEDJ/no8HulvHgqF0Nvbi0ajISxeb2+vXNdUKiVrjMCv0WhIsMngOhgMimqC6+vBXZP42C2jqDRtLIq68Ndne9Af8Yj8u1wuS32vaZqIxWKiqiAQoTzZNE1h2JvNpsi1ec6UmhOc8zo2m03kcjnYto1YLObUdpsWvny708v4nZcsmTXjo+s6SvU2fvVYGvszJbzhtLAA4mAwKGwjg2C1TrvP3cQeeDBSBk4LdczFCBi5BhnAE6wsS/px81bHg+BIgDbXjK7r+M2GMVg2sH5eBEv6IqJ0UNe/ruvSegtAF4gKBoOo1+vSwYCybYJVVbWjynbVvsWp8TS+s8XEvWPOuXzwsvl423MXityZicXxccelm3OTy+XEMJMAiPW6nEO/3y/t6WiAxgRlNpsV8K2ytup9zzmnN4HKZpMpJuDjnsY981B71Ren+ma/7PR+JHy6HBPfy8SkKjnnugGAxXFnv9yaLss6IrtJCb3qPM71z3vf4/FgKGABeeBAFQKM6/U6IpGIKJa4rpicnS5FBzqS+d6wtyuhqjplM3nA+aFqiUoGVTXlcrlEgcXvtizHWJBJNTLjqueGZVm4fa+TMH3ufA8aDYcdZskIpdS8H1k2RLY7n8/LPklPEXoIMEkIdEq9PB4PwuEwksmk/JzeAmqSgM9KPue4HlXFAoG1aZpSCsF7b7ofiOqbwOvK3uHqGiSJcTzHKQG0NU3D6oEI7t2Vweax4hzQnhtd4/v37YVp2XjP0C7o2QoQnQ8Mn3N0H9rn9NJejFEsXt1zDI5ybpwMg72zL1nRi/7IzPtu15ombpjq1/uqc57exVLTNPi8XixOePHkeB178m2c09vpxQwACb2GnBlA1gpgCRwJIrO1S+KOodXW8bJkvk/2odY7qgFZo9FArtrGH7Y67v//fO06XLOmRxiFp2N0yerpuo5CoYBMJiNmZj09PVLjCkCYznq9Ltl9sjqlUgm1Wk3q6OhmztcBQMUy8GjWOY4Lk0243Z6ugIyg3LIs+U4avagyR7UekK1WAODnGxzPgD87ZxDxgHtGIJvnrmka3nLBfLz7ipUwTRMHDhyQ4F8FoJqmwa1ZiBotFEwPJtpehD1NYYnJ7hCcLul3zmNbqoyWaR11i5RjMQhkbtw4AQBYFPeIKoGycDr/EiCRpWOQSlAYj8cl2FflvYFAQCS/BBZkyePxOCKRiEgrWfNMlqdSqeBP29L4h1vHUG/bWJFw4f3rXeiLOUqKnp4e6WfLgJWlAQwe6WrN3sdklDwej4A1BsEscVANigBnL8lkMnKMsVgMAPCbx0exN1NFIujB6y+YHZvNYUPDp29xFGavWBlEtN0xRGMiQ5VT8753yhZC2F+2BCAdqgaaiQ0CjyuWxXDukj4sS/qOCGirSprrp3ogv3hKNs5ExnQjKxUMUSLOGvdUKtVVZzy9FIZ1q5x7vq/ZbCKdyeGrT5jYMGlB14C/u2QAV692JOI8lkAggEqlIgaPbKVE1ppGVqrUns8WJvtY+0pmkm3IKG9WXdZVJ3OeCyW+/B2vicp28z6jomj6eGRfDnftmIRL1/DGcwYEuDMRqYLV6abLVGpQ3bVzooKW2ZEgE9SqrbkICvl/mmTNm/KadJQUBxuiqQkVrlfuHdNBPBVIPG6CP9M0EQ6HZe6BTtswyupt25YEDZMdLEFRJdZkog3D6DK845ztLzSxPduGrgHn9WmwapYYboZCIVHWMAFGmb7b7cbo6Kgcv9frle9lgphrg3PANRwIBIQpJ8vOGmyv1yvPQZaPsLOH2+3GxMQEXK5On2xVTs99lXJ0Dj6HuMdxHbIMhs9UoONEfuPjY/jdxjG874rlWHmMu2U8+0++YzRWDToTsyVVepaPZG6cSKPeMvGjBxxJ5WuDDzs/XPMy4GjrVqPDgDcKWG1gcttRHuXceCbHD+7fi7/96WPYeKAwq/eZlo2fP3xkdd2/fzKFUqON4bgfFyw+fGLG7XZjaY/zcNydawqwYiAT1zotvlTZWqPRwIKIs61vS1fQap8apTRqsKvKlFutFhJBN370tvPw6VeehpeunRnIVh3HG40GJiYmBFjE43GEw2FhslXzIQavBEU0TGNwQia7VCqJ9E3Xddw34YZpa1gQNLEwZIspFcEBpYoESwRQbKWi1jQCnVZOBPL/9oo1+PBVS/Hm84cFPM10MLAjmGfQxeMDOoyRbdvoneqnnW64u45JZeVarRYSXhshr4GmaWHnRHlW1/t4jXa7jUqjjVu3OkD78sXBrr7oTEyRXVHlh0wkMCCloRQTLQzW6aDMAFOtu6ackoE6rzEB/k1PjOH/u3kU9baN0/vc+JuzvYgGHBCUTCZlvRFAM0hlnS2DYjoRt9ttCbzJZBOEUl5KtofXHIC0qQMgyg4AmCg14HXp+IuLFyPgOTKeJhHyoi/ssE97C506TNUQjfcdgZGmaeIPsL9kQ9cNYfwYfKvsFpNiADAUceOCxTHEA255zUwHAQMAtG0NiaAbXpeOa04fkOuoKjpU0y+CNQACHABI+QCZNAJ0qibIVE43CJsslPGFR1vYMGnBa2j415cux0vXDyIYDMox6LrTtWJyclKSP0ywsORElS1T9ZDNZlEoFASs87MoK9+/f78kaFhTTGDH+eZgrTX3LgBSlkNwSHb56cpbvnjrdgBOUqMvaEh9Lz+Pe9+hJOdktQfCHgQ9OlqmjT2ZWlcNPJMyfKawzp6sNZnPeWEXdNiomxryrY7aQ63x5hxwr+YzWS1x4LpWQTj3FnWtA+hKArB0iOw1k1JqfTbvA7LfPAe6kfOaNJtN3LrT2YvPGPDCY9UFrKpSf64dTdMQjUYRDoeRyWSk9VskEkE0GhVzPqoe6P/AOutyuSxmity3Go0GCoWCeJmoJV28Lox1crmc3D8sf7AsC+FwWDwQ+MxSB+X1qjKG+yHXB/dyZ1+38R+3bscNU2D7WI9TgtEGgCtX9yPic+OiZcln+1Dmxgk23n/Fcty5aS8GUrc7P1j7iqP/UE0D+lYD+++DmdqIdnL1rExh5sazM2zbxvfu3YstqRJOH47OSv1y145JpIp1xAJuPH9N36y+d3u6BE0DXnnWMHT98Ekel8s11Zomh13ZBoCABFyGYThBZxvI2k42lg+QZrOJHo8F31QLnT2ZCk4LBZ/6i06SwUBOfaCqbqVLk0796kxANgNkMmeTk5NiGBOJRBAKhcTJlMw1pfkEW2SIKO9kba2macjn8ygUChIEwHDjnrRzLBclG3C7O4wz2QGypvx81nir9dgM4MicMyButVpwu1x43bnzRE4+m6Gaf+kuN6C7ulhOFYRZloWkUccOhJBueQA4EkQVwIhcutHAyv4QHt5XwOaxIlZNmZY+W4Pzdeu2DOotCwtiXiwI2ahWO+Cg0WiIW7DqTqsOJj1UVQOBazgcFjl2KBRCKpWS17CtFuXd0WhUmBjbtvGTB/bgM3c40uTzhzx413ofYHVYTQLkWq3W5bZMRoZrJBQKCZijKRpfX61WJbinE7UqzQScPURlwiKRznV7xyVLce2Z844YZAPOelvRF0S61MTufAunDTbFEIsSYu5zQMctOuFqQIeNaltD2XLBpZhBEaAS0PAe53VnLTCB4kzLadTSkqDPg/98zWko1ppIRgIyj6rpmc/nQyaTkfOczmYzUUJgrp6jKmnl2uI1GcuV8fe3Z7Ej20LAo+NLr16HcxfGBCQSMKitIH0+H5LJpOx1asKH5o/q/qbWTKteBZSXkzkk0CYDqbaaIss7veaaTDmTB6o66VCdMZ4YyeOPWx1Ty7ecNyjJQ+5tqsfAoa6lKh9fmgzg8dEydkzWsDgRk32W6gl+P4EzE22NhrNXB/1eJD1tpJtupOouLHJrXUCbDuxqPT6TblzLVDiQZSWrns/nZe4IoDVN61IP8Ph4T6qdKvh5/JvqE13Xkc/nJXFI9/FKtYq79jtzd/E8N+p1R/YeiURE5l+pVIRZjkajsG0bqVRKfEjoccLnEBMo9BDg/arWzpP1Vk3SuAfyHp5uBMoSLr6Oa3C6RHx6okVVVTF5R68MwFGnMUlDJ/LfP5nC1vESQl4X/vzCY1ebzXHKMNoXLkvir65cgfMWz6yf49z43zF8bgNvvXgxvnVxAVqrAkQXAPPOmvH7S/UW7tw+cegseL8jH//mL36LGx479lmwuXHsx+MjBWxJleBx6Xjp+tnWWDuO4S9bPzTrpMrfvmAV7v7QFXjTcxbO6PUejwdLk072fle2IUEOAUFyynm8aHvRsnUBN+12G81GHe+6cAifuGYZ4n7XSW+IxqAF6JaNl6s1PDJSgmuqfnEmIBtwgASdgvP5PCYnJyWAiMViSCQSXTW1ZJo5/5SZsy6NrGClUkE+n0culxN5cTgcxmM5F0otDVG3hTWRljCJVCEAHdkhA3bWcxLcAp1erTyOVquFVL6CZqstAe6RlAkweP3orzZhzf+7CbfvKso64/Fw3lVGe6LlfBdZHFXmyz6oK3odELhp9Nmv0+7IxtMAgOcti3RJHgHIXJMhUpkRwDlXyiu9Xq+AX7Z8C4fDiEQisG1bXJt1vdNPW+3XzmHbNr7xpx341O0OyL58kR9/ud4Lq92UWkkG4rwWZMQZ1LM+l8wo17fL5ZL6znbb6RfP+v54PC7Xi9ea9ac0eyPLpI6+sA8h75EDbV3XsXKqJeueXFPmmgy/WmtLlYSu69BtC0mPsw+k6oYAZ9VQjkkQni/n7L5dGXz+tt24e2d2VvuhqqSh0iTkdYmngsoqqqUcfB8Del4D9iVWjZvcbneXaznZbAKCA7kq/u6mMezINhHzGfjm60/HOQuiMpdUKnBfabVa0rs6EAh0Sci5XnjcLpcLsVgMyWRSTBypiuDeQzM8VeWjekUQSBIAUuarKo+Y4CEIZ3JHdbjnsG0b9+4Yh6EBL1zTiyV94S6ApXprHIrN5rzwHlvW4zxHt09UJJFB5pTrhTJ6NblB9t/r9WJgyohvtNqZcyZqWcKg1mmr+ybnkQkK/pzXmolVPuPJpnN+uPbYBYNKCKptVIBKk0/e61x7TJ5tTDeQqdsIujUs91dl3SQSCUmGUN3DvuuFQgGVSkU8BbiXmaaJ8fFx6ecOdOqoaR7a19eHeDwua4vPCJqmsRMDSx84jzQBpEqMex2vOZNSaicRDt4/QLf/Ce8xyu651m3bxpf+6Kgn3nzhQkQDx77U7pQB2nNjbjztePKXzt9rr52VbPwDP96AN37jAfx2qm9y15iq015q78VjI/mjP8a5cVzHZLmB//PjRwEAL1w7MKsNtVBt4Q+bHHOZ2fbO5hiK+Wfcr9vtdmN5bxBvOSuB91/YKw8FMosBw4QfTQAacnYHtLVaLVQqFVy3Polr1vYi6nef9ED7UG29bNvGn7ZN4D0/3443fvexWYFsZubpBE2QHY/HpYWNWndL4yuPx4NMJoPx8XExDCJjUalURFrucrmQTCYxb948hEIh3DbizP/5iTrchi7AnNdFZWdYOxmLxaQPrsfjkWCeEnXW4//t9Vvxmu9sxJZ07SBANNNB2aLPbaBl2tiZqcs8MghWmaOky0nyZFoeNKdKE3guao1iu90WN/NNYycG0J4oNXDfbkeOeOmigDAmnGOv1ytJGwa8qtyV9c+srycT6Pf7kUwmpW4xn89LKyUy3bx+lP2bpolyuYwv3roNX7jLSdResyyAt53ugzXVbozrgIZ0lGHWajVhrLmWuIYrlYr8jtJ0fheBXywWE4k5APkMmgW1Wq0uE6aH92bx6L7cMbkOuq53udyrNa0EclxvqnQcAPo8DgAZqUBkodONufhayroty8IdO7L4+j37cMeOIwPa46UW9mcc4EKQRMULgRSBA8GsWsfLXuqsS+VaUsstAHQlTWzbxr5cHX/92wPYX2iiP+TGf79mNdbNi3YxmhxkfIvFoiRz8vk8DMNAPB5HMBgUIEOgycQcQamaIFCVLmRsKb+dnkhgDTlBmgqAm82mlCFwPRHgqm2VeP7VahWvPXsIv/nL8/DXV66Qc53OZk93mVaHqopYMgW0t46XZV6ZSCSAI+vJhASPm/fBgN/Z50bKmgB0tcUX505NvDAJwfVBwEy2nWtFBX2apkkZCuvcqSqoVCqiAOCzXt2j/H4/otEoTNOU60SjQ5qi3bHXmbvzB92w2s69F4vF5PcE8gT8fM7xu1krzoRcqVQSeTmT1FxbTA7yfezgkUgkEIvFuhKVTFw0Gg1RhAFAJBKR9oVcL2qv8OnPPHVeVBUWe4lzf1bLB27fOoGNB4oIeAz8xcVLDrmejnacUkB7vFjHrZvHsWeycvgXz41Tfvzr77fgZw+PoF4pAtt+7/xwFm7jO9Jl3LrFYT/u3jl58Av61wJwWnxtmGvxdUKPSqONv/j2g9iTqWI47sfHrlk9q/f/+vFRNNsWVg2EsW7ezCWwtm0jVajP9nABALGQH284qxfnDvnk4ay240nozsMja/nlgU2JFB/0AE4ZoK2ygM1mEzdtcXrEnjnssDuHk4szMKAhEKVpZCMZlBBsMFglg5lKpbB//37pMcqHOANny7KQSCSQTCbR398P27axYbSCkYoGt2bjvJ52F+gCumWtrBNkD1QAXdeQjB+dYO/dOYkNB8o4UKhjOHl05i2U8wLAtnRVghQ1SOT8h7QWvJoJCxomWx2zI9VYiGqA1X0+vOT0AVy97qnb2T0Tg/fDH7ZMwrKB0waDiLnawpSR5WDLHFUWrBooMWhUZaAEuAQmbN3EQJzrh6ZnLBuwbRtfuH0fvna/k8B75Uof3nx6EI2pkoh4PA6/3+/0rm63kclkUCgUkM/nhVmny+/w8DASiYTUZZK9icfjACBrn2A2Fot1sT4M5gmmGPgzqP9/v3oSL//KPfjJg/uP+lp0Ae1sA5Ztd0lfyRCqHgYEz1RTjJQ6DuMMrsmycQ9Q5arLkx2wNdP9UC2H+Oqdu3HZv9+Jr9+zr6u2VjVUJOgnmFLBAY+RtdL8oxocEujwvHZmm/jIbZNIV9pYlPDjq9etxLK+8EHHR6AIQGpkCdbUUhN2R2BLpoGBAWEFCXw516oyhewq0EkETGdrCXq53lWWmgaTZMUJeqa/jiCbe92q4R4MhJ3zoo+Aavp1uMQin5nnzg/h71+4GH931QoAkPnl8VNNpJbm8F6mfHx4qvqKjDbnmoBNZe/5OWqJAhPh3ENpPMdrx/uZzCvN05iwYE0z2Wx+D/cqAnCy10yAcK2apok2DDww6lzLsxItKZVi2UKlUhElQ6VSkeSIKvVWTTZpdBaPx6XbAtc4Tcf4HKEKizFMOByWJJR6P6j3HJOMqgpAbVNHqbs6uFb5zGJCg9dVrcXn3P7HbQ6b/YYLFiIRPLJk9eHGKVOjDQCfuGETbnh8DB964Sr85WVLn+3DmRvP4hjJVfGft++EZQMXvrSIoVYViC0Ehs6c8Wd899498u9D9sqeYrSHtCwOjI2i3jKPWYP7uXHsRsu08J4fPoLHRgqIB9z4zlvPQ98sHMMB4GdTsvFXnT18kNTt6cYDu7N47dfuw9XrBvHl18+8ZAHoZOwZwDBYZwAa16s4YEWRswIwTQd0SkBXb+DJdAMHyiZeN8tetyfaOJRsPFOs4E878wCA5y2NdNVkTb8+zGhTakeTlmaziUgkgkgkIg9kthMhuGLwnkqlMDY2JsZX6sOaAVsymUSz2RT3WAD43S7n7zNiTYQ8mmT1aTpERpTyS5XN5vnws1TDrlKphG/eP+U0fu58DEYPrnOczegG2mUB1qoEkj13Nc1xgD7QCiDd9GDI3zHj4fGR8VkeceEzL19zyDrMZ3IwOHvtucNY0hdGuVhArVbocm/nvcO/LavTPoisMtk6JrwYRFJmSTa5VCqJIRTBCwM/y7LQapv49K17ccNmhyV+9XId1670i0yX0l/2XM5mswfVTff19SGRSMix1Ot1MR1SgT0NrwgootHoQW1zGPTzvA3DkGD4ti3jeHLUYXyev6b/mFyPJb0huA0N1ZaFyaqJWLQjv1b3Pd7LT8Voc7Dmma/j72q1GiKRCJbEnaB663gFrXYbM1mNXDOmreHGx8dgAzhtKCxO4kxuAg5Ty9Id/pwSbtaX1mo1kZtTIs/AX63R1nUdhYaNT91fQ7VtY+1QBJ996RJEvLokA7n/AB1Zu67rmJiYEEdzJo7INpfLTouraDQqLeJYc001TW9vr8x9sVgUsBWLxeDxeATUMbHB/UHthKDe66ZpIpvNymeoNcoqm03WdSRXRb1t4bQFvV3JYjKpKpt9uOcwn5nzol4sSoYQj4e61AJkkHns9FLg/a320p4fdtZTpqGhaWnyWoJnXgsCRVWhwHlqNBpdUvl6vY5WqyWSfCa7KN9WDS8LhYLcu0zKUDJOSTe7GfCzWXLF7793pIa6aaPPDywK2QBc0gaQJqDqdeV5VSoV8SChakMtcerp6REmns72THKw9EQ1J+SexKQg7xvKuFWvFNaas4RGZaan1+ZPTwLxeqiJes4Jr/E9OzN4dF8eXpeOtz332Ndmc5xSjPbqQYdp2nwCyNTmxrM7vnffXlg2cNGyHgyN/M754dqXz1g2Xqy38LOHR+T/W1Il1JrTHJz9MdgRp1XTEmv/CSGPnBsHj0bbQq1pwufW8c23nIulvaFZvX/beAmPjRTg0jW8/MxZ1nU/PALLxhHVNHo8HhQbFu7aU8bde8siUWXg3jPFaGfsQFfQ12g0UCxX8Zc/3YpP/G4HJkpHxqifCIMACOgG2jdtTKFp2lgY92Jln18CI7I2fA+l9ATbxWJRjGZCoRCiUYcNpzsrGTD+H4BIzMvlsoBsPvhp0sNg2ufzyfelazY2pJ1A8cKkY7LF+l0GBazn47HSoEqtv2WwSelnqVTCo/uLeHikBLeh4S8vW3bU8+xyubCsNwgNwGS5iXzdklIFdf45J3SAHm905Jf8wxpGBqongqKCwZbf68FzFkawJqFLfTZlkmxNw3tJdQQm6CMgKRQKyGazAkwzmQyy2SzS6TQmJycl4OO6q1arAuLrzRY+dsMO3LA5Bw02Xr8ceNFSv5hWEcwUi0Xs2rULBw4ckF61uq4Lg045MkG0yiTRjI3gpF6viyJCDfZVVQaPl2wa2ez/uNXpZfzGY8j4eN0ufO/NZ+Cmd6zDYMQrAIzSelVmS0CqaVrHH6Bmw4QhiTCuMQJMvp/38fyoB25DQ6VpYiRXO7TnylOsmbt25VGst9EX9uD8xT0CLJkkU+ufuV+x9zATo6rSiEkrriWVxSPovWfMRLVtY1nSjy+/cjl8WltAgird5v3JfY4tBZms4N9kSunwrH5vo9FAtVpFMBhELBbD0NCQMODtdltcp3mM1WpVQJBqdsW1qQJgdnJwu92IxWLSM1qtxed8maaJL9+xF9f+10P4xl17uhJBTETwfpyJFwXBHtc1QSSTXVRP0OiS7Lbq5s/9OeZ3IWSYsKEh3XCe5QSLagINgKxH7ov8TpXlJkDWNE2eI3z2kOVmyz9VEcDz5rGxfIlAmAkefjbnyuPx4A/bnfj0/D4AsEU1xaQNEzBqIoeMNOvyCZapYvD7/eIJwZpwAAL8VZUY708mHdhqkMCdx6s6kNfrdZHQM+nAfWz6IIuv3v8sA1M9OGge6HK5sH5+DP/3aoeY7QvPjnyZzXPtlALaa6aA9pbUHOD53zxqTRM/fsBhIP/i3D5g2x+cX8xCNv7Th0ZQbZpY0R9Cb9gL07Lx5OjB7aC0KUO0lfr+Q7Pec+NZHyGvC99563n48TuegzMXxGf9fiZcrljVN+Maa8CRq//2Caf28rrD9M4+1HC73XhyvIZ/un0c3314QtgzPtgJdnKWH7Y9rUasWcP8mHOsm8dKMwosT8ShZqMZmLXbbfxuk1PK8YJVPV3tqAAI4C4UCpIBZ90s24UQZFMixyAMgNR/MYhmWxMGBQCkfRPZBwZuDCrT5RY+eWcWNoDloRYGg5owkQQVBHrMtGuaJq2UVDZblTfXajW0Wi1860GHzX7V2fMxL3b0bLGu6wh6XViQ6LSUU9l6gkzOSa/bmYeJlkfeD6AryKaMtdU2sSNdwvbxZ6f1JgEKj5M1h2R91VpCHrPKalOWyWBTBQZ8L93E1dpIAl3Oi8fjQbXRxodu2IU79pRhaDbevNzEVcs6CR8G7JlMBqlUStYb4KzZeDwuwEc1DWPQTWDJumC19lKt2WZQSiUH54bgJhAIwOVy4a4dk9iwPw+fW8fbnnvs6hd1XcfawTDiQZ+AKNUQDejUHKsScb/WRnAK8IxWO54AqvKA10VVKOiajaVJ53O3jlcOGySra+Y3U/4s16ztg9fj7jJKZFJCBfxcH5xv3u9cG6rTPAABztx3bNvGXSPO9XntOUOwmzW5XtVqFYVCAc1mU4BKJpNBPp9HJpORLghkJCmDLhaLIv11T5lH0iSK8uhEIoFwOIxqtYpcLicJhHA43MXUs6cy9zvOt2q8B3Tc6wGHzVbLZMh6q/fSSL6OG59Mw7aBcxbGZP65v/Iaq72rn26oNf47Jqv43n37cP+evFwr9XOYxFVrigF07b/9U4ZoY/Xulo8EbUygAp32kUwMqPXurKPnnsB9lvNAWTvriakqYAkJn/F8HrlcLkme8V5Q/SAAYKzQwMa0M3/n9jmfxecMP7unp0f8Q6jgSafT4lmhKsu4T/GcmGAi4OczmeuAAJfPzHq9LglvAJJcU13CqTojM87P4Wun369cH2Tb1flXk9k8N8CJDd916VJ84PkrDruepn8fY4uZjFMKaLOX9s6JCuqtU6N/7NyY/bh+wwEUai3MT/hxmf4o0K4B8cXA4PoZvd+0bHznnj0AgLdcuBhnzI8BwKHrsKfk46u0uTrtE22oTsc+tyHXcTajZVr4xSNO7+xXnT07sPzbJ8ZQbZpYnAzi7IWHB/iUnqoPNMp59+YasLUO4NI0DTG9AQMW2jBQsr3yYCG7sazXCWZmU5d4og3Ohfpg3T9ZxEP7nQDuBasS8oBmCx0AEoTSOCqXyyGbdYyQ2K4ok8mgXHaUApTv8XsYoIyOjiKbzQo4U01q2Lc4EolIMGqaJsYrJj5xTxkjxTYSXuAlQzVhs1nHScCsOiezNltliHn+lM1ZloXHDhRx/94iXLqGdx/DEil1ve3K1mUuGbh0GaJNud6nWx5YlhMs8TzUhEej0cB37tuP53/2T/jcLduO2bHOZrTbbVi2jbd87zF8+qatmCxWBQjRoZdgj5J3BtIELDx3MpdMetFdVw3YQ6EQent7uxx4E4kEmraOD1y/HQ/sr8CjA+9d78YL1vShr69PAnoyZATrBEDRaFSC4aGhIWEmGXSqLCcDb1XCz/Mg0CIoUAG3Wn7BtjdfnGKzX3veAvSGZ55kPNzgGpnuygxAgKjKcvH4AaDfQwdorYuJVJkslVHkdXXaJc5sP+Rclhom/rjF6bl+zbo+qa0lgAc6LYJofkZgTSk1DauoKggGgwK8+F1qKcqeooXRig2PoeGqVUlJ8FBhoM5JqVSS60aFhVoXbFkW0um0OFZ7vV5JLFKhY9s2ent7EQqFUCgUkMvlUK1Wpf622WxKl4VwOIxEIoH+/v6ueni17hZw2L58Pi9soir7VevwCS4B4Fv3j8K0bFy6oher+vzyuWoCSDUfO9zgPHk8Hty2LYdP3bwLN2wcl8QNAS7nVGWleU1Vp/8Bn3OcByodYE6GlQkhtd6b80DAz57RZNcpkabppWrqx2teqVQkmRsIBGTN0JVbTVyoigeCWp7fjU86a3h5xMJgxCOJaSaYqVhgoqunx1Fu8Pup9uI5lctluRbq3sjrpc6nmiBhInNiYkLmic9dPu+YAGBSKhaLyfeqXhnq4HzyHKhEYCKMCQyqBbj+jnTMVql1UgPtvZlu07OBiA+xgBumZWNHuvwU75obp/KwbRvfvnsPAODNz1kEfRPdxmcuG799axr7slVE/W5ce+bQ0wPtKUO084MpnLtorrXciTJ++8QYrvninfjnGzcd1YZ6x9YJTJYbSIY8uHzV7Hpn/3SKCZ9pXfd0cKVpGhb2hhFw62hZQKpqy4PN7XZDg42YNmWIZnd6gRLILeuZCizTh2dwTsQxPYvOcfOTKadecjCIeVGvPNzVoQYS6XQau3fvFrMXoNPXlaBocHBQHsi1Wg2FQkF6h1YqFXELJogBHPA7ODgoNdeNRgOTTTf+4a4SxsttDIVd+MBpNvoCTlBHRoKJEDIdPFc6sRJkqaZUDPgsy8Kdu50kwyvOmof5iYMldEc6DMPABYtjeOGaPizpDXXVyqpMj6ZpiBsNaLBRtwyU2pq8hgwCAJGPL51y/d089uww2u12GxtGinh4XwE/fGA/GtVyF7NBkMNrw4QBkwasYyWrTeDEAJOAlq+nARmDOZ/Ph4liFW/7wRN4fKwKvwv42/P8uHLdPCSTSeTzefnDe7u3t1cANlnpaDSKRCIhASylpgTS1WpVAnKgU3bB4JN136pMHOi0QiIgJRi/b1cGD+zJwmPoeOclx9bzxjAMTJab+Nzt+/DpOxzGmKCfJQsE4QzcRU3BOu1yZ61x/lXgzgQEE1RLe5xEwe5MbcZA+7ZtWTRNC8t6A1g9GBHgQEAje/EUyOL+oQI5StgpUWYCi9eHAIvncud+5/wuXBBEs1KQsgbOAROKBKy8drzG7IlMcEvncdZq08yRZpA8nrGxMUxOTmJychKtVkv6mnOvIrsdDoeFbVRN0VQ2m0lOTdMksUlQyK4JXL8AkG9q+OWjTkL7PZcvlfnnnqyujdkMru0liaka/ZSDC1TWn+uE64ZzwqQJ9+OhgLNmDlQgIFw1LlNZcSY/VKMvrlPWyqtKGaokmCCidJ3lBmoJAgApR+H6o7qAr2Hyj2vrlp3O3nvBQKfVIMsbWMbAY2SSIZ932P9QKCSAvVQqiTGby+VCJBLpSnwwzuE9MV0yztaYavIBgJwn1yKPgy0uOc80T1PjqelstlrCpL6W11HXdTx+oIgXf/Eu/OHJQ3QTOszgtZ3NOKnN0B7ek8NpiztuppqmYdVAGPftymLzWBHr5kWfxaObG8/GuHdXBlvHS/C7DVx3Wgy442bnF7OQjX97is1+zbnzEfC4ZsRoL8d+LD//5DadOlXGfbsy+MCPN8C2gXrr6ADmTx92ShCuPWMe3MbM85J7MxU8sDsLXXMA0UyGKi/j8Ho8WJLwYuN4DXvyLSSTelfQldCryJhBZK0A2m0niGAQs6TXYWVPVkabwZYaqNi2jZesiWMoCOhTD286napzRyBRLBaRTqdhmqawCZWKk6BNJpNIJBLo6elBtVrFxMQEUqmUBFs0plEz4aojeE9PDwzDQKFQQL1eR7rtw789UEKhYWFRzI2/PS8Au5pHrWZImxL2PW23212sCYNYrgEGXTx3BmAulwt//bwluGxVP5b1H9vnm2EYePVZQ3j1WUPweDzIZrMCRtU2WLVaDW7dRtxoImt6Md5wI+JuCugjS8z6uEVJJ8zYk6mg3GgfVQ/m2Q6C5huecLpHXLEigVa9KkEeQYqqNFBr9clQE+wweaAyXQxaWfdPFovAYiRTwvt+vg37Ci2EPRo+cmEEqwecekqWJKi1oayV1DRNglrWqWqaJlJOqgxUZ14yUgRwXE8EYZRWs20c54Ggi8dgGAbK9TaGoj5csboPA9HZ1S8ebmiaBkPX8IOHxqAB+Mtz412gheuMQJXnblkW+jxOkDtW67CbBLpqLSaD+Vqthmg0iucvj+EF64YwL+Y77H7IfeSmTc66efG6/i6DLCZXqKYhg0aXbqpeeA/T/DAWi8HlcgmTy8QqP6dlWrh31Dm/yxcHZK/SNA2ZTEYM1rjOmDBk/X4ikUA8HheGlWUBdKfncXK90Xgvl8uJPwHQqf0uFovS+s3lckndNnsnE6xSTg5A9k4CG7UWnewla8YBB1B95tYtaJk2nrOkB6cPBuXeMQxD6rpVRc1MBz9j6ZTr/PZ0GaYNWUts58fEG2unqSahj4bL5cJwyAFsY1UN1tRncJ/g+gQ6ew47Wqi122oCT03cqQoMKht4XamM4GtqtZo8R6iqUUGqKr9uNpt4dH8B41UbHt3Gc4ad5Alb01GRxfXCtoXZbBbValVk2ywx4T7JRATPU/Wv4PrhPsn/UxXRarXE/M22bTlHNYnNZIPb7ZZ7gHvt9DXAxCETcSyFYDKFCTjV6O6Lt23Ck6NF3LxpHFetHZjxelJN3WaT9DmpgfbWQ9R8rR6MTAHtZyd7Pjee3eF3G7h4WRKLkgFE998GtOtAYikwcNqM3r99vIQ7t09C1xy7fwA4bTgKTQNGcrUpdlO5wZIrAN0FNIpAYT8QmwPbz+bYkiri7d99CE3TwgvW9uPjL107Izb5UCNTbuDWzU6g9apZ1lj/fIrNvnh574wdodWsN4fH48GypM8B2rkmzuvzykNK13WnxZfptPhSWc9Go4EFU90vdk9WUW00Z80GPNtDlcJyEFCs6fMJGDFNUwxj+GAnoGawzkCQD2O6Aft8PkxMTCCdTmNiYqILsDDo4QNa13VEIhE0Gg1Eo1EJEsrlMvaUdXxhQwXVlo1lcTc+eI4XXruB4pQjrHqsbLOkBgyRSEQcu12uTv9boFNryJpbTdNw6cr+g1j8ox38HpWVVlk5oBOAa5qGpLuBrOlFuunGCq0lP+egRDJoWOgNeTBRbmJrqoizFz5zyh/TNNEyLfx+syOdfP6yCGq1tEhxyUyQEVXbeqlmUmRY1dpsOpDzeqqsK6XgBwpNfOD6nRivtJHwafjIhWHMj7olOCXIpgEQgQvnkQEnazkzmYz8jkF8pVJBPp+X41LXLkEAa8aBTgscrinuF5ZlIRgMyn3y/DX9uGRFL2rHqQwvGfYhGfRgstLEvkIbvfG2JBU475SgqiofGqKNVgHTtGStEsAQvBBsEGyGPRqiEY/ch081uI9qmob/fMPZ+PXDe3H+opg4MKsSe64L1iJTFaC62TMRaBiGmCEStBC08z576EAd5RYQ8+k4vc8jiQ+qYMgsEvAy8WPbtuxxlLDTwJHrmckXFbQxOcDz4WtUhtPlcokjdavVks4Ltt1pbcWSFyar6HzO/UJNJjDRCDggO1Nt43+munq874plck+ytz2v1ZE8v7inDcd88Ll01NsWRvJ1zI96uuq06ebPcopAICDHWq/XEQgEMBgyYGg2GpaGoulCQOuYPXK+uE9OT5hzqMljPlPUsg9Kp1U2XU2QeTwepFIpKTFj8sLv98Pv93ftTwTaN211fEnO6HFahrrdbuTzeQCQPUx1Wq/X6yL7J8hmvT4VV1zj5XJHHaSWgwCdfuf0CGBpHMtamHjgPRuPx2Vv49ywXIv7wPTnJu85fg/bw/G+VA3ouJ9sm6jiti1p6Brw7stnbiSq1mXPVnp+UkvHtx0CaF97xjx87s/W403PWfgsHNHceLbHmQvi+P7bzsc/vHQd8OTsZePfmWrpdeWafpFlRnxucao+yPDM5XHANoDs7kfnShaexXEgX8NbvvkgSvU2zl0UxxdecyYM/chANgD8asMo2paN0+ZFsWpg5r2zAeDtlyzBp15xGt55ycwNhPgAYa014GzoS6dqC3dMdpyD+WBnL+2c3enVykyzHw3EfAZMG9g2fvKty0PJxsmEkD0xTVPMgdSgvFqtSkadD0W+h0FtJpPBnj17sGvXLqTTaQlQGTyqfUzJUpRKpa46+WaziR0lFz77SBPVlo3VPW781ZkGjHZdgpNoNNolBWR9MINAr9d7ECPEIInSOr/fj5FsBYVaqysIPtbDMAxYto29GSdpwL6tQEdZwMRH0nACqVSjAwzJtDIoqtfrqNVqWNnvZH02PcMJ8Ha7jTt3ZMU1emnYkgBb7clK9o+AmyxwIBAQBofBYbPZFKdgMpI0tqO5FOAYyr37FzswXmljIKjj/10YwrywM3d8H8Et29mEw2FZr2zVxQCRPgE0vOKxsuaWsmGudao9CMK8Xq8wdFzbLpdLWuxwzauJLY9LR9R/eIfnIxmGYWDF1LrYnWvK/crEGBMXTF5wT+xxt2BoNuqmhkyjY4jGvY+ghIP3k1qKon7e9ME1YRgGfAbw0tP7MRjzy3UmCFJrYy3LEqaR88jrxiQIW1/xuvF41Nffuc9ZO5cs8KHZqEu5hm3bUjoQDoflc3icvN5MINEDgsw158Dr9aJcLkufd54LmVHV1JBJj1gsJvPK5JBqkEiwxvudoJ6ybM4pEw8qyHa5XNg+XkbQY+CchXGcNezEWdxn1HZeR7Ln8T0etxtLpkpYtk/UBBSTmSU4U68/fTqYdPN53OhT/AFUSTOBnFqqoTLVvDacM+77XIP8LL6WzDX/TVWBZVkolUri8O31ehEOh6VTBYE6n4GVegv3HnCA6MXDbmk92Wg0xEOC9xiVCFQ3EFhTyUQZt9rqS12DTMBwr+I9qRo1kk3nPUgWm58NdDoHMJnDhCDnSo0H1DlmQomKAPXaMGbQdR1f/uMuAMBL1g9hcfLgXtxPNXg8nIPZjJMaaG9NHeymu35+DC8/cxiLZjGBc+PUG0arDGyfnWy8UGvh5w87dUJvubC7p95M5ONf/9mN+KcbNx3R8c6Noxv5ahNv/uYDSBXrWN4XwtffdO5R9zRnjfWROIaHfW685rwFuGhZcsbvUeVnqgnYyj4n+NiZqQvDwZqwnilTqrLtRcPu1IuaptNy4/8+bwG+9fp1WJoMHFWt+jM9yCoBqiOshdd881F85o/7UWp1HKRZ3xgIBBAOh0WGphrUsBaXxjqVSgUTExMYGRkR6Tc/hwyFbdsoFApiPON2uxGJRJBMJhGJROD1evHIeBufe6SOhgmc3uvCX53tQcCtS1A9ODjYxW6RiaIMkiCIsnbKTMkWUZap6zr+6bdb8MIvP4BbtmaO27wbhoF3/ugJPP/zd+O+fWUJxDgf6nEnXc7aU53HyWIzicCgjiZrqkHhMzHa7TZu2OioUl64uhe1akUCN5WpV2Xjqks3GV+uH/bC9fl8CAQC0l6LAIQB35aJOt5//S7kaibmh3V89AI/BiIdBpSJF4JdAmwyaSx5IHPF9cMaWb6/WCwKCKMsmUE/mUN+LgBJCDB4brfbsvYJtLamK/jZwyNom8e33ETXdaycWhd78k0Bn0DHMIuGS0zyGIYBHTaSbgfwHKh0zPrIHhMwqdJRql1+v3kCH/z5JvzmifGnlI+rShr13wQMnFMCINWgir8jAKehFD0YeF2YsCFIcLvdKNTbeDTtfNYl871d5QwE8axbpUKB7vJcq0yukGHnGo9Go5I04l4Wj8fFo6KnpwcApI6ctf6sz+WziUwszx3oONRzvbHMhN/N+4cAHOiAbAC4eHkSd33oCvz7q9d3gVw6d6vfNdvB5Kvb7RaviO3pjhyf5Tv8QyYY6Libq678A37nuTxaM7pKvXgNud64jtREnsr6qk71BG/cfzhv3Ee5nnVdlzZ/9XpdDDZZKsBj4XOxVqvh3n1l1NpA3GvjrOGQ9E+nqovtvFqtliTyyACzTEpNmPD4Ceb9fr+8hgknOuMXi0VZ7/RJUEtWmGDmfKj3n7oOKCfnPKoJF14bsuvqdeNnqet3d7aBm55MQdOA986CzeY9C3Rq2GczTmqgXay3kSqevD1i58axG9VmG1+8dTvSXA9bbwLMBtCzXAzLDjd++tB+1FomVg2EccGSbnnj+qc1ROtu8XUyAZpTZdy9I4OdE2UMRHz4zlvPQzRwdCzMxgMFbB4rwmPoeOn6oWN0lIcfKqsNOA+WNUMRfOyKQXzm6nndZmiaBp9uIah12nypD5hyuYxLl8Vx2mAQXpf+tHLJE22oAS7P6YHdk9iSruK2HUWEfW55iDP4rdfrmJycFGMy1gmScWG9V7lclhpDNeBRjZMqlQomJyclM+/z+TA0NIQlS5agp6cHbrcbN22axH88UkPbAs4ZcOF9Z3rg1mypv4vFYlIDqWmaMEmqqywTJ3x4s0aQTCfr+DYdyOOWLZOoNEysmKW6YjbDMAwsnGrxtX2y1tXii+Y+XHt9UxLeXNuNRtsSoK065zLwXjplRrRp7JkD2qZpolBr4Y7tTmLi8sVBARnBYFDmmedG4MNkFZULBHwEDXSZL5fLyOfzop6gcdOGsRr++oa9KDctLI3p+OhzgpjfG+syNCIoI6vGelbOGQNq3u+67pisRSIR9Pf3IxKJyLpncM6/CdB4Hn6/X8oOuJZVd34G5wT9n7t5O/7mp4/hX3635bheH13XsVxc7hsyv0wykdUkq6caG/VNGaKl6p06bYIWBv0EMGSbbdvGzokKbt4yifv35A8JtHkMW8fLeNlX7sV3790rv2MNM4Ek5a1cR2rtJu+ZfD4vLZii0SharZaAA95P3B/uGWnCtIFFUQMDfkuuCZl6qhXY1olJOrLY7D1MZpH1/5VKRZIN+XweXq8XiUQCAwMDiMfjXR0T2IKwp6cH8XgciUQCoVBIwBTBHbs0UBnCJAcZRVVaSwCmmm1Ndw4Pel0Yini6ZMIqm32k5V9Ah/GnIdpmZQ9S1xgZfqqXCALVfWKQzuPljiKCwJDPbh6rmiiYLitnoozHR5UDz1etO+b8ulwu5HI55HI52Z/6+/sFWPL71HKCP+5x6tsvGNARCgYl8ckyKCapqHwhIKWniMvV6TOuMslMSAKOKSiTeax5575SKBTkuce9jkkc7nUE2fw8zgk/Ty31OBSbDUD2O8ApqVGTWOra++qdewAAV68bwPL+jnnf0w0+wwB0KbxmM07qGm3AuWmm10Bu2J/Hw3tzuHBpD1YPHr+gZG6cOOP6R0fx7zdvw/UbDuCWD14KbZaycdOyRTb+lgsXHbSxnzkFtB/bn4dl2dBVSXKfA+RX6fuRq7awL1vFwp45RcUzOa45fRDAWVjWF8LQMegrzN7ZV67tRyww82x6odbCn3/rAbxk/RDeeMFCuGZhoAYc2hAtHPDh8qVRYUsoQyMITWhVVGwvsnYAC62CMLcEmoeq/T7Rh8roc/ziEeeaXLIkAr/HJeZbDLAzmUwX+0Nmmqyk2scW6NT80aCFARADAwaPwWAQw8PD0vKkWCzihk05fG1DBTaA5wzqeNtpHhi6JoGn2+2WmlgGQAyAyYhSWq5myPP5vPycAQwAfPGPTpulF6ztw8rjDLSpoNierkDX+yTAZu9psos+swW/1kbNdiHddGHI2xL5Hs+dLPDqfh/efckinL145gqPox3tdhvNtoVXnjmEnZMV9HtbGM+3EYlEpP4S6DY1ItPIBAgDWrWHKxM2ExMTwtqQ0XvgQB2fuWsSLQtYm3Thb84PYyAZl9pJOg6T4SJIYl0yQbZhGIhGo2LGxmtDJr5cLss6VoENA2PW3TIA5p5CqSaDVyaSmDzZMVnDLZvHoWnA646zuaeu60o7uYYE/AT8vEZcbwQsrVZLDNFGq3qXZJeBO4EHwTCvn7hPP4VBJIP9G5+cwKaxEuZFvXj9ecMC1rleuAcTRLJ227ZtaXOlyl+ptGFLLapCmFSwLAt37HWA+sXzXF17NlnrRCIh9d7cU7j/kX3kd3Ids/yE+w8AaTdHUMVkJb+LIIjri3OpJtD4erYs5P2jlo6o4I3lF1QqAI4K7cE9OTx/dZ8kGYEOm81ECRndo1lnmqbh0qUxrB4M44xFfV3MKJNZVLEw2cl1yHWi6zrmTYV1o9VO0odzzOcxz5c17Uyw0VlcTYwBzv2r9pGnESDnkeusWq0inU4L051MJsVBXI0ZyHiXTQOPjTv3yWULHXXC5OSkrBdKv/lMZHKIChrea+p5cb7UvvW8bwhq1XKHWq2GUqkETdNE4s5kABNNfL+qlJiuYDgU0J5emw1A2G8mxCjP13UdI4UGbnxiDADw3suXz2jtqPc99/4jGacA0C7hilX9XT/7xl278ZvHRvGhF66aA9r/C4Zt2/j2PbsBAK87fyG0RgnYMTvZ+G1b0tifrSEWcONlZxzsEr1yIAyvS0ex3saeTAVLpmq2AQijvVQbhRttbNifnwPaz8CwbRu1lomAx9nGHLB99KPRNnH9BqeE4LpZ9s6+4fFRPLIvj3KjjbdcuGjW380Hjwq01fo0Bg1qbVVCr2G/FUfW8qPddtg7Bq3FchV3Hyhgf7GND79wJY5QgfeMDrWWkg/WZtvC76ccgK9ek5SHq+qAyyCUwScluqqsl6CGLWdUyTADVQaVfPizVq3VaqFYLOLXWyv40RYHpD13EHjrej+MKWaKwCkajXbJKWmaRlDD4MnlcomRUKFQkHrJRCIhD/WtYwX8/knn3N//vBXHff5XDzlzs21KYunz+cT5VQ18dV1D0lXH/lYI43UX5gcsYRkYcBFoL/RpeM+li7pkgMd7tNttJEMe/OPL1qJarWLbtm3CEJH1VVl3gibVuInXi+fFtmuU57IsodFo4PY9VXzl4RIsGzhnwI33nRNCPBJCqVQSoMPaaK5N9tHlnLK0AIBIgwkeuV4YVFISrO4ZZMIIVJj0UVlRvp6ATJUDf+UOp37xxacPiS/J8RqapmFpbxAu3XEgLzVtRJX6Xgbbat0wGccO0Na6mLhmsymlFrx/yVbati3Kip2TVdSarYMMttrtNkzLxo0b6Tbe3TubiUsCba4X9d5maU8ul5PvpdEd9yyCLYLT0bKFXQUThgac29eRyQMOmEkmk8J8EjywKwIZu3w+j2w2K7W9vK59fX2SVGJ9Ld3TmZghsOR8kWUHup2W3W63mP9R7aG2xOPzif+uVqsiLWfbOI5v3rUb/3HbDlx7xhD+7VWnCQOpAqejZbOBzjNkIOrDQBTwGXYXi0xgyzng8ZN9Zd25y+XC/LCzFrNNDXVLgwHnPmJyhcw150NdL3xGqWtObSlJAEygrprNsU8695xEIiEJQ6DTckrdy+7YU4UNYHEYWD6VnGWyJR6PSzKeiQ+aPRJwc92zVIHAlvsk91I+L5kcYHLBNJ2uCkwWBINB6ZigGg6qahp13aljejygMti8jmTBmYQC0PVZi5Nh/NcbzsYj+/JYM3R4XKian3G/PtJxCgDtg6VoqwbC+M1jjgPx3Dj1x707M9g2XkbAYzj1tFt/AZhNILkS6Fs9o88gUP+zc+fD7zm4ttdt6Fg3L4qH9+awYX++G2hH5wPeCFyNIpZoo9iwP39IsD43ju344m07cOPjY/j2W8+dsbP3TMZtm9PIV1voj3jx3OW9s3rvTx+aqus+e/4RBQh8kKimKi6XC6myidu25RH0GLh02OhiO5OuOtAGslagq7bZAZ4V/OttKbQsG68/bxirAsduno7XUJ1ZGWTftjmFYt1ET8DA+YviwsQQ9FCaRjBEJo8BLlk+lb2wbRsTExPIZrPyXapckX/i8bgEYz/eWMSvdjrHd/lAG9ctd8MyTQT8fqm1JjtIGSeDYDLCDMRVtqrRaKBQKMDtdosbOseX/rgDNoArV/VizdDxb1lJ47+JchP5Woft4FAddnuMBva3Qki3PNA0B/xMN5pivSAD0KMNnGcyuBaATm0jrz+DMZVt4/FxXRD8TpcqtlotlMtlaVXDcecY8L3NzvlfutCHd54RRDDgl+C0WCyK6Y/a/1hlNlm6oNa48jgY+HKdM5hVjbAAiDEgpexstUaGUm1/xePn+/fmGvjdRqev7GzqF49m+Dxu3Pr+86E1KyKFZ6KDMk1VMs4EzsBUjXa2qaPcaMOlsIsEwTQuIwC3bRt9QQNBj4FK08TOdBlnhzvPcQKAB/fmkS41EPW78NxlCVE8cF/itWFdLNe3CqhZP99ut0Wd0m63u8ztuFcBwJ/2O/vOab0GIt4OY07Hb1VKzWtORQ8BEeXiaj1tJBJBIBAQb4FwOCyuzyrLyr/5nSqjrjotM3Fo27a0veN+yt9z7inFBiCMPkex3sK3ptqoXrV2oIshpeu4Wp98NIPzTSaW9w6TNsFgEIVCocvxm/eM1+uVntXBYBAhj46o20KhpSPdcGHI3ZIknDpvLNvgPkOGF+jUjVPVQjduALLvcz5oHlar1ZBOp+UasUuFCrRVAzK3243bdjtu4xfPc4mkmwmDaDQqAJX7CIEr55xO9Jw/Hj/3VSYBaPDJpBJZdj7vWOtP4EojPp/Ph2QyKYns6eUEHCrpIIn3qfnhcbIkhskClYnn8Ho9uGrtwIzbeTGJxQT90YyTukYbALakDnYxXTPFYh8KhM+NU29ww37V2cOI+NyzdhvfNl7C3Tsy0DXgjRc8tVv9UxqiaZoA+lXavoOdyefGMR8/fmAfPnvzNmwdL+FP2yaO6WfTBO0VZw3PyrV8R7qEDfvzMHQNLzvzyOq6VUmbmsXdV2jhaw9O4jeb8xKEMuBLaE4glLf9sGxIhtk0TTRqVXFbPVlaHqr12RzXP+ooDJ63LAqvp9MLmEwxWRwC12g0ioGBAQwMDCCRSEjAQHBVKBSQSqWQSqUkQKHsGYCYwbDXtmVZ+OYjeQHZVw+3ce1iDdFoFNFoFPF4XIIyPujL5bLIXyuVioCfcDgsgRkD8EKhIEqFeDwu571zoowbn5gCP1csPSbzq0r6DlW3Hwl4MT/urJmd2YYEpWq9YVeSB8B4ozs4Vw3faCI1Warjlk0p3LNz8picx9MN0zRxz64sHh0podVqCxNEsEkQwIQNAZ4K1HiuZIppMJjNZpHP5yW4/N1eS0D21Uv9eMd6P7yeThu0crkszuIMLNVaUHousCcyA3AGvFwTlKxTWk5mieATgAS+ALqAvGE4/XA5WENJwAgA/3XXXtg28MK1A1g5MLP6xaMduq4jEeyAO4IsXgMeH4GJ1PnqFsIuZ+2mpoypuO7UTgNqMoXXcXmvEzRvSZW7EkK8F8hmv2B1LzwuQxIX/H5VGmvbtqwtzjGvOb+TqgUCDBW4uN1u2ADu3OfcR+f3dpI8TPSp7tu8VkzMTWeRCb6YMKL5FQEwE4HhcBihUKjLN0AFmSyfKRaLAsqpDALQxbxOv54E7kwY0SNAHd+5ew9K9TaW94Vw5ape+Rx1DRzLdpRkVR/YW8S/3boHt2xJy++mgyieF0Eo55trcWCqTnu0qnWVevE+AyDrjiwzz4fPbLX0QFUXhEIhUWRxLjnvTHiohnhqEhmAvGZ3vo39RRMuHbhsqSPvJ5sdCASkpzqPk2tGTW6rCS+1DaIq6acDOk0ZWVetOn4zwUNZPlvdqWUETzcOxWYz2cPEglp6o+6rBNq2In2fyWDiifN9tMnhkx5o75oooz6tz+OqQechsXOigkb75DEAmhuzH/uzVdyyeRwA8KbnLAJqeWDnrc4v1147o8/4NjOrawYwHA885evWK3XaB43+Tp32xtEimu2Tpx72ZBu3bBrHR375BADgPZcvxZ+de+xqCdPFOm7f6jyEZysbJ0C/fGUv+sKza/+gjuk11bquS+C7N98AdKNLFh1CHS6YMKGjaPu6DEIqlQqWMbB8irrEE21Mf7AW6y3cttVJply9JinMc7PZFNMoACJPTCaT6O/vF1BTrVZRLDpJVwa89Xod2WxWgl2/3y+9PgFIC51gMAgbGr58fxY373fm7tqFJl4wbGNwcAA9PT1YsGCBPORV4yyOUqnUVR/J7D6Pl8fj9XpF0sfxwK4MNACXLe/B6fOPvv80GSrVGXf6MAwDK/sdpm9Xpi7MImsnVVkrJbwTLQ/abbOrbpHBOQ2gfr8pjbd/7xH815Q8+XiOdruNf7t1N970nUfxkwf3Cvgkc0JgxKQD6yMZRFLeTdk4gVaz2UShUADgMDo3pwP45U5nvb56bRhvWueHdwqk1+t1qal0u93o6emRFjoqgxgOh7uAk2rAxlr/UCgkzA1rgtVWNgSlZOzI4AEQ8yH+f3rdoa7r2J+r44bHp+oXr3hm2Gyg28UYQFcAzWulstpqDazIx2udnwPoqnsmkGBAblkWlk21S9ya7t4P2+02ai0TN29xEkHXrOuDruvCznK9AJ0+v7VaTUA1/RbIZjOZxvrdQqHQxW7yHtqctZCt2wi6gNOSmoAVtWwBgHw/HZ1VMKBpmrhIk9mLRqOwbVsk7GqSjECeNciRSASxWEwYeQAC7pg4nJyc7GJA6/W6nAPXHpl3rkHuoeooN9r4xt2OgvC9VyxDu92SNUBAN91862gHwe2jB8r4nw1p3LFtUuaNa4ysLpOKrCtnso2JxkEB2s488Z7k9/BzueZ4jSiLZhKPqgRVik81gHpdG42G1NFT1k8WmLXbrPEmML9tt7PfndGrIx70ilpG0zRJHFMmzvVIpl1VhjH5okq1eX1KpRJyuZyYNgYCATHso9yeJn1cP9VqVRKOAwMDcp+S6eYep46DysimkuH8uapAooReVfmMFeq48gv34ct/3AHLOrxRMcudgI6x4dGOk1o6HvO7ULSA7eNlnDbckdQNRHyIBdzIV1vYPl7GunnHX243N56d8d1798C2gUtW9GJZXwjY8CNHNt67ekay8UK1JSZLb7lo0dO+loZom8aKqLfM7vZRUy2+ruzJYOjy02Fjznn8eIxH9uXw3h89Ast2FAx/c9XKY/r5v3j0ACwbOHthvLs84DCjbVr4xSMO6/qqs+cf1TEcyhBtSV8EAbeOasvCWMVGz1SA7TA9QFyvYcIKIWsFMAgniKYkdmnCkb9vHa9I1vpEHar0nQ+4VtvEa87sw5ZUGacNxwXEsEYR6NQxsjcoa6RTqRRGRkbQaDTE/IUZb8pqWU9GCSDlfB6PB9B0/Nud47j7QBsagDeuNnBej41wOCpScQbarL8l20Mn4lKphEqlIrXbag0w6x8ZGE9nfl6+vh/rB/3QDddRZ9XVOjr1Z4caL1zbj8UJP9bPC3dJmBlUERjFjQZ0WGjaBvItHTG3LRJrBrEEKovjTqLgeCvNbNvGkwfy2J6uwG1oOLvfjcJkU1og8dj4WrVukMdMBpWMk7rmAMAfCOAnOzX8fqeT5HnbOQlcs9QnLEqj0UA+n4eu64hGo5g/fz4ajQbK5bLIGllGUCqVMD4+LnNLgEmJp8/nQy6X67puBKNqi55yuSxrkecKQIJyDgbyvK6WZaENHectTiDocT2j8ZJhGNifq+Fffr8D5VoD/3LVoDD0aocFmnAxEdFqtdDvaWFn1YdUzYCudxydGWgzyaO2afJ4PFgS98BjaKg1u9UA7XYbd2zPoNI0MS/qwxnDEamz5T3Ldc/Pp8EhnexV12fW3DJBxYQgDRe5D9++x1lT5/Tr8Hs6SZZD3adcP6p5WSgUklpYgv+enh6Ew2FMTk4K4FH7vgOQ1nSqXwCPiUCJa6RcLss+xblkIkFVu6g16Kz5ns5a/uC+vchXW1jUE8DVa/vRqDvnf7zYbK4zTdM6SedUqaummutrug8D6/0JtHVdx2DAWWuj1c4eosqsgQ7QVt/HeeA9zsQdy4ui0ajIxPm84rNI9VMIhULC4Kot5wj4DbdHFBKXLewYsbF8gN/D82OSmAktde9mDTbXIF/LRDf3xkgkIiCbzzuWblmWJcoxt9uNWCwmnTvU+4XPSyYjVJDPa0jVCteY6sPA/6tlNa1WC9+8dwTjpQbu2j6J9xymJEbtHsDEx7EYJzXQXjkQwYOjdWweK3YBbU3TsHoggnt3ZbAlVZoD2qfw0DUNPreOP6fxlMjGr53R+//noX2otyysGgjj/MVPzxgNx/1IBD3IVprYPFbEmQs6Ek8y2svsfVg2V599XMaOdBlv/faDqLcsXLayF//yitOOab2nbdviNj5bNvtP2ycwUWogEfTgilV9R3UchzJEc7vdWNLjxcZUDbuzDfT268JcOPLxKiYQQtb2wzTL8tBtNBpY3Os8LJ7KafdEGqpsnNc25Nbw52f3AOiRBz9BCwFDT0+P1IJRrr1r1y4cOHAA7XZbjKX44ObnsG52bGxMAhkGGG6vH5+5O4uHx9vQNeCdp3txbr8Ov9/pWezz+cR8rdVqIRqNSt9ZBl21Wg25nFMr5/P50NPTg2KxKKCcJkuhUEjcfjkYwM2P+6XVzNHMK0GiWsP6VOvhpeuH0FjVI+Cc7BfQKW9wAp8W4kYTGdOHsbqOpF/rSlrwGtZqNcwf1KEBSJcamCw3kAwd22CawzRN3DhlHnfFyl5obSdwZcsaMkMEDAQ0XHtqXaIKskzTdMydgiF8e4uNO/fVoAF47wU9uGJhh321LAuFQgE+nw+xWAyLFi0SN3F+PoFPo9FAJpORlj1kMFVpZT6fF1k57wvKfwmwNU0T9pGfw9IEVR5u23ZXPSiv/7rhOH78jueg1nxmFYCapsHvNnDnzhx0DWiYttSRMhmlynH5HqCjphirGwA6LtV0G2agzVZuZMuetyyCV5w1D0G/T5ISTPANRn24el0/lvb4oE/NaaPR6GKhCYRpjsjviMViYpLHY6VsemJiQkA/k32GYaBpaXhwzGHozu+zRXlA2TD3cHYpoGKB5+rz+QQAqzXfqqzX5/NhcHCwqyc2lUDValUUE6oDtCrHVeunQ6GQgCNeIzUZQcWL2n1BfUbXmia+dqejaHn35ctgmZ39noBOBazHavDzVvR3OipAYXBZTsIkDQDZvyh55hqh8/hYTYNlQ1QPBOWq3wfnhgomMq38DrVeORQKSbtAtoVk2QCl2Uzo8DqyRztBOwBsGG+h2LAQ9Wg4e8hJLJDNJhuezWYlGcL54X7HNlyq8zj3RirDWIZFQMxnVyaTQalU6jLWm5ycFGl8b2+vlC/wc6jIUduSkcVXa9uplmCiXO26wGvEhAH3jIlSA7/Y4JReve95Tw+yycSrqqZjNU5camMGY8WUnHLzIUzPKB+fq9M+tceHX7Qa9334ebh0RS9QywE7b3N+sebaw77XtGx85x6nT+afX3RwS6/pQ9O0p67TJnteHHHk63PjmI+P/PIJ5KstrB+O4iuvPwvuWbbOkrH/AcA+WHGwYX8eO9Jl+Nz6rB3ME0EvrlrTj+vOHobHdXTb6nRDNP5sedIBWzuznR6qfGAldAdEZa2AsBb8M+B1HpJjxQaylcZRHdvxHkwuqCwIW8cwwKUBEWuM2bM6EAigXq9jZGQE27dvRyqVgmmaCIfD6Ovrk1pttW2Qy+VCOp2WGulwOIxYLIZgNIHPPlTFw+NtuDTgfWd6ceGwVzL9DJgYHDCAIeNGkJ1Op6V3djwel0w8ZYmUDweDwa4He6pQx+YDeQDoChyOZFCuDHT6k6rA61BgW5VAAugyRFPNfDRN69Rp111d71EZr3q9DrQaWDDVo/t4PpebzZbU2V61KiEyQF4XNZlTLpeFTeG9RpDKwAvoBNNtW8N/b3Zqag0N+NuLHJCtskGTk5NSr7tgwQKR2VJG3NPTI/WxBO8AZA0QZDNITafTyOVywiQFAgH09joqFfZJ5jUmG0VQxSCW10Rls1VXb6l9PoQR6PEcmqahN+xFIuCGZQP78h1ATOkxk4nqcWqaJkA7VdfRNju9chmsc6/g66Uu32pDR7exE1939sIEPn/daXjnxQtlHyUTzvuW4J8KAiY0CEqZyFB7bRMosZc2j+m+Aw00TKDfDywKQ2qmKVUnOCJgVZ2QCXR4HqzBp2lePu/0Cu/t7UUymZSe2ezLTGM23hMEhiqjx+8zDAOJREJKW8ik855Ra285P4cyM0sV6+gN+zAc9+PaM4a65oLA9lixiOpgcnBxMuSoGVoW9udq8nvWYpN9VplU9dobhoH+gA63ZqNlaci3O88BPq9VszvOp/p53Ofp3WHbTjtHNUnDvYCAk10zuM4IwJn0ACB7DHtnXzjshq51J06YKOFzis8szhETJWrNMzsm5PN5AbL+KfNPsr5er1dKGnjv+f1+qfVn7/bp6hr1+vA5qPaqVj0bmHgmAOfPAUjCh4kSHvu37x9B07Rw9sI4nrOk52nXCGvjue8cSxLn5AbaU/0+D/XQfsMFC/GLd1+ID155/NuhzI1nd8QCHui6Bmz5LWC1HBl336rDvu+WzeM4kH/qll6HGuuHYwAOUaftjwMR5zOe3HAffnj/vtmcwtyYwfiP15yJF6ztxzffcq609Jr1eOzHwDeuBG78IDANYLDG+up1gwj7Zud2esb8GP77Tefg/159+HV3uKGa/qiyqeV9DtDele0E7XxdjwBtv2Te+WDS2nUMRpzgZdsJ3ImBUjugA/Ru2ZTC7zeOomXaIn2kCywBSiDguK1PTk5i3759YlTl8XgwMDCARYsWIRwOC8igORAlmLlcTkB2PB6HZXjxqXuLeGKiDa8BfOTiGK5Y2SuBIwP4fD4vIDuRSEhwxNrcYrEoYJ8Oq2QcWXPLQHp6LdgXbt2Oa750D75+974jdt4lUFSBJgMIgmXg0PJxwzCQqbRw7+48MpVml3EN2RkGREnDCczTLWeNkRlR2xhRZrhyqm/yptHjtw7v2zWJdKmJiM+FdXGIZNHr9YocFujIBNVaXrWGlefA612u1vD1bW48NmHBY2j46CVJXLTAL4mQZrMpwCsUCmF4eFhkzgzAydyRSSsUCtKmq6enB5FIBOFwGIFAQOp/Od9cK6zTJTBi8KmyY2p/dq4fst9Ah81OFev44u17kK00n3I+j/cwDAMr+p11sTvXFGaOAT+ALvBFcNfjMeGaAjzpakc9QbCgMtUEPmTD+HPVzwLoZlbJHqvgniCTtc+qHJaASA3W2Y6NjB6PiZ93xz7n3rxgQBOZNWuFfT6fqHQIZOjw3Gq1pEUhk66Um1O622w2EY/HMTAwIECSYIosLvtvk0Wkmz5BLyXLXFPValWYdKo8VMdptk/kNZueIFycDOK3778YP3nnc2Cbne4SqprkWAIcdRiGAa/bhcUJhwndmirL76a30AQ6yRf1ueNyuaBrwIB/Sj5e67RAU/cQfg6T3fwd540lK/V6XYAzk3687kzWqjXvTJJy7RL4MrlUbWt48IATC1w6v6Oe4OeGw2HxgvD7/V0qETLvLDvh9Z+cnOzyuIjH49IiDoDsVVyfhmFIq8xqtdq1jlV1zaEG96tgMChJNqBTv6+aznFPpIqI+ywVIZlyAz99xPGdeN8Vy552XVHxAqAL6B+rcVIDbRoEbR7rSHU4lvaGcNaCOILek1odPzeeYmweK+KJkUL3D1W38RmMb9+9BwDw2vMWdNdbP804Y0EMwCEYbUDqtH90w034yC+fQKHWmtFnzo2ZjYGoD//1xnPQc6SS0+03A796j/Nvd6DLkb7eMvGbx0YBzF42ro5jFSQcyhCN3RT25JpdmWTDMBDXawBs1OBB1TLkoUnm4p9fuBA3v/tsnDU/etBeeaIMBjYqc/Vvf9iGv/vNLtyysyj1tSqbzddOTk5iYmJCGJXBwUEMDAwgEomIOVG5XBZjNAKoiYkJ2LYtdWPFhol/vqeErVkTfhfw8Ut7cPHy3i6DJtZgA04AwMCDrOfExATK5TImJiZQLBahaZrUjDMwYh90BslqbfaBfA0/e3g/bABnLYgeEdAmE6XWPE7vUXqoEgV1fPDnm/CuH2/EwyMVkd0TBHBomoYelwMW0s0Oy8DgjyCUjNmypHOem44To22aJn7zhGOOefW6frSbdQkyyRCRCaQpHEEY0GGbKIMFnH7W9Xodj03a2Fl2we/S8I9X9OGceX4BJGT0LMtCIBDAwMCA1D9ynRLUM3gkWAaAaDQqsmLOF+WRsVhM2vmwVp7Xgm3+yGCSSScrr0p3mWji+jNNE9+4ZwRfvXMP/vonG47L9ZjJMAwDK/oItBtdQFRtg0ZWW1hD2OidYrXHG51aYdbF8r5hHSkAAZm/fDyNV339EXzjnn3ynv95eBQ7JyqybzKBQZCqMnW1Wk0YY5arEDjxWCmdzuVyIi9XTbUmazY2Zxzvh3OSHbDcaDREeuvzOfJ2ghgqb5hIYfKGc5TL5WRdh8NhDA4Odrlqs4SE55VIJBCNRoXZpBGWZVnIZrNS++33+7tcqvl/zhGBm5pAfCrpraZpGIx2nKw5t2pS6HgMrp+lU3vQ1vGyHA/3N/W1vFZUJfCZqus6BqeA9litY4hGUM39j4CS0mt1TRLY0TNDrY3mdWUJDlv6qV0q1OPh/BuGgbtHGmhbwKKoC/NC2kFKAZpv8nv4Oyo+1AQ+n2Gs449Go+jr64PP55NjYlIlk8kgm83C7XZLf281wUu1xWzk2GprMNaqk81WJeWqCRrLTdrtNr77wAHUWhZOH446itenGPRJAdBVInUsx0kNtJf0hmDoGgq1FlLF+rN9OHPjGRz//oeteMmX7sJ//2mn84NqFtj1R+ffM5CNb0kVce+uDAxdwxuepqXX9LF+ygtgT6aK3HQWoN8B2uf4nSza4yP5GX/u3Dh4WJaND/5kgwDgoxr7HwR+8ibAagOn/xlw5Se6gPbvn0yhVG9jXsyPCw4jMZo+vn33buzNVI7+GJUxnW3UNA3rhuP4z2sX4rvXLZaHOQMEF0xENOfBlkfH5ZWZ+KU9XkR93eD9RBuqpBdw7tEtqRJcOnD5sriwjGzpRdl1vV7vMpIaGBjoynIXCgXpL0yGhsZelmVJfWW6WMc/3VPBnqKFsEfDP1/RizMXxNBut8VFmJI59temu7lpmiiXyyKvo8EV6zKTyaSAbjJd/N10Nvurt+9Ey7Rx3sIozlvcM+vkDV2puXZUlkkdKrN7qLFqKpG9c7ImTP70WlVN09A7BbQLpgfVVrdcnICQ63BJwjmO4yUdb7Va2DTmBNDPXx4TYKUyZQyeyT7yZ3wd2WkGt7y2G/LOsV+9LIC1fV4B6ZQLUxVBmS5ZHa5BAF1golKpoN1uo6enR+r9WQvKOmUa+NHQiow35edAx/GZjGIsFpP9gdedDBrQYbOd+kXnWfX2S5Ycl+sxk6HrugDtnZlGFwOoSpEpySUwsW0b/azTrnW7PVPircphVcVMsdbCtnQFG0dLaDab2Jet4Z9u2oFrvnQPctWWsGdMfJBB5H6bz+elTzDl1DTQ4vqnozfBaiAQkOuk6zrunOqdvSIG9Aa7pdZkFQmMC4WC7Ffso0ypOhMqY2NjArqCwSD6+voQiUS69g+amlH+ywQf90Q6R1OBwvuC7wM6CiI6YXOOKEtW9weOZtvCd+7Zg0rD2eNVd2k1yXW82GygA7RZgrU/69wPXFeU6qv3Pev9+TwhkB5SDNHUNUfpOdcvVWVUUXA+aXCmJiP5vQDEjZuu5GpyVi0lIoBn68jb9zps9iULOmw2ZeK87ymvVj03VDYYgEjF2Q2D5QcE+Kqx39jYGLLZLDweD2KxGKLRqHRqYF2/6m0w28E9VvUKUJUhTOpyDbtcLpRqDfzkYSdufN8Vy59yXamlGIwfjsc4qYG2z21gaa+zQR/qwX3TxjH8/a824tF9uWf60ObGcRx7MxXcOtUH8Xmr+50fbrnRAVH964Dew5cLsDb7BWv7MS8282b0sYAHi5POmntsOpDuXwcAOM3tSJDn+mkf+bBtG/9042b84pED+OufPIaxQu3wb3qqMbEV+OF1QKsKLHs+8LIvA9OkQTRBe+XZw04ZwgzHptEiPv6bTbjyc39CqX7sFAyHYhuDPg9WD4TgdRsSGKj1ewnNefhNtn3yQFcdQvlZT8VgPttjumz8+kedB+X580Poj4dFAsegj5l4gtdEIiHy7Hw+j4mJCeRyORQKBTEdY50bA1gaqaVKLfzzfTWMVmwkfDr+6fIeLO1xHrqZTEaC12g0KkoCZurVVlkMelQncrbMYSAVi8WE/ThUbfb/PLgfAPCu5y6cNcNDBoSBHhnPQw01mXMolcPqIUdBsX2y1lW3p0rPNU1D0GUjqE3Vy9Z0Yf8ZKPL7a7UalsYMfPKlq/DF1541q/Oa6TBNEz9521n48dvOxZKwJewg1QQEujQXU2tE1XPinFAWOVGsY1vJuRaXzPcKWCHY8Hq9Un/d39+PQCAgEm/2IqZ01OfzoVAodMmDS6WSrE/VB4CyUZolkZ2k477aDz2ZTKK3t7dL/s4AU3UI5vr/1n0jaJo2zplB/eLxHLquY+VUGeDuXENACwN/Gi4REKllD70eJ/hO1TtAm0CGr1evMdfAwqjz+q3jjos3a/ovWBxDzO8ScETwpyoBGo0GJicnYdu2yPyZJFEZX7KErPHme/mau0acY7+gX+uql2WZA/dutv8jQFK/kzLicrncVZYSi8UQCoUO8rog2x0IBIS5pM8E0KlV5v5G9Y7KXHN/U40E+XlqWyQV3Fz/6AH8/a+fxMu/crfs40CnDOBQ9dzHenA9vHhdH3791rX4x2uWdf2cfa0J2AhSVbd5glcy2mzxxWutfh6VKQTYAMT9mwZnfIbTDAzotAEjoFWvDZ8hNONTy1JGSm1sm2zA0IDzB3SZV9UHhMkalqDw2Ak2gc464XpLJBJdZQosZ7FtG5lMRuqyE4kEEomEOOzzfuEaPFIQS9aex0OPAZ4fEyJUkdi2DZ9Lx/ffcib+8rKleP7qpzanVRUF0zt+HMtxUgNtAFg14CyAzWOlg353w+Nj+M69e3HfruwzfVhz4ziO7967F7YNXLqiF0vZgmkWbuP5ahO/fHSqpdeFi2f9/U9tiOYw2sOtPQDsQ8vL58aMxtfu3IVvTvXa/MyrTsdgdObJkK5RGAG+9wrHKG/eOcCrvwsY3Q/0A/ka7trh9NWcfe9sBxQ9f3XfrOu6n248lSEaH1piXuTv1IjGp+q0c3agi6lrtVooVmr48l0jeM//bES9eXDv5Gd7TG/rZVk2frXBaZf2vGURBINBkeeWSiWRylHOHYvF0NvbK8Yt7MnJWkXV5KZer0udWjQaxVjZwj/fX0O6ZqM/aOAfLoliKOQwgtlsFqZpIhQKCVOpsgI0u8nn8wKeyT6xRpJ9RHXdaeECQFqQTK9j/K8/7UTTtHDW/AjOXRiblYxtuulZMBh82lozzgdwaFZ7zVAMALBjstvJmtdJZVZ6puq0x+qdJJDqQkxQ6rFbeMlpfeL+eywHk0u6puGsBTHUpxgjtZ6UjvM02FPPnc61KrvtdrtRLBbxaFaHBQ2LwkCvz2HwGLRSxtvX14dkMikBWy6XEzMgguxwOCySW0rDmQhjAMxBVtXn8yEej8MwDPEnoHqCrDyZIyZxCFCBg2uzdV1Huljr1C8+76kZn2di6LqOJckAwj4XFsS8qLXtrr7PlHOqQBtwAEK/x9nLUnVDACwAYZbZQojsIpMNCyPOfbU/V0el0cYNG51yg2vW9snaYKKM64ES6mKxKNc0Ho/Dtm2pj2dyg8daKBQEcKjAaHu2jfGqDa8BnNnbOU8mggikyCLzfazXVl2+TdNEsVgUhRMNpdT+1WTWuTYI7qbLZpkcazab8jncp6jEobs9h1rCNB2wA07ryy/fvgOA05JTbUXFcbyYxOnDMAzEAm70BN1d30+gTzaaCTeuKaoUuPcNBpy/800N1anHKYEy15ua6OG8cO64d1BqTQBOpQFZWiqpuPfy99xD1GTmn6bq/c8a8sGHVpcag4CeyRm1vlldA0CnjRefIWSkgY7pHfcsekz09/cjFovJ85DqGqoIjsZJnvcBz51ScV43mpixnI6/WzkYxYdeuOop9za+D8BBZVXHepz0QHv1IIH2wYz20/1ubpyco9Jo4ydTjI/0va5mgV23O/9ec/j67P95cD/qLQtrBiM4d1H8sK+fPigfP4ixTq4AdBe87TKGkMGG/fkTth72RB6/fHQEn/ztFgDAR160CteeeYTt0qpZ4PuvdJzgkyuA1/8U8AQPetkvHh6BbQMXLElgfmLmbZSabQu/2sC67qPrnT19qKYqqkRq22QDn70zhR88mhHmpOM87jDaWavjoEpWu1Wv4vonJvGnHVnsnCgf4huf3TG9rdcD/z97bx4nV1lmj597b+17753OvpOQkISEBAgIyOIuogIKCIgyIDguM87i8lNHR+c74zLOKDojCgKCCrK7DKIiSwJZIAnZ963Te3d17eu99/fHrfPWe6urO92dTujGPJ9PPkm6qqtu1X3ve5/znPOc51Af2mNZ+J0qVs8Mi5trPB4X8m/exAlQyNrzBsoqtWw2RqMyJsW9hhffXJdBNGtiatiJr11cg6BqgR4ZSDU1NaGmpkZIRnlTjkaj6O7uRiwWQ3t7u/i3aZqiT5eJEx2gyZrQQZbRlcgKE8XbL5w+bPfdoUzPjhdD9WnTA6U7mUdfKj+gKMDCj6qqqC/Jx7vzdjdYeSarPF/4ZKgqUpkcCrqVXHLsEgssQLkPlICVxRKCGCba/B3KOZPJJDb1W0DgnIayySClhoFAAA0NDQgGg4IpSiQSiMViYvQWJd1OpxOpVEq0ERBoE9hz3bLA5vV6hWqCAJuFJNm4qLGxEXV1dYLx4mfhOahks+9fdwzZooElU8J4y9z6MT8XIw2v24k1f3cefvSBOQi4y4ZkQNmoSi468b7aVJqo0F9QkSqUGTpZCiv3zvLaCzhN1PkdMAE8urkDR6JZeJ0q3jqvTowJIiCRe2cNw0A0GhX7h8/ns4EL/g4jlUrZ2ETAujaeL8nGz25Q4NYgQIlsmEagxN56snlkILm/y+0R7OsOBoO2a5WqBxYNWRCQC3Myu01Gl9cMizjsf2VBgGBSZusrZeNPv96Gw71p1PicuH7VdBubzb1hNJLi0QSvayofZFaXEnH5Z1xH3IupTPE5FNS4LKBOfwDew+SCj8w8AxD7NN+fhS+yxGxNIpCVr3Oef6DsJC7OkarhuYPW+rqgxSHAMn+X15Bsysfj43sAED3aPL8cM8bPzuIei0umaYo2GTLP/L5kQD9aJ3m+D4E0fSxYJKGsnHupoiiIp8v3wcGCygzAPlFjJMHzPZyY2EA7GxNjvHZ1DGS0F4jHTgPtN0s89lorErkiZtb7cdHcksHBzqcBUweaFwP1Q8/KK+oG7n/Zko3fPIyRXtViaWl+9gAg7XABdXMBAAu1o+hJ5nGs/wQkz3+F8cKebvzDI68DAD52wUzceuEoewfzaeCha4HuXUCwBbjhMcA3cE66aZr49WucnT0ysPznXV3oS+XRGHTjwpOQrFYD2n1ZHb/d1Y/nDyZEUkUmpFax1lq/6UG+aN2IKH/L5XKYXXdyjahOJGTXX8CSGgLAhTODCAd84nMkEgkBKGWDFyYDPT09tl5UmqkEg0Houi4Yak3TkHDV4ZsvpxDPm5gZceCL5/qgJ3pFAqmqKgKBAGpqrOudIDqdTiOTyQgDGIJvwBq35PV60dLSgrq6OtTV1Qk2gayWrutiNIqckO7rTMLv0rBkcgjnzogMS0o5HNOzoWKoPu2A2yHGcR3oy4oEjABUZm1qNWvtdebLDCKTTybxBCSHelK4d80hcY7HKh55tRVv/a9XcO/LR4VigYkej5lztGV2kUFgw+fT6floQkd71gFNMbGsVrc9XldXh3A4DJ/PJ5LAZDIp2GyaUjEZjcfjYqZyKBQSrKQsfZQBDCXvHONFBpstCZFIBLW1tUIyWclmA7DNzXY6neiJZ/DLYfQvnsqQPy+l+7KMnr3a/BnPlVs1EHZYCW9nVhPgiQoZMtoyqw1Ye8eckvv0d/9kzXW+dH49nIph+11ZNu73+xGLxcQ89HA4LMALAQzXBh2juQa57gzDQNFUsLHTut5WllStZItl13F+doJ4nuNsNisKVnJvL1sdvF6vjc2W3dBpuOZ0Om2yWXpdyACGBScWlAhOPB6P+OxAeV2RFZVl47ph4gd/ttjsj184C24NovjL3z9VbDZQLij8bmcvPvv4Hvxue5dYE1xfsvqJa4efSd7bWkqsdnumzH4LVU3p98kYc9/nd0vALzvFu1wuoXiiPJ/nmRJsFkDk1inTNLG9p4jedBFBt4oFEd2mouB9Uoy3K60rHgsLfWxjoukoANEXXigU0NvbKwozZJhZaJQLDSxa8N+jcZJnwTyRSIjPSoWWzGZXmqDFUlm864cb8KWndyOZr+49Qr8QoNzvPZogUB9OTGygfegl4cR7oDuJbMFeJSejvb87NeCx0zHxwjBM/GztIQDATedNL/fSjsBt/I87u3CsP4NavwvvXdIyquNYMCkIl6Yimi7gaF8FkC4Zol0Ytnq+TsvHhx+He1P4xM9fRdEw8Z4lLfjiOxeMLgnUC8AjNwOt6wFPBPjIY0CkOojecCiKw71p+F0a3rG4eURv8+uSbPyqsyfDMdqZ3kNEJQhSVRVnluS8R/pzKBplRktVVfiVPFwowoSKftM7wHmcPce7OpLjyhBNNili4nGwp2RoNSeEQCAgDMnomMvnKYqCSCQCwzDQ398vTM/Y00rGtVgsoqurS7A1mdBUfGtjDukiMK/WgX9a6UUu3iuSCvZas5c3mUyir69PJNk0P+I4pWDQ6iEPh8Oor69HXV2deC2CJ34+9khWVvnPn1OPP332AvzblfPFcQ8VZN2PZ3o2VFSa7lUGW7P29WRtplRMOHmcNETrLbpRLOoi0ZQdcXXdGgX02pEovvH73WM6AtE0Tfxmawf6M5aLM4sP7M/meuf8WSagHLXFhJUJML/7eDyO1/qsc7cgbMDvhGA3aWJGxQKLHmxvyOfzCAQCwsAsHo+jra0N+Xxe9NkmEglkMhkh9eUIMiaXPMc02mLfLM2JeP4oNWWSK0s9mWALY7ViEe86sxFLp0Zw6RD9i6cy+H1rmgbdMG3zc2UjJVk6zjXGedpsWwAgGGGCX55n+igoioIZNdZ51Uu1lnee2SCYYoIa2YDJ5XIhFoshk8mIXmnZOZqFMwItzjXmKCQC+I3t1r5T61EwL1JmEVlMIGOsqqpYR/y8bEnh8cmsIVk9Ah9+D/F4XHy3BMUy8PN4PAIks1DDtcbfoacFAPGeLHhSJcHjloHz77e1Y393CiGPAzeeN5DNlpUXpyJ4bR/qy2HNwRg2HS3PfeY6415BhQnXA+8jACqAdpkFJ6PLQi33Stkjhd8XP39/fz8A6zyEQiHB4LL9iYUOFo3YZiIrAmiCduE0H8xiQRRI+FmCwaAYvcXjYhGHhTu32y3YdFHIKplGclIHVRHcL2m8WFmYAcrqtOECWXorsKBIk1MAopAJlJlkqj343WmahgfXHUFPKo9NrXH4XQNZatn8jJ9vNDFSVdbEBtrtr6Mx6EaNzwnDBPZ22iWRzSEPwl4ndMPEvq7xJ5c8HSOLtlgG6byOgNuBD7CXNtUDHHzB+vcw3MZ/ttbq+/3wyqnDHulVGW6HJoyCNh2tMNor9Wm/szGKJ+5cjcsXNo3qPf4aY2qNDzecOx3nz67Dt68+a0SmZCJME3jqU8DeZwCHF7juYaBxwaBPf2SjBZbfddakEc3m7k7k8NzubgBjLxtnVANB0+r88LtUFA3gWLwobsLWDVQR8vGoWZbAs+duRtj6fLs7xxfQrhzrpSgK7rlhCX76wZlYNiUo5LWJRELI1pgcMdlMJpNob29HPp9HKBQSc22ZAPX09CCRSEBRFPS4mvHt9WnkdODMegf+frkbxXRcVN89Hg/i8bgwuorH4yLRCAaDCAaDwmSLs49phKRpGiKRiAB6ZNzJPJE5qJSYMpyKgak13uMmJ7qu2+bdyqYzIwm5mFOtzeX6c6fj6++ej4vnWmoQAg5ZGqlpGmqdRWgwUDBV9ObtbI7MCGWzWUwNWr+7oz0Owxib1pqD3XG8djQOBcDFswKCNePxkVmk1JYMsmxUxMSQibVhGEim0thSchs/uyYvXOI5bouJGhPgTCYjemFpgOXz+ZDNZgUjpCgKQqGQMPXTNA21tbViHfO8EqzxWP1+P+rq6tDY2CgcrBkEOjw/DMo7aWRXLBZR53fhX95zBh79xPnjgs0GrGt/V0cSH7p/O25//JCNhSbjSuAn984CEECbfdoMFtXIgskGfYqiYHZN+Rqr87uwYmrQBqzkEUVer1f027PPn98n2T1+Dr6fbN5EdYOiKHi5zdrPz5ukwSzJh+UiGYG0PNqJLQcARNFB7uU2TVO0osjjyOhsz+IQUJZEAxB7K78bghdKjeUZ0nxvj8dj6/mXvQ3kfc2Q2OyPrp4Jn7PM7vI8nko2m59d0zTMbbDuj3u6krafy/sui7k83/w/98oWr3Ue5RFfspxYVshw/BnVJ9wHaBxG0zHuI/l8XhgkUqHAdc82CIL4dMHA2iPW2ji3CaKQS8DPc8K1TUk5ZdemaYo1aJqmuMdyMgf3S96b+Rlp8slWBxYmuI55fofaY/h5U6mUzU+F68TtdiMYDIoJC/J+zb2cxaBMvoh7SibHd1w0uyr5QdWGLDUfTYyEzQaAiT1kumMLFEXBgkkhrN3fi53tcSwu9c8CKD0WxCsH+rCzPY5Fk8NDvNjpGO8xpcaHF/7xEuzpTJSNpygbn7QEqJs95O/vbI/jlQN9Ix7pVS2WTY1gy9F+bD7ajyuXSj3ETWcCABrS+9BQMk07HcMLVVXw+XcuQL5owOUYZQ3w2S8DWx4CFA24+mfAtFWDPjWVK+K3Wy1DoKtXjAws7+qIw+fUMKcpgDmNY2/sBJRZHrlXzuFwYHadF6+3p3AgmkeTRxNyQACoVTLoQAg9RTcMIy5u/oVCAVMj1uvt7krZ3KDf6Kgc6wVYAGF6xAW/z0oOCXjlajvZPbLdTGZCoZAwlnE4HIjFYujo6EChUMBRpQEP7spBN4GljRo+foYJFHO2ueRkxGWDIiYjTqcTyWTSluj09PQglUrB6XQKQxgAIhln8gCU2VA5wYym8lh/qA+XzK2z9coNFrJJkmyeM5qQ5YfV1sRF8xqQmRoQiRATK5nVVlUVmqqgVsuhW/eiI6thSri8dumaTaasxW3AqSlI5opojWYwrW74vgiDxZN0qJ9ZA5eeQa4kq2WySeddXgtyoYkJHRktFkx6e3uxK2oiUVThd5g4I2x9XiZ+cp8nTXkIeNkLy5aGdDot5Oy1tVbRgmCF46EIsinJJFCkwRUTWwC2hFzu5yWDz89FoMhElQDL6XRCG00h8ySFpmmo8TlxsDcDVbH8LwiIZaAt984zSZZHfPFcsNBCpqsSACmKgvOmePDqP5yLQDiCHUd6oBfyYpwTTZVY8CCbTTMp9maThSOgYC8plQTBYFCwv4qioC9dwPZSbX5FvQXUwuGwAM1UJRiGIYosAASLTkkwQS2P0TCs+e3BYFB8L1TjsIBINpOvSfdmWdIszwEnyCarSEDDzwZY7Cy/a/Yc816UyhcxuzGAY/0Z3LJ6pgB1LByMRlI8FmEH2mkBXPm5gfLMdACiYELzS+6Xk0p+b+1pSxWhKWVTT96veb1SReN2u4V/BO/NhmEIl3gW2SgbByD2GlnKzs+RTqexrq2IXNHEtIgLza4cDEMTxWBd10UhmOuTezH3EBbhWMyRpeRAGbhTzcEWHO43BOX8fCz48V5RGVwv3CflYLGTn4/rnT+TcwW2VLAf/Gcv7ENvqoCWsBsfqJLP0XsBwAndM3n8I4kJz2jDNMvO41V6sfnYkdLMvNMxscOpqTizRSqYjEA2fl9Jdv72Rc2jd7EuxZKpgxiilYA2evYAxZFVvf4aI5Ur4tvP7La1dowaZK/9PrD2v61/v/f7wPy3D/n0321tRzqvY2a9Hyumj8wU78K5DVj/xcvwn9csHd2xDiPkG7Xcpz230UoSDvUXRGWW0jbZEI03ZVZ+m7wmNBWIZYo4Fh0/+6EsG8/kdcTTuQEzW+PxuJBJ86YrsyuJRAKaptncfRVFQSqVwqFDh5DJZLArF8ED+5zQTWBVs4Zb5upQUQYoTEYdDgfC4bAYa8I/NI6hlDyRSODYsWOIRqNQFAVNTU22Kn8oFLL19gH2XkzGT186iNseeBV//8gWALCNZaoMsuz8/D6f74Sll0P1afNxJmZMyBhkggCgjn3aOYcA7QQiLBLlcjnohTzmlGbZjoVfgGEYeOp1q2D2rjMbBADlcTJpJsjg8cizV3nOCFgNw5pF/lrUeo0lkQLcTgto1NbWCtaSSSnfjyZGZEQ9Hg90XUdPT49oMwiFQqJ/lwUjgmz+jHLiUCiEpqYm0RNL52z6AsgMDftzGWSzKTuNZ/L45yd2YGdHctwU2RiKoqAp5EbE64BhAkfjRQESAdhANoNgpsljJb1dOQ0GytJyggtZucB2BoKhTCYDp6pgesQuE6e7Nlm5YrGIZDIppLycSZzJZETRTTYxkwsfBLOFQgHrOgwYJjA7oqHOWRR7jdfrFX2pBNDs/WYLEAAxo5jggo/7fD7BSvKz0zSSIJ5MIVAGNPLoM7nvm2s5Go0KA69isYju7m709fWJdcWCBH9PBkpBjxN3XXc2XvrHtyLo0USRa6SS4rEOTdMwq8EPh6ogldfRHi/LvXkP4PqgKoe/xwKjaZqodZtwqyaKpoKenCqKCHIRkuCdzDUAMfpRVj1w3jmN7/r7+0XRh2tDXlssCJqmKWTjF03zCAacex2VDvx9qiF4TDxvXq8XhUIB/f39onDE80llB9c/C9JlJV15bjgA8bdcTOa+Ra8J2fGbBRya9Mk92DLIBsqFQgC2lphcUcfdLx4CANz2lplwVrDZvLZ4XKMxP2NwnxjJHjqxgXYuDkQPCtOzau7id1w8G69+6TL8/RXzT/XRnY4xjB1tcRT1ikQw2Q0cetH693Fk49FUHo+XzHc+ev6MEz6epVMtYLatLS6MpwAA4amAOwQYRTy3di2+8PjW020Lg0RBN3DnQ6/hB8/tw2d+ufnEXmzLL4E/fMn692X/Aiy7/ri/wtnZH1w+ZVSVda9Lw4z6gS7mYxmVQFvTNJzRZO13B3pzIukjOOOIrz7DJ2S5TLD0fBbTI274XRpaxwnQJgMAWJ/tyc3HsOrf/oy7X2kX/eeZTEbMieX3wMfYmy3PMGUPdz6fx9GjR5FOp7E5HcGjrT6YAN4yxYEb5uhwaJbBCmWbZMAjkYio1JM9ltlD+bg4BmfKlClCMi47vZK1oCMxzesYsXRB+E5cOr9OfLbKICjgTZ4S0bFghI7Xp721LYGHX+tAd7IgCgdMrpiMORwO4TzemXPaTKe4/pjsZzIZzKm3AMFYAO3Xj0ZxsDcDt0PF+dP8NqaEckYmprL0kOeFjB8Ace6y2Sz6U1nsSljJ4rJaCyBQ4k2vACbWnCFMsExTIdO0Rmslk1a7Rm1tLXK5HGKxGHK5nJB48vV8Ph/C4TCCwSAaGhpEDySTVAJyuffd5XKhtrbWNoaHkmagbGh035qDeHprF/7piV2o0iXwhoemaZjXaO2nB6N5wTQCZdMi+TyRGQ2rBbgUy2SsL19mu3l+ObZK9goAykZQHJXEeegECHI7SC6XE8Cbey3BgwzAKNHN5/OinYOS2GKxiHXWFDGc22xdt9x/CNJZpJHdqWUwxs/D/Y1gi2w2ADGuiUBNZmYJuEzTFAwlAXV/f7/4zjKZDGKxmG1Os+wHIftS8HUJ6Csj7Cs7+3MfOJ6k+GSGpmlwOx2YWTLD29+bFWuNQJStJlTD8HuXVWaqArSUbv90HpcBMVlorkX2XMuzsQmEuX+woMP7CAu3fA1ZnZDNZtGTMbGtMwsFwIp6qwAQCATEnsvCKOXfVGrJTvwsYslu+oFAQAD8QqGAWCwmns98w+crK5F4f+P3Vllg4Nx1OY+hkRqNQenhwccr72/yfs21z33hkQ1H0ZnIoTHowjXnTLOd78rWh9E6oPO1CPZH8joTG2gDQNsmYXq2qyMxoM+sMeRBXeDU9oGcjrGNZK6Ia/73ZVz4H8/hqKxM2PkUYBpAyzKgduh52L/ccBS5ooFFk0NYPkL2slrMqPMh7HUiXzSwW3a8VxTRE7xj88t4aN0RrDvYe8Lv92YL0zTxz49uxV92d8PjVHHbRaN0FweAvc8CT95p/fu8TwKrP33cXznSm8a6g31QFOCqEY4Pa42mq/bQGs6WAAEAAElEQVSznoyoZBsVRRGTFpKFctLCfqOIkoECEzk4kNTLlXk6j3/rHVPwpzuWYtmU0Cn7DENF5VivxzcdQ6ZgwK2Vx61wnJGu6zbQ6na7BcNLcyImRIqiIBqNIhaLYU00gN93WtLZK6ZruG6OCQWmcCRnYs1+OgAi6aFDNUd6hcNhBAIB4ULc0tKCmTNnoqmpSfwOk28mS/yMTChkIH3PmoNI5oqY3xTAJfPqBrB2QNn0jK8j9waPRRwPaH/jd7vwzT/sx9bOjADVMovO/9eXZmn3FN3CVZhghGABsL7bWbVWkrKj7cSBNguol8yrAwoZca1UmhKR1WDCT9kmzwlZd1VVEYvFsLlXQcFU0Ogx0OIuCtaFQFfXrRFtBGLxeFysRb/fLxLRaDQKwzDEmC6y0YFAAC6XC319fTAMA6FQSDjVRyIR0S9ZmaSycMBEtXJMHABbn6Xb7UY6X8S9pf7F2y+aOTr/i5McqqpiXqkNZ39fboB6RT5P3NcAQNNUNEiGaHxM7rcGYGMbgTKLS5mu3JstJ/yKoogiH1lPAKKgQwaUQbDNfYiy4WMpBa0pwKECS2us64OGemR7WSikSoLXkVwAILAnoGbxjuCbY+XIimcyGQGiWJCkfBmAzTWdbUiyCz7fl+u/sbERNTU1QkrNogcBlmmauOu5fTjca/UNcw8giKvshT7VwT12dqnYt6czZWtHImDkfsDCBPcRgj3TNIUhGv0BeN74PvybrQC8ngnEaZbHfmjK/bkW2HoivycLR7lcDmuOWfeEZZN98JhZUcylNNvv99uuBUq+CaB5jNyjVVVFOByG3+8X649rha0YLpdLtKLIBVVer2xnoAeFrMZjGwzNQHl901QQsI8Yk0P2cpGLiADw83XW3vax86fD6yqvLdM0hcRc/j5HGzLbPhJW/E0BtOc0BqCpCvrTBXTEs8f/ndMxoeLRV1uRzBXhdWmYHJEk38OUjRd1Aw+8fAgAcPP5M8ekkqooCpaUerA3D2KIttxj9Q0OkJefDnz7D7vx6Gut0FQFd113NpZNG2Xx4+gG4OEbAaMInHUtcPnXrWLHcYKO4RfMqUdLZPhtBNmCjnf+14u47LvPn5LRbZUgSFEULJ4cxm9uWYAfXTVLyNPEHFbFRFix9sCo6RNJJZMyr1bu8RoPhmiylPFYfwbrDvYBAN46OygYa7ous4pNuTwdUdkbSGZIURT09fXh2LE2/LHbj+d6rcLEe2c78P6Z1uemGzTZSXkWJwAhO+deQSdxspT8zgmMZIO2mpoakbAzISALLgOieLaAe9ZY5oy3XTANahU5ZTXTs7FOUmWWptqaOKNUyD4YzYtkU2YWyXA3OK0EM2E4kcyVmQsmeTzuTCaDaUHrPcdi9Ob7lzThY+dPxfsWNwjAJLPuLA7wMSbDMrBmMs2+x0wmg01R6zMuqynA6XQIdolgJRQKifdiKwEBM0fRcO4sXz+RSCCRSIi1SmDu8/kwefJkAcYHY4DIJlG6y+RVDpkZYn/nz18+hL50AZMjHlx19skxbzzRsDHafTmbrJlMsjzii48BZUO09kx5xJfMYhPwEhAAZQDEYh33FNM0be0OZMQIxvi7LNTIfeNkeOV1RcCyods61iX1KpymJfENh8M2p3muUwIbmj253W7xMzqAcwoDQW4mk0F/f78Aazwm2cHd6/WK74TSb9O05jcTQHNvk/vinU4nvF6vTTUBwMZ48xyu3d+Lbz2zG+/4rxeRzJU9EXicp9oArVo4HA7MbfDB51SRLZYLjLJPAwsHAGzqCgADgDb9AfhcfidcQ1x/vb29Yh9iSweZYxZT+bjc+sL3YyGALSPPHSrPzi4UCqJ4l8lkoGmakI2ztUVepwAEi8+CSTgcthV+6CtBlZjf7xfTPOQ+ZbqkV7Y68F7h9/tFQbCy1YlrH4D4PipzdLlgzfVEybmiKPjZjUvxmUtm4sMr7Xsb91B6o5xI7s+CETAyNht4UwDtzfA4NcxusDboXe0D52n/9KWDuOme9XjlwGlmcaKFYZiit/rm82eUK/GJTuDwGuvfx5GNP7ujE22xLOr8Lrz7rEljdmxLS8Z7m4/G7A+U+rRnm0dKj/eP2Xu+GeK+tYdw13P7AQD/dtViXLpglM7s3buBh64GCmlgzmXAlXcBw+hXNQwTj75msWAjNUF7dkcn4tkiMnkdzaETq44OJyoN0QDA43Kixu8WjzOBEoZopT7tXsMrkkr2g1HmNxioOpXBSjtgJThPbbYKU0tbfJhc4xP912QQ6XzKRJCVbSZxBMzRaBStx9rw23Yv1katyvu18114z4zybGwaVVHO5/f7UVNTA6/XK6TqTGrq6+sFYGEPHeWanEfb3t4u+sTJKpBJ4/mpZLPvW3MIiWwRcxsDVWXjlN0xaZNN78YyZC+AamuCirEDvWV5vsxe8fe9DiCoWolIZ94pqv6y0zCBxLSAiQduWoJnPnPhCR27ruuYVe/Dpy+egcWNLsEyEpjJihAmmFxLAARYJcimEqE9nsfhjAsKTCyN5MX4LXlWMJPxRCIhRvSEw2HhSJ7L5dDV1SXG6jDZBiAMiJgANjc3iwLAUAwQJaByga0yeaRTNUFNtqDj7hetgs7fXDAdLsfYr6GxCFVVMa/JyuP29+Zs8lag3DstM4s8b01uKwnvyKriuyHIJNBhoQ6AMEskGJf7YZmcc20TPMhuz0z8CTgIqsmA0hSMjsoGFGywJn5iVaO13wWDQZsigsdH0MK9ieuEChleT5S6E1zJwIej4sh0RyIR1NXVCYaaoJmAnPshi3r0uOB54Xglea1RnkxQyH3gv/+0FwBw9fIp8Ls0G5stg9c3MjRNw7XLmvDnT56NOy6YKoAsj48FGbkVg9+l3Jfc4rX2y2NpiJ9xr5FNCunpQGUW1xHbCyoVBjKDzvYbnjsW0g4kVLQnCvA5VSyuKRdiuZ7JDMuFJPpQ8PV5DckybAL5eDwuCt18bQJm2fgxlUoJY0cAoqDM53OPrRaysR6L0dVCvh65d3PvMwwDfqeKj50/FUFf+feZ7/CYTtTLRC5YjdTj4k0BtGEYwvSsWs/XpiNRPL+n+zTgmYDxwt5uHOhJIeh24P1nTyk/QNn45OVAzdAO4veWgPp1q6aNeqRXtVg6LQJgcEa7NmmNttjblUQyNzKXwjdr/H5rO7769HYAwN9fPg/XnDNKdiXWCjzwfiATBSavAK65H9CGx/S9fKAXx/ozCHkcuGKE49ceKfV1f2D5lFPi2juYIRoBGRMfmuMoioJaxWKzevXyjYjJWb6o40u/P4R3/2gD4uk31qyvcqzXE5us7/bSOSFxY2R/K9kcXdcFaGUCwaQwm82iv78frW3tePSoBxvjASgAPrrIg7fPcAiQ7ff7BRspO5UXCgW0tbUJmSgr8YBlYMNecHlskGma6OzsFM7aZKj4+eQeXrkKnswV8ZOXLPBz+4XToUrMB3ByTM+GiqHk4wuaLUXAvp6MLSFjyKxNXUk+3plz2kZqERwS3Oj5LM5s8sGtndg1xDUky8IpgSTgknsSyRbyWHjcTKoVRUEikcCmkgna7KCBkENHMBgUTDIVFJQlyiO0IpGIcJ0+cuSIcGqXizo0rqK5HPuwATu4rmSAyCwRfFVLHuV+RI4E+tWGo+hO5tEccuODJ2kU4ViEqqqYXe/D/EY/Vk71QzcVG+AjcOQ547lQFAVNbo74ctgAhGwAxX1QlrmyH5mvS8VCpQGTDLrk4hFQ9iHg+uBn4Wvruo49MRXxAhB0AfNDutgrOJWAwJ8giaMI2cMqF05oEOlyuRAMBtHc3CxMFql6IIDj88j88ZjdbjdisZi4ntkSwXYZ2bBssAKfbEzFAuj6g31Yd7APTk3BbRfNtrn8jxc2GygZcLkcUFBuMZHHAcoScT4GlGe3c+01ew0oMBHPK0gWFZtiQi4iyy0ELMQAZbPPZDIp1o78HPn+LwpnpWLvi63W/fvCmQEYhaxYG7xvBINBm6JBNkrkGpZd1LmfFAoF0U4hnztKytn6QiDL43a73aLQOBzDMbmVgWt0sOBn4D2bwL83WS6ayq1fVPDxtU/U/PFE2GxgogNtzQPkE0DfflufdmXwsWpmaadjfAeNgq5eMRUBt3SxbH/C+vs4svHtbTGsP9gHh6rg+lUnNtKrMpZMiQAA9nenEMuUbzposoC2lmjFvLAB0wReb+0f0/eeqFEfdCPoduD6VdPwybfOGd2LpPuAn38AiLcC9fOA6x8BXMM3JePs7PcubRlR4aU9lsGLe63Z2R9cPuU4zx67qATamqZhw9EkPvvUIfzwlW6RyBOwCkZb99gSznw+D72Qx47ONI5Es9jZHhv0PU9FyP3ZO9vj2N2ZhFNV8JYZQduMWv4ByrM53W63YAeY6BYKBfRGY3jogAuvJ3xQYeL2ZT68fW5AfEdMLCnjIzhLJBLo6ekRDFg4HBYmUrJTNcE6k9lEIgFVVREMBjF58mTBUMngjRV++WbfGc9iaq0Xsxr8uExis5mcnwzTs6Gico3JMb8EtLuSecRzhlhn/DxkFQGIPu2OXFliy/NDkzCCwWrjXUYS6XwR//joVry4rw+5klkdUGav+X3KDrvs1yOIkHslVVUtycaz2BKzAMHZNQXRk8hki1JfJqUsIhAwZ7NZdHZ2ijm49BJg0YWAkYUcsoVDySsBCOMq9l1XSx7JSAo2q6jjR89b6qGPnTcVPs/ojYBOdiiKAq/LgV/fuhxfvmI63E7N1kcqG+/JbKuqqmh0FQFYo9hSxTLYkfvwyULTWEoGWPz+CYZkYzPZsJGy9UpTJJqBVTKYNFBbV5KNn9OgwOmwmMxQKCQcnbm/sSeWBYKmpiaxt5MB597CcYJkIAGInwMQa50gXJbnElQriiJc8Al8+H5er3fQWcMsaPEc8Px8/88Wm/3B5VPREvHaJgAMtq7fiJAN7Livc7+Wi44s1sk927JKRjUKqC/hw/Z0GeQBGLBmeB9moZzS/Hg8Lu5LLLTIihw+xgkGqVQKeR146bB1nz+vSRH911Q+OBwOMeIrnU6L+498bHJvvczkJxIJ0e7CQhdl7rLxKJUWmqYJFY8M5ocKeXSd7ANQLWTZOH/HWpcqrv3xK7j27g041Ju2Se1lj4WxKO6woMA1MNIYH6t+tNG8yPq7bZMwCKoGphcShFeRlZ+O8RsHe1L4y+5uKApw43kSSE50SLLxK4d8DcrO37F4EprDYyv1rQu4MbXW2li2tkqgxVsDhCyDrbc3WD2nWyrl5X+lcc6MWvz2Uxfia1cuGh14yKeBh64FuncBwRbghscAX+2wfz2eLeD32zoAYMTszmOvHYNpAitn1GJ63cl1G5ej0hBNVVUUTQWb29N4vSMNTdNs0j4C7ZjpRk4vm/TQHGdmjZVs76xSlDyVIRcOnigZWp03I4iI3y0SQ7k/mzc5StHkn2cyGRzr6MJPdqnYmfLCoQCfOSeIS2cHBVtgmqYwh6GzK9+fjHRjY6MwPKOjMxMJ/qGJGhNyt9st5mdT+su/yUpVzoyd3RDA05+8AA98dAVUpaxcOJmmZ0NF5RqTI+hxin3uSKw8foogGoBIHOscNETz2Po3CUjZ/5jP57HlSB++9ptd+OFf9o3qmP+wvQNPvt6Jbz6zD8USu0JmUD5GBo+B4JvJJcEw18XBhInevAaXamJhKC9k20xM5eJHMpkUc2MJPuiET6abYE1RFNTW1oqk1e/3o7m5eUhwLR871+tg68IwrJFkQJnNBoCPnjsVC5sDuHrF5JNesDnRkHuggXJvLM9ZJWAjUHKpJmoc1nXTllFFUUMG2gAEa8nzxGuaxQ+aN/H3CTaYZMtuygRq8nXAf5M9zmQyyJkaXi91La5sLDPI3K8zmYxgBzlGyeFwoK6uTozwkoFZKpUSUuZAICCKhbLxG1tqKOGV1TEyEOHvc9+hvNjv9w8JKGQHaJ6LbW0JvLi3B5qq4BMlNpsFJo6EGi9BIPuz9e246u5NePL1Tpt0nE7d3Ce4J8uqBp7zyX7r7+5CeY/g9S6vB6AMcBXFmnjBAgfBLB3qK4tJ3DPIJL/eB6QLBiaFXJjuL4pCDP0AqGygxJvFE35uWc5fqdCpNNJTFEUYjVKlROWOPOJrOHPRufZkSffxGGJ+93Jxx+/34/+2d2BfVxIHetOo87tsa5/f8XCB//FCLqqNZg+d2EB70lnW322bBJg+0J20zeQFIED4/u4kcsXRV9BPx6mNP+20ZmFcMr/RPkZpx1MATGDKOUBkWvVfBtCXyuOJUt/nzaMc6fXYa6149/dftLudS8ExX4PJx8/xWfNdj46TcUpvRLT1Z2wFsKm1vtHJrvUC8MjNQOt6wBMBPvIYEBkZWL7ruX3IFQ3MbQxgyZTw8X+hFKZpCib8gytOHZsNVDdEO6PEMh6O5qCbijARUVUVXqUILwoAFERL87QBCCA4M2LdkHZ1lOVqpzpklkjTNNxw7jR88sKpeO+CiJCQZTIZcVNmXxkl2Bx/A1gStL54Cj/d58G+tBtOFfjH88M4b5oPsVhMJCoEvABEb2JNTQ2CwSDq6urQ1NQEr9crWFeCJwIb+QZLmTqTFBkgkO2lo2zl7GmGoiio8ZQlwyfb9GyokL0AqhqiNZcN0Qg2KhMkVVXRUBrx1Vd0IV8oCtArz9Al8D7Sm8SDG1rx29IM7JEG3cbfdkatYF4ItHnumCSzr5HAjcmv3I6hqpbbOE3QFoWL8DisJJP9tixoqWrZ6IyJMddJe3s7uru7kc1mBXPt9XpRW1srQIzf70dTU9Ow+lVN0xQsJ4FTtWRPNuxigul2aLj+nBb88pZlCHhPvqfEiYYoNqga+tLlfnug3KIg93zKvaw0ROvIlqW/bDnhWpUBMoNsIfdHWU4LYIB5FFAe/UWWkOuNx6PrOhKJBHRdx+ZeBUUDaPEBc+rcQo7Nflpe93QMZ+9ubW0t0um0WM80z+Nap2+EvIbJ1hOcBINBm+sy23G4l1ImzH2Ms9iPByZk92V+N3f95QAA4H1LJ2Nanc/WZvNGjvMaLJxOJ+JZHYejWezsSAilAvfrSkd57s1yq4xhGJhi2YCgPVsuVrLAA5RBvWmaSKVSgqlmuxMAsf5iMYuQke8h8kgqFlBeOGLts2+d6UchnxeFDLnnXi4sslAIlF3xZYM0VbVGCPb29iKRSIiCE1+LLuN+vx/BYFC0BBF48zMOFQTyciF5OPc4rjVZ5eVwOPD9P1sF2utXtKAm4BH7P19/rJRgzD+G8xkHi4kNtJvLQLsx6EaNzwnDBPZ22ucWN4c8iPicKBrmgMdOx/iNj184C099cjU+VzkDfZhu479YfwT5ooGzpoRxdqmfeiSRLej4u4e3YNuxOP6nJL+rjCWDGqJZQHulrwOvfukyfPOqxSN+/zdD9KfzuPGe9bjmf17GhkN9o38h0wSe+hSw9xnA4QWue1iMURtuPPDyIfzv81Yy8Mm3zhnRJvzakX4c6k3D59LwrsVjZ6g3nKgGgqbW+uB3qSgaQFuiKKq3fG6NJB+X+7RzuRxmRKybxa7O5AlJd08kKsd6NQWc+MiKJiyfEhCJAMedECDxRke3cbLG8WwRd+/z4lDaCY8GfOWiOpwzxTKuomSc4KZQKCAej6NYLCIUCgkDNEqDKZ/kDZW9Y3RGJfCn8RkTD74He2/5vVYmmZm8jrtfOIBkriieRxB6sk3PhgqydUB1+fidl8zBL29diSsXN9r6n5mI8me1LhNO6NChojdfdu8lG8IEslAoYJLXep+9nQnkiyMz5utJ5vDSXosmvHROSHx/ckEGKDtLU47P64PXBAsBmqYhlUohnc1ja8xKas8uzc7mCBkm4QS+0WgUqVRKnP9sNouOjg60t7cjl8shHA4jEomgtrZWzGbnmCq5L/t4Ibvic7RcZTCJB+xstmwiNB5MqI4Xqqpi45F+vPWuTfjH3x8VoJdBZo9B1lBVVWGIJjtAy7JTADYQKo/rogkiH+N7EKhwXdGQjoyuXGDjvwmI2ev8Sml29qoma7+jgoGyce5zlJCzb597HGXcPB76ShAo8/35+QhI5HnKBIf8jGQ1s9msWFf0ITheUKEhv6+qqlg0OYyIz4k7L5lta9MYrND4Roeqqphbcrnf05UWfcsyEOY9hwUM/ozrTjZEa0vbvQF43clqDKDM4nItUjrNcViA3WyRrDHXSX/OxKZ2S5Gwqsk6FsrKWfTz+Xxi36AChKCdewV9C2iC19vbK4ouZG5ra2vR2Ngofp9SbKoouPcfr5BCJlsGwcNZE/J3yXXt8/nwx51d2Nkeh8+l4YaVk0VBVZaWj9V+x9fkOhhNTGygPWmJ9Xf7FiimMWgvtswAVevhPh3jN86aEsHCllD5B/E24MjL1r+HkI0XdAM/f8WarXfTeTNGdYE8vaVN/Pujq6vP6V4mDNH67exgo+U87u7b9Vc7xz1b0PHx+zZiX1cSfrfDPpptpPHsl4EtDwGKBlz9M2DaqhH9+v9ta8eXn7JM2D572TxcuXRks7OXTo3g5x9bhS+9ayH87hMz1hhpyPI8Am1N0zC3wQIAB6J5G9C25OPWjbhH9wxgtKeWRivt604hX3hjTPrksV5AeY4nb/6ABTAok6QsUu4/BIBc0cQvOhrRmnHA7wS+cJ4fi5o8oirvcDgQCoWE7I43e86DJZtlmqZwN6eMlAl8f3+/mJFM5sHpdCIUCglHctkZmOCZybScUDy0/gi+8buduO7uVwTjQJaNLQBvVB/jUH3aS6dGcO7sBoT9brEe5cSDyaSqSoZoJaANwNbTSrYopBYsV2LdxP7ukRXAn97SBt00cWazH9MiVs90JpMR54wsjTwup9LQiskZWfb+/n7sjDuQNVSEnSZmBXQxpos9szzHHR0dYvYwP1uhUEA0GoVpWmNympub0djYaJOo08BquDJaMqMAqs7LZgIai8UEcPR6vdANE39z/0Y8uakVumGeUJJ4KkNVVUyJeJDXTRztzyNX1IXcWzbikx3tCYBoiNYpMdoEyPLzub/I/ad0/iYjSIDEtcNjY5Go0jhLZskJMovFIvqLThyIAwqAC6a6BdAmcKbpFCXBBElOp1M4OZOp43N1Xbex+gRP/C6oxmFRAIDwpaAKSC5eslVmOPsOWUm+Lz+zw+HAZy+fh1c+fylmNQQEm02vgPG49jRNw7zSPXRvd0qAaZ5ToMxicy/hHiD/rMlj7ZcdacBA2SxNBt0suEYiEVvfN12+dV1HLBazeUZwrdN4kyzzuk4ThgmcNcmHiKMg7huU6cs9+YZh2BQwPp8PqVRKnEO/3w/DMBCPx4V6goXDSCRiM9UDIMbDcc+Tx78NFrIpIF/jeH3OVKOk0xZhIHukuN1u/KDkBfCh5S0Ie8vfD4ABZp0nErIyYTQmaIyJDbRrZwGugDXep2ePkLftrDKbc8GkEIIeB5LZwoDHTsf4CsMw0T+YIzJl41NXAeHBJbx/2N6J9lgW9QEX3r1k5AykaZrCiO2f33EG5jQGqj7vzJYwHKqCnmQObTFphnuJ0UbnDouN/SuLom7gb3+xCRsPRxH0OHDfLStHNK/aFmu/D6z9b+vf7/0+MP/tI/r19Qf78KlfboZpWs7zn7p05CZsmqrggrn1uG7V4K0KJzMq2UZN0zC/yVqTh/sLNukqANQqZLTL3znliQ1ewONQkCuaONiTOpUfA4B9rFfBAG5/YCOe3HwMuUJRAAL2rslyasrjKAMuFovYmXSjM+9EwGHin1a4sbA5gEQiIYBuTY3V2iFc10vy3+bmZsEyFItFJBIJYSLDvkjAGpVEYxiykpwlSgMYfiYmE/l8XsjiZECVLehCGfPhldOQSCREMko56RuZkA7Vp82QnXAJNHjMTETqSvLxjqxDAFSCHiZngFVcmddgrc+RGpWyp//yeREBtHjO6ORLIE0QLCfPBEayrDKZTArZ+Nm1BTg0y/iO/Zr8u6enR6xPMidMuovFInw+HxobGxEIBIR7cCqVEiCLMszhBEfssA2BQRDI9ckiAwHTb15vwx92dOJrv92FXNE4bmI7XkJVVTQF3Qh6HNBNoDVWBrVysU3uYQUsoNfotHK7rpwGQ0ptZTUM16HMUHJsG9lrAmeCVDJqbClhe0Il6OLvErCbpolXOqxraUEN0Bz2ij3H7/eLeek0wzIMQ7iMk8mW2U+5XYXPZ2GVe7vcOkAmjsUBgl8WEzRNQ11d3Yj6WNmewAKFfD8CAI9TEyOhgOEzl29EaJqG2Y0BaAoQyxTRky4XKbgGuI/IxmlycUVVVQSUPLwaoJtAd65crKQpI4GzbP4os+csqsitHyyYcU9lv7uiKHjukFVEv2SGz8bA815C5ZasupD/0FeCY964jyiKYvMrINMuO9Vzn5Vl8cczMuP9ky1RQ+1F8r7GQgG/T8Da21/c14strTF4HCpuXDUZmqaJ622szM8YY8FmAxMdaKtamdVu24QFQxii/dPbz8DrX7kCNw/CTJ6O8RPP7+3Gqm/+Cd/47Y6BD+54wvr7OLLxn621Rudct3Ia3KOYG7rxcBTb2+LwOFV8aIgRVB6nJjwANh/pLz9QP89iX3MxPL9xM274yTpRhXuzh2ma+MpT2/Hsjk64HCp+cuMK4Vw84tjyS+APX7L+fdm/AMuuH9Gv7+lM4OP3bUC+aODyhU34+mhN2N7gqGS0VVXFvFLxZ3+fBTDkpJ+GaH26R9R5KB0vFgqYV+/G/EYf4plTP+JLHpXy3O4e/N/2Tvz380fAtn1VVUV/NmfaMknwer3CuCefz2NnxiquXjxZwYyach+apmk2KST7Jf1+P2prawVg5PtEo1EBwgGIsTtkxWmSxoSajrwMMlicbcvChxy/2nAU3YkcWiIeXDE3JBg1Ss7f6JCLOdV695/a0oZv/fEAutPlhFMetcS1R+dxmgMxIZX7tJmwzSgZ8+1oGz7QPtiTwpbWGDQFuGhm0DZ7mgUZgg8yEgQlsmpC7lns6+tDPG9iX4pAuygKJUyWmTTSTdzj8cDj8aC2tlb00zLRpTLB4/Ggv79fuM9HIpFhf85MJiNYmnA4bGNZU6mUuDbohB4MBkujoEz8oNS/+JGVU+B3j4/ZxcMJrqt5JUnv/r6caDkAymxVJfhRVRVhpwG3asCAgt6CQzzGHkteu7IhGr9fftdUsnDtyOoOrmECHrLscmKvqmqZnXa6sK7TWmPnt2hCPcN9LJPJoK+vT5jmsTjH96GvBI3JqMrg52C/djweF0AJKLugAxBrPZ/PC5MrgpG6uroRgWAyqkB5VJRpmvjxS0fw0v4+cT3xuGSvgPEaAa8b02utvXdPV9rWg83vXFYyAOWRmgSMul7ElID1s44sf1ZWTgAQBT3uD1Ql8LlUYHEtUwnFNcY2gsNJ4Eh/Hi5NwfIm65rg+WZLAVsEWBykBJ1rLh639tpAIACv14toNIpcLifuaby2XC6XTbFAhQTZZh7fYMCZBRfZd2SwfahyX6Psnq0i/L/P58OTpSLrNcsnoc7vEt81JfRjld/JLRInwmYDEx1oA0DLMuvvtk22EV+ViYLHqU3IBPuvMX625hByRWMgESzLxhe8d9Df33Yshg2HotZIr3NHN9LrZ2sOAQCuWjYZPck8fv7KYWw6Eq363KVTIwAqDNEcbqB+LgBA6dqOl/b14KV9PaM6lokWGw5F8eC6I1AU4L+uXYpVs+pG90J7nwWevNP693mfBFZ/ekS/3tafwU33rEc8W8Ty6TX4/oeXjcqE7ZMPvYZ//c0OdMazx3/ySYpKRltVVSyYFETYoyHk1oSkipLCsJKDCgMFaIgb5WSKUuV/fWsDfnL1HCyaNHx2baxC7s9+YnOZmdRKCS4r1GSm5ZEomqYJ5jheVHE4ZyVJq6e4BONH9iocDosEk4kC53wmEgkkk0mk02n09FjXZU1NjUiGgfKonFAohHA4LIAiARaTf44EYqLOBFO+3+SKOn70l/KYJb1Q7rkdL268ZMeA6qz2vWsO4r5XjmJvX8GWEMr9zg6HQ3Ied4tiAhkcJuCAtQ6mlpbfjhEw2j3JHOY0+LByehh1fqdQONABHihLZZmgyRJAsvFkq1wuF+LxODb3OWBAwTS/iWZfmY1jzyIA9Pf3C8VCXV0dGhsbEYlE0NfXJ96P0nAmvHyfhoaGYbcFkO0EIKTElYkoWU0a+HHN/d/2DuztSiLkceDDK1oGsL/jPawiogW0D0pAm5+ZnxWAKD5Y61ERhmjHUhA/JzggICCTTTBN9oxrk+xgZaJNeXklqynPzyZzbBgGDiZV9OYUeDTgvKk+AXBZzItGo+jr6xPXkTwjnGCPYIegjyZqBEVsmaBbtNzLyu8mm82KmdmqqiIUCiESiYyo+ML7BmBdF7x+Dvam8YPnD+HmezdgX1dSKEPk543ncDqdmF1nraW93SlRZCHYlO+3XE9AuaAHWHvl5NI+1pUvy/hZzOPveDweMdKNr+lwOER7FNclHcNZBJHVOs8ftv5+y6wQnGZRKDy4z/K+JMv7CYY9Hg/6+vpEC1QkEhFMOgs9LLJSmcHiDgsNbK/iZ6SsvPIPfUxY5OI9lUVP/mGbBRVlskyb+x4d8tni8a2rl+C/rl2Cm1ZNsc3xlu/JYxGyIuREX3di6ImGCgloz7k8AE1V0J8uoCOexaTw+K6mnY6Bsb87ief3cKTXDPuDO560/p56LhAevMeWku93Lp6EptDImaJsQcfmo/0AgJvOn4H7Xz6E+18+jFtWz8SyaTUDnr9kSgQ/x5GBI7yazgS6d+EM9SiAGmxtjUE3zNE5bk+geFxUHKfiHaM1Dju6AXj4RsAoAmddC1z+dWAEyWIsXcBN96xHeyyLOY0B/PSmFSOamc040pvGb15vh6IAH73gjVPDVBqiqaqKJVPC+N2ti0VyJ/f4qoqJGiWDXtOP7oIbtS5rTAdZbTkZ4OudqmDyksjp+MvuLgDA5XMjAiBTekmgDUB8NrIzhUIBO9MBAApm+ouYWmPNvWbiGggEkE6nReWdoNbhcCAajSKdTtu+y3A4jPr6eiEbp4zU6/WioaFBsOuU1MnjgmTmezAJ+CMbW9ERz6Ix6MKVixuhF3LC0Gg8BZNLuZ+ZsWBSCJuO9ONgNI9ldQ7RM0uAzgStyZ0DYCJtOhHPmwiUEldZzkgWZlKpv7EvNXxlxdlTw3js1uVo77bMFcnmABBAm/+vNEkDyk7VlImSLdoSs87F2bV5YXTH5yuKIkAuHaHr6+sRCoXQ39+Pnp4e5PN5RCIRWw9iMpmE0+lEbW3tsFkRMlhkXjn2h8fPJJ8GaaqqijVnGCb++0+Wcuq6cyYj6HFMGNk4Q1VVzC8B7QN9OVFoA8rMoDxmR2bdGl0FHM260Z7RsCRc7tOWlRSyAoKu37x+ySDKZlayqzgBDEG2zDQriiL2HEVRsLZNB6BgeQMQDvjEMbKftr29XRTuWBQkm02gxdenekFRLBf8cDgMTdMQjUbF6wKw+QZQwcEik6qqiEQiwkV/uEEWH4Btfruu6/jJ2qMwAVx6RiPmNgWRSqXE+eL1M57D4XBgYbMfh6NZBEvKD/Zis8+ZLKlc1AHK87F1Xcfk0kdtz5Sl/LIaQpZwc2oGX4OqKq5Vn88nQCPPXbFYhAEVLx6xlGpvnemHYaTF3suJBATdbJVhwcbttnwsuF5qamrg8/lw7NgxkTvIyg9+BgJwmvUx16BZG9eFHLIRHlU9BMvy90Fjv8p9zeFwiPnrAMQ+xwKVpip424J6oSJjcWIs9zl+58CJs9nABGe080WjDLQ7tsKjGphVGgNVbWb2157egYu/9Rye39N9Kg/zdIwg7i+B5EvPaMK0Op/9wWG4jfckc3iKI71WzxjVMXicGv7yDxfj5x9bhTOaQ4Kx3tLaX/X5NETbeiyGoi4xQaURX/Wp/fC7NKTyOvZ1vfld77/ynoX47w8vw0cvmDG6F+jeDTx0teW9MOcy4Mq7gBEAwWxBx633b8TeriSaQm7cd8tKRHyj2ywffa0VALB6dv2JmbmdYAxmiMb+UiZ+snRKGKIVy4wp5c0EU9l8webKe7JDliU/s6MbBd3E3AYfZtd7BZudz+dFNRwoV+XppGrdYHXsSFvtCKuaLPaEkjgyEvy8ZLOYeMZiMQHAnU4n6urqUFdXJyTrTE49Hg8aGhqEiZDMNvCzEICT2apWVc8XDfzwOUvK+7HzpsKhlg1hxhvjM1Sf9oJS+8eBvpz4PsnsMQl1Op1wawrCqpUkdWQdNgaRIIfApdFVwDO3L8VvPnn+sI+RKgeXaoqiCwELj4WJJo3X+Jl4bpjAsjjTmjDQnnNCU4BldWW3XxYc5L5TFmUCgYBwGqe7byAQENdgIpEQrQHh8PBHCXKNy9JnWUrp8/lsP5PVE3/c2YldHQn4XRpuOKdFJNoTKWTpOIE2Q3ZiJtCRi4V0Hu/IlhWMsnO5zGRTRk5wTDUQ1xeBLf9w7RJgA7CxjpyUYJomCoaCTSUB21umlUEz94j29nbRUsAxXTIwYvGEa4CeFCzOud1u8TOfzycMrAgQi8WikJTTZMvr9cLv949oz6FjPz+rDDoO9STx262WpfrfXjpXuFkDeENNHUcSqqri+hWTcN91C/Dhc6bYCnDydSMXafi5ZBM8FgyPpezrTPYDYHsHiyFsM6AqgX4OPI9cU+y939RVQCJnoN7vwBk11vvQI4OsMZlo5gT0BPB4POjq6kI+n4fX60VdXZ1gkQuFgq3VhSw1j4XXGgvzLK7SfJV/eBwE37xnyw7uAGzmfzIY9/v9A3qh+Z4ulwt9GQPZQtmBnMUxKj/GMmQ2eyzu0eP/Shgifrb2IFAzE3CHgWIW6N4l5OPVpGhdiSwO9aZH1A92Ok5dxLMF/PpVC9h8tBIkx1qBo+sAKMDCwWXjv1x/BHndwJIpYSwrAeTRhFNTccHcegDAktLrbDsWQ0EfmIDOqg8g6HYgU9CxRx4f12Q5j6tdO7C4NAZsS4kpfzOHx6nhvUtahDnhiCLWCjzwfiATBSavAK65H9CG30emGyY+/ctNWH+oT5iwjRYgG4Yp1uPVp3h2drWoZogmHHKhCMkykz95xJfs/pzP51HQddz+2EGs/s/1p1QSL8vGHy/Jxq+YXyMSWCYfyWRSSNCAsnSTwKoj50Bv0QWHYmJFk0P0jem6LoBIMpkU35Hck02A5fV6hSO5LM+jNLi2tlYcg5x4MKGQZ3wTgFeCGtM00RtLYsmUIBqDLnzonKkiiRqPJkGVa0yOM0r31n09GbHumMzJ/c4ARJ92Z67s8g1AMD387HqxAL/DrPp+1WJrawyJTNkdmswHQT4TQr4XWSl+JgI1AmMy1a9FreNeGDEQdCm2AgJQls6y/YCjlaLRqDAsk42EOFrH5/ONaJRXLpcT6x8om/DQhI+jo+S+R5nt5WzZ686ZgrDXOeFANmABmNkNflw6rw7vXViDol5mpJl0s0jGa5Fy7kYnCzwaFKXcw80iHiXPBNHVVBa83mUTNe6bBMJk32QncxbdAGBrVEXOUFDvAZZODojX4fnr6OgQxaFAIIB8Pi+uKbJz/Lw0aiO48fv9Yp0AdhUHgbRcYGFfOOcsU5kxlOkhUFZWABhgMmWaJu5+6TB0E7hwbj2WTo3YTK9GYvj3RgaLcQBsLQq89isN0Vh4477ANVijZaEASBSARKH8e9zvqJIgiwtAnFtZEcEiCguXXI+qquIvJRO0y+dFYBr2HnwCairWeHy891EhZhiGaJGijJzrjaMqadYXDAZtzuM+nw8ul0u0HgSDQTE2kz4jLBCFQiE0NDQgGAwKgz+uRxYkObWjqakJNTU1CAaDtj9UoNHz4p8f24oL/+M5/GVXp81hfKz9TZhL8FjHIiY00N7dkbCYrhbZEK3cp10Z5cdOA+3xGL/e2IpUXsfcxgDOn13R10vZ+LTzgFBL1d8v6AYeKI30unn16EZ6tUbTdlYawMw6P0IeB3JFw1pzFaGqCs6aynna/eUHSow2evZgWamJZ9ObHGhXM1EadqT7gJ9/AIi3WmZy1z8CuIYvPzNNE199ajue2d4Jl6bi7htXjA7sl+KVA7041p9B0O3A285sHvXrjFVUM0T7w+4+XPPzPfjWCx2iR4uJYK1i3Zg5SxsoM9owDGSLBoqGOWLH5xMJgqCORAEbD0WhwJKNM5lRFEX0TsuMUigUgqZpQpq4PW1dTwuCeXgdEKwUACGDY09XJBKB3+8XlXT2XVMNQMaBAIygRnbrpfsvHbQJspksV5sVy+cFXAr+430L8MynViPgKxc9xjPQlqXWDBoadsRzSBbKpnM0kALK/Wzs0+7Ku0QRhSBYlqWz7284QLugG7jpnnV4y3fXYsexfgAQySuZB74OE2CCJqDcdsHCAEe+pTNZbEtYxbhlNRagCwaDgiVlH69hGEK2S9lkd3e3KMLQUZxARtM0hMPhYSeCmUwG/f39Qm7OPkWO9VIUZYAhVSWA/7sr5uH82XW44ZxJ4nuYaKGqKnwuDd+7+kx89JwmaGoZKLN4QmAB2PfDJo8OBSZSuoqUodmub8BeSJLZa7J0bEOg1Jd94ZVycrlHl4CK8m7TNPFKyQRt9WSH7XgdDge6urpEEZCAlNcawSxBv6ZpwsiRoByA6Llm4Y9GWuw1J2AnGGpoaBCvzaJBKpWymerJwb2rmmoCAI72JvHk6xab/akKNpsM/UQJIbsvFGEq5QKbXKRiIUfuuyZIVxQFDhhoLAkwu/JO8Ty5gMy+Za5B7iGchkGAy57qXC4nlDfxnIFX26w99ZIZPqHS4BqWTfRYMJCl2IlEQrS9BINBZDIZMTObRWKPxyP2S6fTKc45Wy/k9otKAFosFoXyQfYoYTGBDLb8OAuHg4U8BWBXVwbP7+lGX8qamsJ84WSMjiObzcLcWMSEBtp7OkugR+rTPmMI5/GhXMlPxxsbpmniF+uPABgEJA9DNv7M9g50xnOoD7jxzlH0BpumiVvvfxVv+Y/nbIBZVRXBag8GlJdMsR63MdaRaYArCBgFrI70DXz8TRa7OuK45Nt/wd0vHBj5L+fTwEPXAt27gGALcMNjgK92RC9x13P78MArh6EowPc+tBTnjtaErRSPlNjsdy9pGVV/91hHNUM0n8uBrmQBB/qy4gbIyjKdxxOmG3mzXIXnTXNGxLrJbW+LVXm3sQ8mHoDVn3321DDOmRZCvd8hEht5XBGBttzXmEwmkS/q2JWxEs5zGsrzY+UedTpG19bWCoBOaTlH2sggTZ6PzYo7e8UJopmosjeMALxyjBc/qwwgvV4vaoI+mxx+PCajssSvMvkOeZyYUmMB0qNxXTyPn0V2gG5wWMkKDdEACJklmUEmrusO9OLWn2/GFx/fOuSxvbi3G33pAjwOBdNr3CIRpcyfgIjsIXtqCbj5+ZikapqGeDyOAykHEkUNfgewuE4RwILAnCyR2+1GTU2NeI3e3l6hkKDJHiWNpmmipqZGFHuGChqfxWIxwVyyD1zuRea6A6obTSmKgkvmN+L+j65Ard8lPuNEDBYQZOM8WTlBcMCfce25NAW1Tus7akuXry/KVPl8gmmCII7bIoPIx2SALT9flpkTiBCYxvIKdvdb73vRNK/YG1RVRT6fR29vr/B/YE8twTjPNz835eGmaSIUCsHr9QrgzXVCgyrZyEqW4IbDYeFIz9YGgkhej+l0Gslk0jY9gftvNc+J/33hAIqGiZUzIjhnRq3Y63hMEymcTif+358O4/zvvoLf7+iysdpysYVFVjm491nGjtZ31J61zh0Bm6wm4+sCEOqHZDIpDPF4XVMeTUD50tEsdBOY3+DFlKBmywHkooC8TuU+cyoTyCzTBI1+ByyWyvO15eOUzc/kPQmAWPv8Prh3DgawjzfiCygXUAFLkfGD5ywj0fec1Yw6t/V9BoPBMW9POBlsNjDBgfbh3jSyBd0GtBeWWOsD3UnrMSnIbu3vTiFXHJ5U7XScmlAUBQ9+fBX+7vJ5uGpZhdFZ/xGgdQOOJxunU/j1q0Y30mv9wT7sbI8jmi5gZp2dSRV92oMA5bLzuPS4ogCNCwAAixzHEPQ40BhywzDenHO1H97QikO9abx6uLo7+6ChF4BHbgZa1wOeCPCRx4DI4CPVqr73xqP49h/2AAC+8u6Foyq0yBHPFvD7be0AxodsHBhoiKYoCs5oLs3SjuZhwO487lZ0+BXrZs4qOwAhl5wetq6RXR3JE1MiDDPksV6LJodx341L8J0r54gk2ul0IhaLCdk4n88+L7LZB9JuZAwH/JqOeeHyjO1AICDmCLtcLvj9fuGCy+S0pqYGkYglc0ylUoKJ5PdKYzSZGaI8jfJyJhYE2ZWMJft580Ud3/nTAXSmy0kab+LjmWkcsk+7dH89lij3LlcmTZqmodFlJUn9hge5YhkAkNFmz6JpmkhlclhzIIo1x5nK8Pgmy3vj0rkROB3l8Uxyry4lrkz6yYrILQtkjwALyIjZ2XUGHCpsjDcTPtM0bQ7xnGlcKBRsPdg0LfP7/bY5uNWCTHkmkxG9vTSsquyl5boDYDNbY8gqvYmwxo4XPAfdaR17e7IDnMepImHCz59ba8/6/G1pxcZGVyor+HzZgIkyXVn5wLVDsAVAABOuZcq7AWBjjwoTCuZGFEyp8YjzyF7cTCZjA7BkrlksolSdTCTXE+cjy14BiURCrDkCLpkxJXPI4H7m9XoHgG7uT7FYDLFYTPTAVisILp8Wxux6H+64aJaNzZYB2kQJp9MJt0NDQTexuzMpzrvc784CCwDb9yEXLGiI1pEtF4TYWiSrIHi/YzGDa473ObkNiuv3L4ctIPv2M2psLvosbPJ1WcSU1xF/zn5rFla4xgjuCbLlfYvrWzYVlfcVFhb5XdDorRJg0y1/OK0sBOl8zT1dafxxZycUBbhxeRMAiDxnrEMuso1l283EuiIqwjBLrLYwRNuGRi9Q43PCMIG9cr8sgElhD8JeJ3TDHPDY6XjjozHkwacunQufq2KBUzY+fTUQrC7h3doaw8bDUTg1Bdevmjaq96db+VVnT0bYZ09SqjLWUhBo7+lKIJmTzKWaLPl4JLEXW758BX720ZVQ34Su47mijsc3WQzwtUPMHR8Qpgk89Slg7zOAwwtc97AoTgw3/ryrE59/zGLDPnHxbNy8+sTdwQtFA9etnI6VM2tPqNd/LIM3VaAMgqbW+uF3aSgaJo7Gyuwsky3Kx7sLLpGoFgoFpFIpzCrNMN7dmTxuv95YhAx2hMMpDCHbplyRoIMJKHu14vE4TNMUsvGlNUXA0AUL7Xa7RVJEWThH9xSLRYTDYdTW1gp2m/22sgtsKBQSSQ7BIHsxKSMnEyDL6xjs1dR1HT94/hB+9korPnT3ehT0sotppSxxvMVQfdpffOcCrP/CpfjwOVNEryIldrJ8PKjpcCs6DCjoypb7HGXQw6Sy2WN9L4f70va9U4pkrohnd3QAAC6Z6RcAiPNfKfPmeSE7KY/1ItAiKMlkMohn8tiZsBK25fXl9Sb3VzJ5JTABIMZ5ORwOwVyT1WPRZ7BkTQbYZBTJkvL35CRSduCt9AEwTRN3v3AA7/ivF/HAy4cGFBUmaqiqiuf39uH9927Ht1/osIGVSr8EAl7A+sxNJaDdkS3P2pYZbTKQNKsiSOHeyPXMfUBWaxDk87vl2mCvrWkC661BCrhgitPWFy6P/iKIAyCuHYIb7ieyE3UkYk1loCrH4/Egl8uhv7/fJvUlC0uVx1Ay7krQzQkIMtig1wVbZQggL59fh8f+ZjkumNtgY7MngtN4ZaiqirkNFgu/qyNp63FnMVFud5ENPfk8XdcxyWvtM21pxbZWud+wwM1Rffl8XvRTy6ooPs572aFoHvv7CnCoCi6e6RfAXGbeeTxUaMktDrKBGa+VVColpmew4Emlj9xfL48SZBFT9q0gK8+9n9MSgLLD/lDzs6sFrxG2wv3gOWuKwtsXNGBK2LqmTsY6o4oAGFs2G5jgQBsoycAj0wFvDWAUoHTvFFX3nRW92IqiCPl4tR7u0/HGRGqQ5EqEkI2/b9CnECS/a/EkNI5ipNex/gye2W4lcjefP2PA4ytn1eLnH1uFR++o7o7bGPKgJeyBaVqgX0TTIuvvzu1vSoDN+OOOLkTTBTSF3LiwZCI3rHj2y8CWhwBFA665D5i2akTvu+lIFHc+uAm6YeL9Z0/GP75t/giPvHrUBdz48nsW4uHbzhtXEt9qhmhzS81hR2JF4eDJ59EQrUf32G68uVwOM0vS8SPRLJKZ4Y9XGm3wmLcci6M7lhZgiDfwRCJhGyNCBoBMTiaTQTxbxIGsdZM9p96wsaQ0kOJNP5lMIpVKiQSQpkPsk6upqUEoFBLJKxMCSoUJsNkvmc1mhQkXZX6VIDudTiNXKOKLT+/BT9ceBQB85rK5cGrqhGEahwLaM+r9aAx5xBpjYs/krpzUKagThmhOkfgRzMgyXK+qo97ngGkCuwfxT3lmWweyBQPTazyY3+C1SXxlKThbAijdl0EYj4/vm81msa3fgYKpoMlrYnoAtt5feY5sMBgUUt9kMinmaYdCIeEkTOAdCATEGpGDDtfyvFi+HxlSAi65zUMerSSvnaJu4EtPbMM3frcTpmkp9WTVyESVjQMl8FNyHj/cn0OuUBygXCAQ4jnmmqLzeHtGtRlXyaOLAAgDMpfLJaTXPN8s2lHWLV8LBLTcp+Rz1J5zoj0NOFXgvMllBpFrL5PJiD1aluPKxpYsPBLkUN0ggy9FUdDXZ7WjeTweBINB8Vr0p6hmzjhYyC0jfr8foVDIBtKLxSJe2tOBX7y8XzDqaqnIMVF7sxmVuIDfWWXrBf0nuI4IPvlvqng6Mwp0s7zmZK8R9unTSZyFGhZ0ub7ZEqNpmmCzz58Rgt9h7yGu5iUgF+Nl0C237nAdcXY2Q2adeX+mAkg2juN+JxczKwH2aOaoywaoHo8Hr7fG8PttVl7+sfOnCnf1k3EPZbHtZBTC3wRAO2FJdOU+7ZJEvFov9pKpESyeHIbLMeE/+psiXj0cxUXfeg7X/+QVu+yaET0MHHsVUFRgQXXZeE8yh6e3cKTX6NjMB14+DMMEVs+pw7ym4IDHQx4nLphbj5Bn8At8aWnMV1VDtK4d4kfp/Kkbp3Sq4lcbLVDxweVT4NCGeW2t/T6w9r+tf1/5A2De20b0nge6k7jlZxuQKei4aF4D/v0DZ03IG/1IgjdRuUdLzJyNlvs7KfOqk0Z8yQ68uVwOQaeJiEeFMQTAGasQzquGiU/+Ygsu/t7L2HQkakscac7DSjklZ5qmob+/H4ZhYHfaBx1WMt3kLtqYJSaZ7IMka03GhlJjMkSRSATRaFTI7NgHLptrsd9MdhR2u90DjKgIsuOZAj7xy214emsnNFXB/3v/Ytxw7nSRcAHjH2hXtihUCzrVytJFBgFDPQ3Rcg4BaviaTAIJLGbUWN/JjipjOQHgiZJD/aVzLFM89s/LrKDf7xfMEftnZfaSRRQCnHw+j80xi0Va2WhCUSDklkwcyXCSzS4Wi2hvbxdjcurr60URhtceE2Yem67rNt8BAKKAxGtS/t74XXK98vnyd5zIFvCx+zbiwXVHoCjAl961AF95z8I3BZsNWN9FS9hdUusAh/uyNkM0yr0rneYVRUFTSSHRk9dQNMvzgAmk5XVAOTe/awITFoQqwQrbcgCIohv7qAFgQ4/12LIGFSGv07ZW2dJA0CX318o91dyjuTYCgYBQb/Cz0JzP4XAIbwAWBPh6I5HWymO8eC1RYeHz+fDbHT249cGt+PJv9ojWMH52FkvJiE/EmNccgqoA0XQB/VlDAER5fBtQdvlm0VAujPmVIvxOS2nbW3SKNcegTNswDCH352sTgLPdheA2ly/g+UNWYeNt8yNin2GhieuIa5m/L5uW8d7D9ZbJZMT7sTApt0gxWAwAYFPZsOeb5557Dc3cRgOwgbIBH1/L4XCgPZaFaQKXza/HrFq3rcA71iGz2WOdR05otHne7DrMbSrJHCSgPZTp2effsQBP/+0FeO+S6s7Vp+PUxZObj+HDd7+CnmQe/ekCWsJVmOgdT1h/T18NBJuqvs4v1lkjvZZOjQgJ90gik9fxyw0lI7bzRy87riovL0nHETuK/UeO4cL/+DMu/+4Lo36P8Rht/Rm8uNeaTX/NimHKxrf8EvjDl6x/X/YvwNLrRvSeXYksbrxnPaLpAs6aEsYPrz8bzuEC/OPEb19vx5p9PeOyl76yf1bTNMwv7YEH+nLi5sobbY1i3aT7dI9VrIJ9rMjKyV5cMjsEFSf3szIRfbU1ga5EDn63hlk1TiHFpGspk16gXBlnn3WxWMSOjLW3L68rgvdCJjtMgtl/TaY8n88jGo1afdP5vOippcyNfdlMZMnKUiZHkC1LVuVEgkCqPZbBTfdvwbpD/fC7NPz0phX40EqrjUXuVxvvPYzVWhTkuOu5fbjtwU3oSpfXjJycMBFsKI1a6imNl2OiRxBLoKDrOqaUlIDVRm9GU3ms3d8LALhkVsAGgmXTIhZFCKj4h6wLk2PAWo89GQMHU04oMLG8vgykqJCQpcIE2p2dnULS29DQIF7LMKyRcbJrNIsvsikek1GOWpIlnvL3KKYDlH5HBk1t/Rlc/T8v4/k93fA4VfzPDcvx8QtniWPh70zk4BqsnKfNkVcARM+p/HxFURBymPCqOkwo6M47bOdcXoc8b2SOySSTcaQkm6/P65/nloU3ekeoDhc2dFrHdsEUp41BlFlzstemaQrZLv/mNUEWXAZKZJL5WVgcZGFJZk3lgsDxggCH340MmA3DxHee3Yt/fnwHioaJKxY2Ycm0WlGI5DFNxN5sOUI+D6ZErLW0rydt+z5labbc/851WGaidUwpGaJ1ZB22vYi/w0IumWwAthYT2SvA4XBgS2ce0ayBsEfDyilWIZjMMvcOAn+5sMgiNX8mt80QkPv9fltrhDw5Q2azqeyiiVo8HhdFKf6OPN5rtMHrkPtwsVjExXMi+Lcr5+PL75wrrpuTxWbzezwZrz+hy55337gCoVBpfI8MtJeXR3zxxJ2O8ROmaeK//rQX3/uj1XtxxcImfO9DSwf2ZgPHdRuXR3oNmL09zHh+Txf60wVMrfXirWc0Dvq8/d1J/GrDUbg0FZ+rIlGuaojmrbFctBNtmJQ/iNZoBqYJdCdyaAiOvZnDGxG/frUVpgmcO6sW0+uG0Tuz91ngyTutf5/3SWD1p0f0folsATffswGt0Qxm1Plwz83nwO8em61MN0x8/Tc70BHP4n8/snxcjPWSo5JtVFUVZ7aEsGiSH/MbvOJGwZt/SMnBAR1FaOgrOFCjWckhGZI7zokgEAigvn5sZ1FWBoHGb7dZDYyXzauFpgB6idGJx+Ni5AyTECaMTE56skBb3gsFJs4K58E5uUwqCNry+bxw2qXEkzJfJq+yw3NdXZ2o3tNJnJJSzkMuFApixql8I5YT4LteOIK93Sk0Bt245+ZzsGhyWDxvosjGGXJvYiU7+uyOTmw+2o+LpnmxIKCJdUhFAdcoZ2n36h4UCr02+TjBLPtjW3xWMrqzfaADfo3fhT9+5gL8YcthtIRcgn3j67lcLgSDQRuDRGaEa0lONAHrfLzaayXNc0ImalymSBTZtsDkkgA6m82ir68P+Xwe9fX1AtjTaIi/L/fjMmR5OI9Lbv9gQkwDNtnFV2aZkrki3v/DteiIZ1EfcOOnN60QEzFk2fhEBj0MVVUxr8mPTa1xHOjLCUMmFlBk0yauVavIaBmiHc5qaEspqA+W1xwZZPZfy74VZLqdTqfwg+CeQomu02mx1Gw3oXzcMAzsSTqRLBQQdgFnNTqF47MM3uU1y/cEIHr8yaazKMB+Xc5wJ/CTJfFcNwTp1doWhgp5LrvcDpPJ6/j7Rzbjd1st6e4nL5mDv7t8nmiBSyQSAvCP9SzjUx1OpxNz6r04Es1hZ3sCZzXWiWtINuHj904gzvsJAe4UP7A7CrRlVJzpKyvIZHO9eDxua7WhhJv7lNzX/VyJzb58Xg30QlnyLa9LvgdBPYssfr9fFK7l5wAQAJmGoLLhJwBRFOLnVFUVPT094j7mdruFemcs9hoWTrP5An74UiuuW9GC5pCVH797UZO4NoGTo9Yhmy0rS8YyJv5uzCDQ7tqJOTUaNFVBf7qAjni26tPzRQMF/eQbAJ0Oe2QLOj77q80CZN/2lln4nxuWVwfZfQeBtk1DysZ/v60DXSXQ+o5Fo3OafvuiSXjiztX42pWLoA3RR92XyuPHLxzArzYeFQmbHIsmh6EqQEc8i46YtO5KrLYvuhtzGy328c005uuCufV4/7LJuOHc6cd/8tENwMM3AkYROOta4PKvAyPY2PJFA7f//FXsaI+jPuDCfbesRH1g7AoWL+7tRkc8i4jPiYvnN4zZ645VVGMbz5oSwb3XnYnbzpskbtp0JlYUoEYyRGNiRyDABFQ2jRrr4HtkCjqe2WHNXr10jlUMZcJJeSWTPrnXlcns1oTViz4nUETQYdgq3OxhjMfjYnZsbW2tYCUikQjcbjfC4bDNsIxMUzweRyKREN8rAT6Pi+yZzCyy5xawwNLXrzoL713SgsfvXG0D2Sez9+tkxVB92lSMHYoVbA69DAKEelcRCkxkTQf683Yww8IGE7kWr4GAS0XYW70Q0Rx04oo5AZsJmgx+3G63ML0CYGN3yCIykbUSTkO4jZ/bpNhArmxap6qqmOHe1dUl5qZzljYLEWQBKSPmtVSN7aEHAADBoPPfsnySTtRyBNwO3Lx6BuY1BfDEnecLkA3ApgR5M0Q1Rlve+zjKkOdWbkkQzuOZctFBHvHG12CCTxDPQoncO0u5NvdUnj9FUZBOpwUIfqXDyglWNgIoXRP5fF4U5+j07PP5xPFzD+Kxy0wpDdnkFglKffk5CNplpcxIJOMckcfX5mt0xbO49scv43dbO+DUFHzn6iX43NvmC5AtF5JGKxUeT6FpGlZOD+OSORFMrXGLtcCCmyyvlhlq2fPBMkSz1kBHpjwajEU1rhsWc2UmWTbtY5tNIqdjXWvJbXx+RLRTyYUW7oGyu7ms7gEgfAEcDofwrfB6vTYPAr/fb2tZoRIDgLg/8voJhUKoqak5YQaboes6EokE2nvjuO0X23Dvy0fxqUe2wzAhVBuVxoFjGTw3wNiboDEmPNDuT+cRTeWB0GTA3wAYRXj6dmFWvbVB76rS83XbAxtx5lf+77jjRE7H2McXHtuKJza3wVHqX/z8OxcMbhJG2fiMC4FAddDzszUHAQA3rJp+Qn33S6dGcMn8wdlsAFjUEoamKuhO5NAeG1jA8bsdor97sD5tysur9qNP0Dh7Wg2+e+1SvPus47RjdO8GHroaKKSBOZcBV94FjGDTNAwTn3tkC9bs64XfpeHem1cOj0EfQfy6NDv7yiUtoxoRdyqiEgTJN17+W3YH5Tzt7oKVgBEgpFIpC4zoOg50JVA8SSMPmci9sC+KVE5HS9iNM5u8gj1i0pZMJgXrw+SUkvJCoYhdWQucL6+zXo8SbyYaspNqbW2tSFoIdoLBoHBUpRyYRmuyEZJhGIjFYujr60MsFhPMZiXIzmQy2NwaE4lL0OPEf394GSZH7L2KMps9UdRVQ0nH6YFyoDc3YN3JzI9DMVGjlQyCchaAZiJDsx8mhjWOAh758Az8+PqlVY+H8msWSSjzJRNDhkh2kyZgonKBBQ/TNHEkpaInp8KpmlhaX5Z/EkDJfa5OpxO5XE6MiAuFQuI8cq1S2cA1PZicUgbScj8wvz+ymkyW+T6yYehtb5mFJ++8AFNqfLbXnSgeAMMNTdMwr5FtMeW5zjyXbBeRDdG4npolQzT5e5Z7pAkm5HFJAMT4rcqEnu9HcC332hpOHzZ3We95brMqmGiCYK5ZFgcJzgjm+XoE2wBEAYASXRqosXjEvlkCdR7jcEEv90cAA9phntrShtdbY6jxOfHgx8/FB5aXR1yapikmOfA7eTPEtcsn45vvmoW3zIqI+yf3foa8Jiql36Zposlj7fXHUgqAsgEZ/6RSKds9q2weqYp1zeLdmqMZFAxgZq0bM8Jl1QtBsryWeT54n+JaoY8AUC4MsP85mUzC5XLB5/OJgh5/h0ouFmJYEKivrxdeGCcSVJGk02n09fVhV1sUt/xiJ15rTcDn0vDZy+YiFAyIdXkyFWEsGJ3M+/OEBtrf+O0OLP3as3ho/ZEBhmh0Ht9RpU/bqako6KZlpHY6Tmnc+dY5mFbrw/23rBT9i4PGcWTjW47247Uj/XBqCq4b5UivTH744MLr0nBGcxUgLcWyaoZownl8R3XDtL+GiLUCD7wfyESBySuAa+4HtJFtmv/2+514aotVpPnRDcuxeEr4+L80kkNMF/CHEuN69XB7zd+AqDREY+KW103EcoZgwnhTqi0ZonUXy320NHDSDQPXP3wY19y/Awd7Ts7IQwJtysbfNr8WqtSXyrEnrJoz+SSIy2azOJzWENOdcKkm5vmtIheTY7IGAATbKLv20rzM5XIhHo8LZqKurk4YWHGeNlkrJht8HyZJmUwGqVQKiUQCP3j+ED5y3xbcv6F90Bs0E2NgYgGgoQzReG/d250WBj5k1uReY1VVUUdDtLxTsIRy4sn3IgDld8X4z2f34JZ71+Plfd0isYzFLHk5RxMR6BJQM4GV/yZbTBZoXWkE05JaAw7oQllBMESPA7o5s5+fpmRMoAHYGGw6QA/G9rAvm74CsgFPZZ+soijQDRNfe3oHPvCjtUhky4ys12UHU3ydN4tsHCgz2jevasHt5zYJoEFlgtw7CpTPg6qqaHRzxJcGis8Itvna/JmsNOE6ZB8sgS/BkaqqtrFsZMI3RzXoJjDFZ2BqqDweir/HvSQQCIhzzP2Lqhp5nRJIq6qKYDAoXo+sOADR0sDPxWtwOCF7AMi9uYyPXTATn7xkDh6/YzVWzqy1PSaPm6Mp4psh5P5kFkQACF+Ayp5t7iUE2oqioM5RgKoAqSKQ0MszsVk803VdKAcIgqmkYZsT1/BzB60C+TsX1AkwKLuc83ogGCYI5x4lj99isZDFGSrHvF6vKBzSZI9/uFezaBiJRE7oHsZjzmQySCaTYsLIS/v78PFf7UFrLIcpNV48fsdqXLGoxaY84Zof67V2KthsYIID7eaSeZYA07Lz+BBjvJgo7DrJTrunw4ouSb4/uyGAP/39RTh/znFGQPXuB9q3WGOfFryn6lPuK430es9ZLaPqd26NprHiX5/F5x/biuIw2wgo1RtM+j2kIVrndiwpSUq3tPaPS7OtkUQsXcC/PL29qumgLdJ9wM8/AMRbgfp5wPWPAK6RMdF3v3AAd79oqRe+dfVZeMu8sZd1P7XlGPJFA2c0B3FmS2jMX3+sotIQTVVVPPxaBy7/36348foeIR+vNETrKXrE79MQTQHQ4LNeb0fbwP7YsQhd15HO63j5gDWO5rK51jUgJ5g0jSLIZtWdfdPbktZ6WRwuwIGyLJdBSW8gEBAuvUwGOYebQI7mZ/J4KCYn7OumHJisNxORTCaD3mg/vvDULvzvS5aBYjydF/1ylTGRTNDkIJsDDJSPzy8VG9tiWeRhd2QGyuBFVVU0OEqGaAWXTfpLcECpLwDBouilfdEwTPz61Vb8eXc3OmMZ8Rz5/QhkCIh4Pgm42UMqs9mGomFzn/XZzm1SbBJPghX21TIJjsfjAtyReWLiyuP3+XwIhUKDnmeO1QEsQM61oaqqkNLLfbLpfBG3PfAq7llzELs6Enh+T3fV12WRATi5yeKpDlVVLXbrrbNw+bwam1SXPa8EiQTfXLONbgMqTGQNVQAeoFz04/XMn8vjvOTXlhUaXq/XBnSpPnC5XHip1TqXKxoMAdLZJ5tOp4VSggXQyl5tuYjgcDhscm6qJMhaFotFhEIhAXLlcUjDYeS49wMQDKhpmnj01VYxEUVRFHzubfMxo94/4He5Z7+Z2GwA4rwc6k4gmS+b1snfKfcruWDNc6YoClRTR7PPeqw77xRrlgXfYDAoDDq5N8ku+FwHXRlgZ3cOqgJcOjsowKas3OD/WcTh+ed9US7qUeHDayWTycDhcIhicz6fRzKZFKoy7ok83pHOwpaDRR0WquVi6kMb2/D3T+5DKq/jnBk1ePLO1eL+wpBbYsaacea+yYLxyYqJc+evEvNLErZdVYC2mKVdBQQM5Up+OsY2HnjlMC74j+eEKzWA4blDUzY+8y2AfyAo70pk8fTr1kivm6rMvR7usaXyOo72pYc9koqGZ5sGAdpkrF9v7RcJI+rnWQWDXAxn+OLwOFUkskUc6EmN6rjHSzyx+RjuXXMIn/3V5qogAwCQTwMPXQt077JM4W54DPDVVn/uIPHk5mP4xu92AgA+/44zcNWyKcf5jdHFIyXZ+NUrpo5riW81Q7TmsAeGafUysp+QN1Uy2mnTiYxRlvcywZtRmqe9/SQAbSYQPpeGP/ztKvzru+Zgek2ZXWQC0N/fLyTcZKoURUEymUQ6V8TerCUhXRK2KvQyg0qpHWe/kpEuFApinmehUEAymRS937LxDN+LlX6COVbxCd4dDgfimTw+99QB/H5nHzQF+Mo75+KOC6cinU5bx1pKqgnsJpoJmhyVyglG2OsU8vijcbthjvxvAGLEV49e7i2VZbwyU/TqsTTe8z8bccvPNgAANh6O4lh/Bn6XipVTrLE47KMnYyzPtq38Q0aHYJnvtbXHQEZXEHYamB20WB0yPwTXZJwJvjgjW5bHszhDJQST5mpR2ZetKIoo9PB4FUWBz+eDqqpWj+z/voI/7uyEy6HiB9ctq9qaQ6mnfOxvdPAzsd+dEuiRhswgysVFFuAqnd75voqiwO3UUOekjLd8XPJalpljvibBCd+f/6aZHa9vOsprmoY4fNgfLUJVTJzTUN6b5IkJuq4jEAiItSr7C8h+EfSkkEcmAeViiq7r8Pv9NoM+AKIwNJxzw/2NyqeCbuALj2/D3z+yBZ/55eYhCQAykbw+3ixsNmB91599Yh+uumcr/ri9Q5wPWYFAdYOs8uFewALc5FJtoi1j35eoVGHRhGwxCzsym/2XQ9Y9e8WUALxKQbwvv2/2a8tqGvbKu91uW6sCvSq4N/PeFAqFxMQP9o7zvky1EI1GRwqyWZBJJpPCkE0uLvl8PhhQ8fS2bhgmcPXyKfj5x1ehrorfzsnynqBHA3DyC5QT+iqZX+rfOdiTQragwzNpqfVA9y4srLcWxoHupPWYs7xQCML3d6eQK+rjthdzIodumPjGb3finlIP9R93dOLCuSNgIY8jG//FuqMo6CbOnhaxGcIMNzJ5Hb9cb81+vnkEQH1Z6b22tsZQ1I0BAH1uYxA+l4ZUXsf+7qTVs+1wA/Vzge5dcPTswvuWToamKnAMYbw2EeLh0uzsa88ZBJjqBeCRm4HW9YAnAnzkMSAyMkn2S3t78LlHtgCwXOX/5i2zTvCoq0csU0AiW4RDVfC+peN79B+TT/kGzj3tcDSHogHRu6ppGpxGAUEli4TpQVfBhamlBJQu3zNrXADS2Nk+9lMaZAYp4nXgrbOtIieTcErYY7GYYJYJaCj/3p1wImdqiDgNTPcVbMk3j9Xv9wtAHIvFkM1mBQhSFAXxeNwmE5cTajJQrLxT3ieb/BQKBbT2pXDHr3Zhb1cKPpeG739oKS6cU2tzipWlaHJMxIRU7iOsjAWTgoim80gUVUzyqOJ8kI1jstZYGvEVM1zIFHQES8kfzz0BhtPphEvR0RrTkdOtgg9nZ79lVggaDOTzZcMfmtPx/LC3n4CaRSReHwBED+O6Luv8nF2nw1kCWDx/ZIVkhoMsJsEMPydnDBNAD5asVfZlyzJxslpA2YxqV0cct9y7AW2xLGr9Ltx943Isn169OMnknN/JyQpZgcB/V/tzPEPFkRYCNE1DfyqLTcdSSGdzuMjvF+CnWCyK61QGEWR6G10FdBdcaM9omBfQxPogyCT4kI2hZFM07i0EB2STWRAk+PlLu/WZF4QNhNwWi02g0tnZiVwuZ3PGl83OTNMUoIlrj3sX9yQeay6Xg9vtFmy2rIIYzrnnOpSVE/FsEXc++Bpe2tcDRQFWzqxF5fYv99NyHRPoj+eC9EhDVVVMrfFi3ZEEdrTF8K5FjaI1iecKKLd5sFjL/mX+f7LfxAZYbQsIQ6hrWEChfJrrStd1uN1upFIpFItF+Px+/Gm/5R/19vkRm/KH933usTxu/uFx8P5Gk1DZwI0tCpSMcw8BYDN+I5M9XKZXNheU94HKNgrAup+qMPD9a87EiwcT+OjqmVXXkqwUG+t7KNlsuU3gZMXEu/tLUR90o87vQm8qj90dCSyZOgkITgIS7WhM7kGNz4louoC9nUlbP2dzyIOw14lYpoB9XUmc2TK2vZ5/7ZHMFfHpX2zCn3ZZjXD/8Lb5uOPi2cN/gZ59QMfWQWXj+aKBn6+zRnrdvHp0c6+f2HwMsUwB02p9uGSIkV6VMashgIDbAbdDRUc8azOkAQBNVbB4chjrDvZh85F+YY6GxoUWq9u1Hf/vA1eM6pjHU2w7FsP2tjhcmor3LZ088AmmCTz1KWDvM4DDC1z3MNC4YMTvcdsDG1HQTbzrrEn4/9618KTd2MNeJ/789xdhf3eqalV1vEXl+KUpNV4E3BqSOR1tSR1Nbvss1VolbQHtvBPTXGXZWzqdxqxaq2C5pystqutjFfKNkpV0ALZe3WQyaWMUZWY0l8the9o6vrNrizANHUYFEHI6nYhEIvD5fMKQqlgsIhwOw+fzobe3F7quw+fzIRgMivfiZ+XrZLNZ5PN5kbwTFORyOcRSGdx432a0x60JB/dWjO/i6xE8MgHj8U3EhFSWjlcWYL5zzVIE3Q7090dx5EjOxpgwVFWFXzPgVYrImA505TTUl5JSSiflNdzstVoZupN5tPVn8NvX2wEAl8wMiOfLYLg8v9b6ngkCuW6y2axgs8kGxbIGdvRbx7eywRSySbJSBGlcGwQ4/DyUq9OJXP6sgyWCsoTT4/GI9UkABkCwRusO9OJj921EMlfErAY/7r35nEENH5nUAsOXDTOqAeShAPRogow0UE7CRwq0VVXFuoP9+MwT+zG3zo0L5tTZDPV4XnkdE2grioImdxHbU0BbpmygJsv1Ccw1TROsM49bXvsEwWxtACDYbJfbjRePWqzy2bVFeDxBsR+lUikxJszj8cDn84mRWGRAyUiz1SeRSAh5MJl6GgASrNO1vFIhcbzgyCbAKuoc6Uvjlp9twP5uq3D43x9ahssWNonns2BF4JTNZoXqguz8my3OaA4CW7qwsz0u9m2uFbn1pXJt855VKBTQ4jUAqDiWUoRLPb9HSr25dnlt8bs2TRP7Ygq6UkX4XSpWTHJB01Qbo07Q7vP5xN7J9cpWBbknnHusrDai0ot7MI8tkUiIUYXDMT1jwYvFJzlkcM3X2deVxLoDvbhyUR0AYFp9CLdMHpyAO1mycVltdirabSb0laIoitSLbZePK+2by/Lxil5sRVEk+fhpQ7SxjLb+DD74o7X4064uuEuStzsvmTOyi2RHic2edXFVmfHvt7WjO5FDU8iNdywa+Zxj0zTxszWHAAA3njd9yJFelaGpCp773MXY+KXLBoBshpin3dpf/qHo094x4uMdj0E2+4ozm1Djr7JR/fErwJaHrGLJNfcB01aN6PWP9qVx870bkMrrOG9WHb57zRIM6k4/RqEoCuaUVDLjPSplvQ6HA3MbrIT8YLQgeu+Y/FM+3pV32X43k8mUGG2gO1VAT6L6OMTRBBmkH685gpvu34y/7O4WCYosXY/FYqKHkTdll8uFVCqFnmQOh3LWdbY4lBEJAxNV9k4SwDAJ8fv9oi+bvbScly1L7gELUHK0GB1befPlDG6vU8PtF83E3MYAHr/j/AEgm+eESgIy7LK0daKFDJwrmcqw1wlVVWyssgw2ywyMgnqHBQi68y7x/cvyYsA6B07FRHPAeq0f/mUfYpkCGvxOzK9RBTgl08JzLyeTAESySjkumSiOFtvQZcAwFUz16WgJlBNo9lAC5cIImaFKh2v2UFeamVWLyr5sFgFk8C4rJ6bV+eB3a1g1sxaPfeL8QUG2LBkn2OT1xsSX0vlMJoN0Oo1UKoVkMolEIoFkMolUKiVYSq5zXpP8TmWQLStJmETze/F6vfD5fGLd0+Hf7/eL77Wa0uN4oarWLG0AONSfR65QtLmM03Vb/plpmrYRXx3ZclFOLhxwbWcyGdFqwvPAIg4Bi7xHsJCmqir2Jxzoy5rwaibOjBiiD9flcolWEpfLhVAoZFNOEICRDaWhHw2yOFaMBQquk1DIymllc6zhFC94bgELZL96JIb33bUG+7tTmBT24Ne3ny9ANu8LqVRKXK8Ehjy3b0aQDZTVrnu6kjZ5PIEu90Q5n5XbABRFQZPHWuddGUBHWU2jaRpCoZDYU+QioDxqi7OzL54VgkMxbe1NAGwjJVkMpIkn1xivVfl+x88hj8wim822HO4l4XB40Jyd60E2NZP3cXqllEeMWq/zwp5uXPXDNfjiE9vw3O4e8f0OFiwAAGMPhmXzyFOhNpvQjDYALGgOYc2+3jJgblkG7P6dZYjWfBHW7u+t2ot90bxG1AfcmBQ+eXKrv7bojGdx5V1r0J3IoT7gxt03LseyaTUjf6HtT1h/DyIbv7cEkm9YNX14/d4V8fKBXuzutMYIjMZd+njGawJoH+kv/7DxTOvvLgtoZws6drTHcWZLaMK1LmQLOp7YZMk6r6n2/R17DVjzX9a/r/wBMO9tI3r93mQON96zHj3JHM5oDuJ/b1x+Ur+jjpg1N1tuLxnvUc0QbX6TH5ta4zgYzeEt09yCfQPKI756im6b9DyTycClGGgOaOhI6tjWGkVTZGxGppGB/M3WLhzqy+CdZ9QIZ1VGOp1GLBazJRNMPGOxGLbFPTChYKqviBotD8NQhFEZJWk+nwXEybwwmXC5XOjt7QUA1NSUzZTIehLYk/3kCB0Cg2w2i1gqC5/LSnxvWj0b166cMex1IjNjEzUIXmSjKTmYiPL7ZIGEn11VVTQ4czha8KO74IKup8XoIxnEERBPDShoTwI/f8Uymrt4VgC5bMbmAEypLFlnMsZybzaTP8MwxKgbh8OB9V3W9bK8TgdQdg6Xe7PlsXOUXfJxrit5ZA7XYWVU9mUzKWbPItsY5O91UtiLh287D5PC3iHHVcosOWXE8nU13JCBw2B/KpUKI43K8UIjAWmqqmJyxAOfS0U6b+BwXwZ1NRFxnkTbQclYUd4Pm0uApzevIlc0AckbQGYpOaJLluLK/c8ERFS88LmqqmJNm/UeS2sK8HstqW04HBbGUlyrwWBQACxFUYRyhn4aNKji9+R2u4W/AGCBYwJcFkMADEsyLqsy3G43dCj47K82I5ou4KwpYfzkxhVoDHmEgaRcEKmU1Y5UOTHRYuHkCACgO1lAbzInCroMFl/kv1nwIZB1m3kEnU4kCkBXzoEmZ1H02CcSCXGe5dYAKiqc3gCeP9ABAHjrTJ/YM/idU4XGYiPXQ6VZH13GWXzm/sM9zufz2aYycJ/zer2IRCKDyri59uS9m/fbwQzFTNPEfWsP4Wu/2QHDBM6eGsJZk4PHXUuykehY3kdPNZsNvAmA9gVz65ErGriALtayIdq5Jba7Cmv9iZFImU/HsKIx6MbF8xqw9VgMP7lpxaCM75DRvQfo3AaoDuCMdw14eNORKDYf7YdLU/HhUY70un+tJTv/wNlTEPaOvXkMDdF2dyaQyevWKJamEtDu3g3oBbz12y+gLZbFo584H8unj6IY8QbGM9s7EM8WMTniLV93cmx71Pp74fuApdeN6LXT+SJuuW8jDvakMDnixX23rETIc3INfr785Da8cqAX//6Bs/COxZNO6nuNVVQzRJvfVPKsiOZFDx5vfrWGdXOP6i6YSnlmJyVfl83yowgVNe6x7c/e0ZHEob4M3A4Vl8ypEQkyACEbZ7+q3ANrmibS6TR2ZCzmeFlNeSa2zGYT/MjmUgR4yWRSyDb9fr8NiBBEyCySx+MpOz6n0/j+c/vx+x3dePhvViFYuiFPpGLMWEQlYyzH5x7Zgk1HovjyJU1wATZWBygzoA0lRrtH90DXy/diyha5hl0uF6YETKwvPX7W5CDOa7GnKFzPnB1MhpB9p6qqIpVKDVA+mKaJw/0FHE0p0BQTy2p1KEqZiWcyJwN6ef3IBkEAbEBMHmvGqNaXDQCJREKsY6/XCx0qPvPQJrzrrEl4Z2nvGYzFZlSy5DKQqgaQh/pzKoJFF5kJHm6oqgpVUTC3wY8txxLY35PBslllgENQyu9XdiWPeFT4NR0pXUNHVkOLW60KtMluyeCJrTlAeToCXem5zxRMFRs6rN9dGinA4wmgtrYWTqcT7e3tSCaTcLvdwnyRey3XI0G47AVAt3OeYxZLObaJPd08ruN9l2SngbKhGwD84LpluG/tIXzzqsVwKIZY6wyuWU3TBIM6XMO1iRxhvwdTwm60xnLYcawfK6aFRAGY64NtJlRKcR1yHygWC5gSULAzaqI9q6HJae0H+Xwevb29Ygwhi5cyC72lT0G2aGJS0In5dU6xN/FxFm+4LjKZjK1FjMVH2aeC+xpVEmyL4jpiHkBPE1khIbcPVKpb5LaNwaKgG/jKU9vx0DqrcPq+s5rw/71jLoJ+75C/dzLBMD8LCwSnIib8VXPx/EZcPF/qsaUhWs9enFln3Uh2dsTH3OTndFhhmibyugG3w9qMvnHVYuR1AwH3KJcW3cZnXVJVNi5Gei1pQf0oe2n/5cozMa85iPcuGZ3pVbag49O/3IRtx+L4w2ffAn/FZ20OedAYdKMrkcO2thjOmVELRKYBriCQTwA9e7GwJYS2WBabj/ZPOKCdLeioD7jwweVTBsq5DaOsSFj8wRG9bkE3cOeDr2HL0X5EfE7cd8tKNIVOruKkJ5nDn3d1oWiYmNUwMWTjgN0QjQzc0ilhvGNBHRY3e8XNmDd/v5KHC0Xk4UB3zoFa1UoQyf5duzgCTdNQGxzb/uzfbLXmkl84K4yAxyESBkoZE4mE6A+jjMvr9SKTyaA1YaCr4IYKE2cGsjBydmdmmf0GIKRwHHnDSn9NTc0AkM2kQR6NQhAVS6bw5ad24snXrWN/bk8vrj1nbFj+iRZyr2pl7O1MYH93CofjOs7wldeNzAwCQEPJEK1X90DXy72IsoEck54WnwVe5zT4cdf7ZqKjo8Nm6kMgAsA22giAcM1Np9NChslrRNM0vNJRBKDijJAOvxNCbs0kmcdAuS4LAWTEqXhgIUjuwa8MMs4EU4AFpNjnGggEEM+b+Ph9r2Dz0X68sLcbq+fUH7fwW9mby/ficZxMQ7QTCYKFkfZpc5+b1xjAlmMJHOjLCYBC4Orz+cSaYIJO5UOTq4ADGQ1tGQXT/OV9Qe4dlUEPANGGwnXjdrvR29sr2lsA6zxsTTiR13NocBuYEQQikQj8fj8ymQwSiYQANbLcm8WGQCBg8wMgG8+Wn1QqJYAxR4Kxp5sg4XgAhIolACgYwN7ONM6ebq2PJVPC+H/vW4BCPgNe2QRPfC8Att7bidACwwLFYHPsjxeqqmJOg9cC2m0xnD+nfkB/ML9/BtcKn2eaJib7gZ1RoDOrwfAb4p4nM86GYQjlQj6fh9vtxrPbLPUt2WyuTZl55j2QQDoYDIq9kE78suxfNtpjAV52Q2erCFuwBjM1A8ptKsMpuPSn87jjwdewdn8vFAX4u0tn46aVLbbC42Ahg+GxLO6w4AGc2lGIb75Gi0ADEJ4KwMRs/QA0VUF/uoDO+EBZlWGYONSTErMDT8fIIl808LlHXscnfv6aGGXlcqijB9nAkG7jXfEsfrvVMsgZiVN4ZTSFPPi7y+eNuh/X49TwemsMx/oz2Hps4EgkRVEGyscVpWwG1rWj+rztCRLXnjMNL3/+0uoO4Mc2WvOyXQFgzuXDfk3TNPGFx7biud3d8DhV/PSmc05Jv/QTm46haJg4a0p4wPzG8R6V8vEzJoXwr++ei6vOahQgtCztBWpEn3a554xjr+Qq+PGcg4cTuq6joBv4/Q5rrN87FtSJ/lQecz6fF/OJ2ffpcDjg8XiQSqXwetxKCueHCtD0rPhMBDtMSmVwZDEK5R5T9kYCsCVLNPchkPL5fFAUBT2xJG57cDOefL0Tmqrgm1ctxrXnjE4582YIeY1VmmKxn/FgNC/AE2XUsqFdjSMPDSbypoZoXhFJqcy6AFYS1+I1MCviwJLJQfT29oqkmcdC1lw2+yEQIItMQEPAoKoqirqBjT1WurM0krMlywQYBNAcvwPYperySDEma9WM7mTGmQqJQqGAeNxKon0+H1rjBVz1wzXYfLQfYa8TP7lxxXFBtsySc/3LrPl4BdnA0AWb44UFtK1C14G+nCigMWl2u93CEIxKHbLSjW7rPLSnVbF+Wezjv9mDz33D5/OJc8g1xh5uAAKov1JyGz+7toBAwC8AdSwWQyaTgdPpRDAYFO0pBNQsJtLUDLCz2bJrP9cf3al5DMczQONaMU0TvekCPvrAFlz/k/V4/WhU9F/LxnBU/cjsqMyeyz8fr0HvA/l7Gk1csaARH1nRhIXNPpvcGiiDanlvYdFNbj2Z5LXWeVtaFb/L+ePyfsUCoq7rKDgDeK01CQC4ZKZfAExFUcT9ki0H/Bll4EB5qgJbVsicy2uFfhD8fqjo4OfM5XJIpVK2NgzuLYFAQJj2DSee39ONtft74Xdp+NF1S3Hzqsm2wuNgcTLBMGXvg7X7nKwY31fOMCOT17H5aD+O9Vs3HbQsBQC4u7ZgVr21QVfr037vXS/h4m//BesP9p2qQ33TRDSVxw0/XYdHX2vF83u68dqR6Im/aNcuq4dZdQJnvHPAww+uO4KCbmL59Bqbi/xwY7TuqdWCQHowoLxkSEO07UJevnkCAm3AmoVeyeQDKBdK5r8TcA4/8fvOH/bgkVdboSrADz589ilh+U3TxK85O3v5yZnNfTKjMnmVHbSZiMt9ULWKJQHsyrts0mmOfOlLF/HS/j5kxqDwWCwWsf5QFL2pAsIeDefNCNsSBtM0xQ0dKI8oYd9aKp3BzpLb+LJIQYzAockZkxS3221jF/n6uq6LJLfasTHBZoKpqioOdkZx/T2v4pWD/fC5NPzkxhW4bpTtKW+WkCXGlSDpjFJh6kBvVgBt2TgIsICoU1NRW5KPdxVcNsmkLP/WNA0Rt4KvXxjA355bJ0ygKKVln7QsG5aPS1VVpNNpG9DiNbG7H4jlAZ9mYl6gYJN7E6BRmktgTLBDZpJJH98fGJgIVuvL1nUdiURCgPhtXXm8/4drcbQvg2m1Pjx2x/lYNavuuOdCHufEmc4yYzWeo7JPeyQhG6KR0eZ6oxGULIu2Ae2SmqIjq9nk4LLDuKzAkNcvzzuLN5QLA0DSdGF7TwEKTCyN5FFbWyvmsSeTFliiSRz7r1m84Wglrn/2blM1wetDNp1TFGWA+d1QwSLinq4Urrt3E7a0xuByKIgmUqIIxL5eyoUrgTsVIsNhz9/oILBkjKagw3jvkkm4Y/VknNlkAVjZrJDXG0MuRMrFuklea50dSwGKog4oKnKt8WdOpxMvHs3DBLCo0Y2WsFvsRwKIF8omp9z/5P0QgG1MGM+bXCigLwD3EZpGkomXcwm2PfD6Gqki+Mqlk/EPb5uPR24/D6tnhMTxHa9gczLBsAzgT6XC+U0BtD//2Ot4311rhEGTrU97EOdxAJhR6oXa1XHaeXwksb87iat+uAbrD/Yh6HbgnpvPseTRJxqUjc9+K+C1A61cUceDpT6P0bLZv1h/FB/56TqsLc0oPJEQQHoQoLzsOIZoZ5UY7SN9afSl8pgIoRsmXtrbI9QLA0KWjQ9iZFctHnj5EH7w3D4AwDevWmwbMXIyY3tbHLs6EnA5VLx3SZURZeM85L4s/t+AgkN9WRyNFWzOwIDkPF5wCdkk5YWGYeCO37Th8//Xip3HTrxopus6ni5Jry+dVwOvpzz3lUlCIpEQUlpZJpnJZLC730TScMCrGZjlsQoEHG8jOx+TAWLyQHknmXz5u6JbKsE454RqmoatR3rwoZ++ij1dKTQE3Hj4tvNGNPbvzRyVygkG7617u9O23mZZWk2gW++w9rjugkswhXxNJlVkaPL5PGKxmDAMkxkgWTYuz0Gl1DGdTguGRpaGr++ykqrF4Ry8bqdIYsmOyv2GmUxGAGR5RA0TVibLleY/1fqyaV7EY3p2XwI33rMe8WwRy6fX4PE7zsfsYbSsyL3ElJsSBBHMjecg8AVGDoI0TcMZTQF86YqZ+OrlU0SrAdlD+RzJjLbD4UBTidHuzGkoFO0FHhqRkVmmJJemYNxnWLyRVR0be6zPMjtooDnkFvtSOp1GMmk5VgcCAbE/ySOdgsGgKCiy1YF7lgwwZDZbLrIcT8Kdy1nj9p7f24uP3LcZbf1ZzKj14qGbl+HsqWE4nU74/X7hPF0tZFZ4vBdxaFIHlNs45ELcSEMu2NADQDYE5L2E+xz3CtkfpNZRgKYAGR1IGuVjYpsUYO0RNG0MBoP4v93WffcSSTZeLBZF0YRrg8U/XddFWwv3WraC8buQj7ESlPPez1YGAnOujZGCUdM08fDGo7Z89s5L5mBGxPr8ctvPUDGUWuhEgtcwX/tUxkkB2seOHcMNN9yAuro6+Hw+LF26FK+++qp43DRNfPWrX0VLSwu8Xi8uvvhibN++fdTvdwbBNFlrCWifMcQYrwWVv3c6jhtr9/fg/T9ci0O9aUyp8eLRO87HRfMGn4M3ohCy8fcNeOh3W9vRk7RGer19lCO97l1zEC/u7alqjjfSWHocoL14ShiKAhzrz6A7UWpbkEZ8hb1OzCqNY5oo8vGX9vXghp+uw3u+/1L1m1jreiDRBrhDVrFkGPF/29rx5aesa/+zl83Dh1aeOgbxEY4oW9iEsO/UbrxjEZWGaJqm4WevHMOHH9iBX23tFzfO8oivsvM4oNgkbbquY1ZpzNfW1hMD2qyMnz8jiHOnBfGuhQ22nleyM/F4XCTFZLPZh7g1wZFeeRTzWdFbxtmfct8ZvwsZ5DBhJuCS+27z+TxcLhd8Ph+cTifS6TSCLhUuTcWcBj8ev7P6+K6/1hgMIJ3RbN0/22I55AxFsDRy8s6EpsFZGvFVAtpMXMkc8/UJTgl23W63SE5lCaTc6sDfJaBlAsr1kc4b2NRj7VdLwjmR8DFZZVLJtUnFA9USHNEmZOgloF2ZNFb2ZTORpWmSz+fD/t4MioaJd581CQ9+fBXqhuEzUgng2d7Ba2K8g2zGaIG2qqrwuTS8f2kzzmz22xQMlMtS0koQxCJEg8eABhM5Q0U0XzY54/1LLgwRxMp93vJ3L7vYv3DUWs/L64oIhUJiH5Hl2IFAAA6HA+l0WuyxwWAQfr9frD1KdAmoZRM79ksDsBVZhjrfhUIBmUwG9649hE89sh3pvI5VMyJ48KPLMKc5LOS/Q7GKpmkOAGvjNWRJP0czDqbAGW5omob+rI5XDvWjK56xSfgZLArKBR/Z60ExdUzyW89vz1rfH8+tvN6okGjLuXC0Pwe3pmD1NJ8wOeR5Z3FI3qf4WgBEO006nbb5l8jHyD2JKg5ZeUE/l9G2CBR0A196Yhv+8dev4/afv4qCbgFa2cV+uA75sgnhWMYbxWYDJwFoR6NRrF69Gk6nE7///e+xY8cOfOc730EkEhHP+Y//+A9897vfxQ9+8ANs2LABzc3NuPzyy5FIjA4ADQDMNETrO4DFdab9MdvvBQd97HQMjCc3H8ONP12PWKaAs6dF8MSdqzGvaYz6Wrt2At27LNn4fLts3ALJhwAAHzl3dCO91u7vxd6uJPwuDR9cceIy4cWTw1AVoD2WRWd84OzhoMeJOSWmQgDpxhLQjh0BsvHjgvXxFg9vsIDpypm11TeqEcrG1x/sw6d+uRmmCXx45TR86tI5Y3m4Q0ZBN/DUljYAGNWIt/EQvNkC5b5DIbHszYqEnzeWiJKBAhNZ04GkXmYUWQWfVWsl/Se6HxKIXDgjgP+8ai6Wz6gVjCNZAvaCUXInSyT7kxnsSVvGZEvCWcE+BwLW9URAR7aITBKTa7/fL/ooaYZFUEYGjOCK5jQNQTfuv2UlHv3E6tFNS3gTx2AAKexzYnLEOk+H+os2gEAWhWu03mHtkb26VxQ8qDCQnc1lsMFES3YQr5SNM3EkIEqn00JeydjSp6BgAPUuHdP8pjC9kw3TCLBYtKLbeKX5D5PAypEzlX3ZTHpl5sntduML71iA/7x2Cf77Q8uG7WAvG2DJ8k6v1zvu+2bl4PfF72m4IbfD8HqWVRAEyGT3uK4AwOXQUF+ap92WLruty+uGe4gMalm4lNlS/uxQUkVnyoBLNbGk1kQwGLSZXXFvIhNNF3y5D1pms2XTJ34ustqyuz1ZycEil8uhv78fv3m9Dd997ggME/jAskm49+YVaKmPHBekM+RCzng2QJNBNu9zwIn5AQDWevuHp/bhU4/txZq9XbbRfwzuUdzzeD4JJnVdx5SSUKUjW57NzjUsjzj0er34434L9J431YuQ1yV8IthGwPeg6kFes9yTyE6zOCK3IPBPpZ+FYRjw+62cYbQy7f50Hjfdsx4PrjsCRQEuPaMRDlUZYNw4nL3qZLHZspfHqWazgZMAtP/93/8dU6dOxb333ouVK1dixowZuPTSSzF7tjVOyzRNfO9738MXv/hFvP/978eiRYtw3333IZ1O46GHHhrVey4o9Yod7EkhW9Att+qaGQCAM3EQAHCgO2k9JgUr8vu7U8gVR9/T8dcSs+oDcGgK3rukBQ/deu6oXb+rBkHanEsBb8T20Kaj/Xi9NQaXQ8WHR8l4Eqh/cPmUMRkX5Xc7RJFhMKA8AEj7aoFgyem8ayeuXDoZX3jnGXjH4pEz9Kc6+lJ5/GGHNd+x6uzsEcrG93Qm8PH7NiBfNHD5wiZ8/cozT2mV0ampePQT5+PvLp9XfUTZBIkBhmilPe1QNAfdLEuonU4nHIqJsGIlbd0Fly3xTSQSAmjv6UqdkJ8BZa5yMkuWiECGbuNMKHnzKxQKeD2qomCqqHMVUQcrAfF4PAiHwyLZlaW8LBYoioJgMGiTh5FtoPyOUlun04nvPLMTj29uE5LRWY3BCalsONlRqZyQY/HkMM5oDsJUy1JXmbUhOKSEN264kNXLiamsNADKTuAABCCheZrcm8/fJ6tJIyQWWFiEAYB1XdaxLgnn4PVaTDd7Otl7LbPVsoMwgTiLB9V6syv7sqmuME0T3fE0frCmHbqplNajgquWVZnWMEjIfZ18L8DeNzpR4kT7tDsSeTy9M4o/7YuLfYD7itfrtQFJuU+ba68jWwYSBGjyjGK5F5prOJlM2t7LMAys5ezseiDkswA+W2BYWOEeQ9Mx7jEENTS2YoGU/fyqqoq5x2Q1h2IE+fkTiQSi0SiKxSLeOq8OF82twz+/fT6+fc0y+DzDA9jAQFf78aiWIEiUQbYMnggYRwu0FUXBvJIR6462uK3IxyKPzGjzvUzTFPuGZYhm7WPtGW2AZwSVWwDgDQTxxz0l2fgMS7VFkM0iozwSjHuRvDfR5Z5FQx4Tiz4Oh0OAcwCiwMNJBbK/y0hif3cS77trjTA9+/FHVuC2i2bbPAWGKxmXwfDJYrMrCyanKsb8HZ966imsWLECV199NRobG7Fs2TLcfffd4vGDBw+io6MDV1xxhfiZ2+3GRRddhLVr11Z9zVwuh3g8bvsjR0PQjTq/C4ZpJfAAhHy8pn87anxOGCawtzNp+71JYQ/CXid0wxzw2OmwQk64F08J4+lPXoD/+tDSsZ0na5pDuo1zpNd7l7QMS2pXGUd60/jTLqtf9MYTcCuvjJUza7FsWgTaIDcj9nFvqWqItg0XzWvA37xltgBH4zke33QMBd3EoskhLGypcrxHXwGSHYA7DMy+ZMjXauvP4CapT/H7H14GxyhUCicasxoC+NSlc6ENM+kdj1FZvZ9a60PAraFomDiWKApmhTcXysfbM6qolFOqO7PUS7W3Jzti1kmOrlgaP1lzGN0p6/3lOZxkl/v7+20GV5Rw5nI5bIlZCeVZwSwKhbzoKZQZHyadiqIglUoBKDN8lJM6nU4hpbQBFKcLn3t4M+56/hC++tu96M6Yb8jNd6KErJyoBEg/uuFs/N9n3oLVs2vFWiRIkZk5r2ogoFprqqfgFEoGmv3IPY+UArOIQvk/X4/MDBNHnmN5HRA09eWA3VETCkwsq8kLIyG6P9OwimuGIIO9+5Sv8zrhd8FkXpbZcs2RKTrUm8ZHH9yOB9Yfw7f+dHDE3zuNsuT/AxiR8+94ihPt097WlsC3nmvFY9ujQo0AWEk0+425TuSCXFOJ0SazKKsWZIUCHZvl0UKZTEbI9R0OBwyoWNdhreNz6i2zNK5fGcgEAgHkcjlR4KP/BGcZ67ouZiIDEKO+5LYYeT1WMoKyKiiTyeBARxSFojUuqqmhHvd+dBVuv3jOiIEy3+947PkbFbzeZPVI5XHKa2y0BWOqXXeXcIFc2JJbF2RzNHmvMk0TLT7ZEE2xrXl5dvWWbgOJnI56n4azmr2i11pWBdEMlG1QlILzeAgkg8GgKEKS7SbDTT8K7itsZxmt6diLe7vxvrvW4FBvGpMjXvz6E+fj8pK/zkgl4/wdYKD3xYkGi7nAqR3pJceYZxcHDhzAj370I8ydOxfPPPMMbr/9dnzqU5/C/fffDwDo6LBYsaYmu+FRU1OTeKwy/u3f/g3hcFj8mTrVzqgpiiLk46L/tgS0lfZNAshUGqIpiiKcU08bog2MzngW1/zvy7Ye4rlNwbGvcnbtAHr2AJoLmP+OAcfw29dPbKTX/S8fgmkCF81rGJbxzHDja1cuwuN3rB7UvEtmtA0aiFE+3rVjzI7jZIdpmkI2fu1gMmsWSs54F+AYvBgSSxdw0z3r0R7LYk5jAD+9acXYFm3+yqISAGmaJkbhHOoviL4rXrM1ykBDNPa3Tgk54FCBVN7Agc6BY+uGE7qu43fbOvGjte348jNH4HQ6BaPMRDuVSglZLZMHwLrBtvVncDhrrZ+FvqTolY1EIoIhZ++izGSTAeL/KR/nvG6C8wIcuOVnG/HE653QFOBf3rsQMxsm1li3NyIGA0hcV2RNZNMduZ9aVVXUl/q0u/Iu24gmJkGyQRWZP8oleb5lx1weCw2DslnL/ZzjmRRFwfoSmz3TX0RjwGkzUaOUk2wiTavYWsBjZ8GGSbucOBJIcQ2yqLPpaBw33LcZR6JZtIQ9+OjqmSP+zgmy5eIGx9lN1DiRPm2xr/XlkC8Uxb4hM8By7z/3l0Z3GWizUCe3LXAfBCB6pslm85i51+yIO5ApAjVuywiNbQIEKzQ8Y9GQ78F1SYk5i4+cfCAb7TkcDvj9fpvhHc85QVIymRRgbN3+Htz00E5876V2hMPh0vU28hxNVpaMRwM0MtkyyK4GEGXjstGy2gtbIgCAvV0p4T4vK0gIsvn+LPjJRUkWeHqyQN5QRHsMC4iAVZD5w17rXnvxDB+8HrvRIdeEDFoJurl/0kzP4/EI53uCeO5xfF8qILhOZXPJkURRN/CVp7YjUSJLnvzkaoHBZFXEcOeZn0wwfLIA/EhizN/VMAycffbZ+OY3v4lly5bhtttuw6233oof/ehHtudVgjVuVtXi85//PGKxmPhz9OjRAc8hYN5RxRBtKNOzq5ZNxicvmSMqWKfDim3HYrjyB2uw4VAU//To62WgONaRTwNPf9r695zLAI/dhOjBdUdQNEycM6NmVAZFqVwRvyqZXt28esaJHu2IYn5zEG6HikS2iIO9FtuCppLzeKcFtFujaTyx6Rhel1nvcRZbWmPY3ZmA26HivUuruHMbOrDjSevfQ8jGswUdt96/EXu7kmgKuXHfLSsR8Z36CuNPXzqI2x94FRsPTfyxftUM0eY3WcWkw7GyGVjZedxitLsLLpu0N5/PQzF1TAtbz9s2SkO0YrGIp7da6pG3L6gTlXsy2YA1Z5bJAUEOYN07NkUdABRM9+bhV3Ki55pJKoG2/Ln5OvLNnZ8pk8mI6n8sr+BDd6/Dywej8DpV3H3jClx/7oxRfc6/tjgeQFIksCL3CDLxNE0TDaURX93F8ngagiKuRcpu+VpMEOUkl2udjB9nVMvsDSWXlPmeXTPQwdzpdIr3UlUViUTC9jOuNYIjXkc8FlnWzQRX13X8bnsXPvbgFsQyRSyaFMTjd5yHuSP0MiEjJCtLmDhP5DiRPu2pNV54nCpyuonDfWkBkGXneJ4fmXVsLknHowUNmWJ5zwPKoIBrjECb+4dsrqYoCl4uzc5e1QS4XU7b+iSIkZUaAAQI4h5Gd/zKx6jIoBeFLI1mMbRy/vXTWztxx693oT9TxK6uNDLF0eVpsjJDVkCNlyDIlpVJQ4HDE+3TJmboSOQRTWZFcZdFGhnME/Ry3fD+5FGKCLsAE0CfbhWPuTYymYx1Xp1+rD1oAe1LZpTnY8vqnVQqJf7N92Rhh2oel8uFQCAgWrZ4XCwYVs6ep5ybxdGRnm+HpuLHH1mBj5w7HQ/dukq0kVYaNw63KMg1Xel9caIhG2a+kXvnmF9NkyZNwsKFC20/W7BgAY4csUYzNTdb/aiV7HVXV9cAlpvBuYPyn8p4+6JmfOldC/CBs0tGV5OWWH/3H8GSOmujreY2/aGV0/C5t83HmS2nXWYZz+7oxDX/+zI64hbr+OOPrBhVhfS4oReBRz8GtG4APBHgsn+xPZwr6nho3WEAwM3nj5wRAACHpuDL716It5/ZjIvmjpE7ekWkckWkq8wedmoqFpeKA2LMl2C0twOmiZ+8eBCf+dVmPPbasZNybGMRf95pAad3LGpG2Ftl4zy8Fkh2Wudw1sVVX0M3THz6l5uw/pA1Eu6+W1YKI6VTGaZp4qF1h/F/2zuwr2vit4tUGqLJzM/+3rLDMlltjvjq113QUR7xxZ7VDy6K4NPn1WFO7ehYs/1dcWzvSEFTgHctbkahULDNyuboJlbUeVxOpxO5XB6b+60b9qKANQvU7XYjHLauIXm8CcEWPzOTCyauZH0Iwg/Hirj67vXY05VCnd+JX912Ht664NSMkXszxGDScdM0cfX/rMXKf38JnenyGBnZWZcJan0JaPfqbtvsVvbJktXgmpDl5Uxs5eeRheY8dkVRRPuAoijYGy2iO6vAqZhY1qiK35VdbdmfyHWqqioikYhYV263W7Djcq8hVRoAhDN6oVDAj186gn96YhcKuolL59fh/o+ejabwyMz1KG2XwWKlwdtEjdH2aauqCk1VMKfe+i739WRsxRn20dIsSmasAy4VQc36LinjBcpgX07s+b3LLSpkUTOmE693W7+zos4QMl5KvbnP0R+A/bTc52TZLh3y6WgvFwxk+S+fL4NMq7XCi7teOIwvPLUbBd3E2xY24pHbz0PAPbqWArLjiqKMu2JOJcgeaiwZ40T7tGsCHkwKWd/DjraYTUovF2lYZOFeBJRdrXVdx9SgtdbaMqpQDPCP2+3GXw4mYZjAvDoXJofKI+qovOG9mUofKh4IsmXHda/XK2Zos9WAijIeM4tBVAnJ39XxIpYu4I87OsX/5zQG8PX3LYLbYTeFHKmRnlyUGuu1d7IA/EhjzIH26tWrsXv3btvP9uzZg+nTpwMAZs6ciebmZjz77LPi8Xw+j+effx7nn3/+qN93xYxafPzCWVg8pQSYPWGgznIxXqIeAmBJx0/E5OfNHqZp4u4XDuBvHtiIdF7HhXPr8egnzse0upPgwmuawO//Adj9O0BzA9f9CmiYZ3vKb19vR08yj0lhD644c3RJsduh4eoVU/E/H1l+UooF//DIFiz+6jP4TUneXhkD+rQb5gOKBmRjQLxNyMu3jGNG+7OXz8Njd5yPOy4ZxBWcsvEF7wYcAzdK0zTx1ae245ntnXBpKn5844o3rC994+Eo9nen4HGqeNdZk96QYxjrqDREWzWzFredPxk3rGi2Va5VVYUXBXhQgAkF3fmymzIBy6VzQrh0pg9Bx8jMigDrPD9RKhidMy2I+oBbVLeZxKXTaTFdgjd7mrYc6C+iJ++AQzEwx50QLq6cUSs7qvKYyWwCEJLxXC4nGCNKSv+0swtdiTxm1fvwxJ2rxRz70zG8GMwQTVEU5IoGckUDh/oL4mcyk0HgSyllb9GDom6I5J5MEAET3eHZF8veWb6/bK7HdcvkkS7Nmqbh5RKbvbimCL9LE0kXATwL+LquD+jvZhINlE2FyHRX9mXzWLoSedy3rhUAcNOqKfjO+xciEhjZvZOvTSaGjNN4lPKOJkbbp801xCKiDLS5ftjnXGmIpigKmkry8a6cw7aWmQ/S1VlWV8gsNQBs6tNgmMCskII6lwWqZDMpGkx5PB6bczf3ORYaCdw1TYPX60UwGBT7FUEkHczlwhC9KhSHC5/+1Rb88Hmr7//WC2bgRzesgM81OpBNWTwA23is8RCURrMwR++E48WJ9mnLa21nW0wU3bgmeGxyAZD3I9mks8VnN0TjMXHv+e2OXgAWm031BH0kaCjGYg7NIeXieqFQEG72PI+8T7KtgQUA7q0E8nyN4QDt/d1JvO+Ha3D7z1/F2n09VZ8j94qPZEyYrNAYS++JkwngRxpjDrQ/+9nP4pVXXsE3v/lN7Nu3Dw899BB+/OMf48477wRgLeDPfOYz+OY3v4nHH38c27Ztw8033wyfz4frrrtubA+mJB+fnNkFTVXQny6gM54b8LTOeBZ/2d2FWKYwtu8/gaKgG/jC49vwjd/thGkC16+ahntuPqc6gzkW8eJ3gI33AFCAD/wEmHau7WHTLI/0umGUI71ORdSUTPiG7TzucIsCELp2iMe3t8WRL44c3JyKUBQFZ0+rqT7KTS8CO5+y/j2IbPyu5/bhgVcOQ1GA/7x2Kc6bXXcSj3bwaI9l8OlfbAIAvPusFgTHwH1+PERl4jqrIYDbLpiG82ZGbEyPxSyW5eMdufJNrVgsikSR7ApvgMONfD6P3+7oBgC888xG2+xsVvz7+vqEJNPr9docfTd0W4nIfH8WLsUQvYry7FAmgkLuXkrcmQgxMcvn8zbzoVtXT8XnLpuNx+5Yjam1/hP+zv/aYiiAtIBO9/3lcVmyHJGJaI2zCIdioAgV/UWHDSjJrvBkBgmE5P5U/k0wksvlkMlkBLjnWsnrBl7tsdbTysbyGDDKiim1pKlUNpuFy+VCJBKxueHzGvD5fOLzyH3ZBE8AML0xjP/5yHJ8+Z3z8LnLZsHjHrkEl4xqLpcTyepEmpU9nDihPu1SW8zBvnIvNWAl64FAQBQVZQmuw+EQzuPt2TJQYs8sCymcg00m0O12IxaLwTAM+Hw+vNRqrYVVpZo/TftogJfP54V0nf278qgvRVHECDqy2exhZXEoEAjY5idTycD514qi4Nb7N+J32zrgUBV848oF+OK7zzwhEkEuGo0nkz3u5TyPI3HaH4s+7WtXTMHnL52GVdODooAi+0rIBRm5+EvpvWmamFyqs7WlFbGmuE7aMir292bhUIHzprhtCi8a63F6AYEi+7Z5jwas8xYMBoWyh9eAPEaOx0pGXD7u4+1RL+7txlV3rcHBnhQag+6q7X7VTCGHEycTDPN1xxrAjybGHL2cc845ePzxx/GLX/wCixYtwte//nV873vfw/XXXy+e84//+I/4zGc+gzvuuAMrVqzAsWPH8Ic//AHB4In1SR/sSeHJzcewr8tuiObs3IJZ9aXqVJU+7evufgU337sBm46Mri/xzRCqoqA7kYOiAP/fuxfiX9+36OSB280PAX/+uvXvd/wHsPC9A57y2pF+bD12YiO9vvLkNty75iCSudE7KB8vBCN9HKC9sz1eHi8n+rS3Y3qdDxGfE/miMS7nuR937N3hNUCqG/DWADMvGvDwwxuP4tt/2AMA+Mq7F75hLHIsU8DN92xAWyyLWQ1+fPGdC96Q4zgZITNv/D9/RjZMnktJ+XhHtjyOSWYOdvXk8eSOKPriqREdx8aDPTgWy8PjUHDp/HphLCX3PPb19YmbPRMBp9OJgm5iS791c6YJmtPpRE1NjQDWTJpZ6Zc/H/vXMpmM6Fl7ensfMoXy7Mw7L53/hngCvFmicp0xzij5mxzoywngLAMOwDpPCkzUOazkp7vgEkCJUnACbc6kZq99JQNJWS7H0skybzKFr3XkkdEVhJ0G5obKCbHs2BsKhcQMeUozaaQmvy/ZbMDel+1wOHCgK4bXjsaESdnK6RFcvcxqjxup1JsAi6Zub0aQDZxYn/b8plJbTF9OSK0BiMJa5dg1At5Gl7XuOkuMNr9TGiY6HA4BqjkqjJJth8OBqOnDoVgRDgU4K1IUSoNAIACHw4H+/n7hJ8FxcwQ8siojmUwim80Kwz26k1PuSzac4N/tdguQzrhhxSTU+p346Q1LcN25o2upY/C9gJGv15MZhmHYQPZwmWw5TrRP+9IFTbhycQNaQi4xB10eGcl1RLBKubjsRE4jvra0AkW1VA9UJvx+p+URs2KSCyG3JvrOuceQIa5sl+J7co9i7z+VEi6XS7TQ0HjP6XTazP94fMcDoPe/fAg337sB8WwRZ0+L4MlPXlB16owsGR+J+oaFAN7bxypkJcobzWYDJwFoA8C73/1ubN26FdlsFjt37sStt95qe1xRFHz1q19Fe3s7stksnn/+eSxatOiE3/d7f9yDT/9yM57ZXuojqGaI1jEQzAjH8r9i53FNVfBfH1qKB25ZhY9dMPPk3dz3/RF46m+tf6/+DLDqb6o+7WelkV7vW9qCWv/IL5RDPSnc/8ph/MvTO9CdGKhiGKugNHxXRwKZ/MANfUqNF3V+Fwq6WTbqEyO+tkNRFCwpyVjHm3z8YE8KK77+R3zpia2Dy6+EbPw9gGavYv55Vyc+/9hWAMDtF83GzaNw3h2LoAnb7s4EGoNu3H/LStSMYk2N15Ar0gQvfeki/rK3D7t7C6LCzCpzrWIx2l0l6TiBNsemfOulHvxwXS9ePzp8szjTNLGjtQ8uTcFbZkfgc2ni5iv30soSSf6eqqrY3mcgravwazqmOJIiuQiFQgJcMRGUHUppcOV0OkXvo6I68O/PHcPXn9mPf35ytwDjbzbAcqqjskWBwTaQfT1lZlmWTzIR1TQNDU4L8HQVXCIpZUIo92WT6ZPBMR8HIKTl7N2krJPSyQ3d1jWxvM4ATEMkv0w26c6cTqfFqBu/3y+OWX5POqDL47Y0TcOrh3px/b2b8cmHt+Nw1LrHyH26I1lvvP54LHSpHm+mVGMRJ9KnvbA5iB9dfQZ+/IFZ0HXdBrTZOsD2Er62qqqC0e7MOpDLF2zGfeFwWJjqKcr/z95Xh8d5ndmfD4ZBzJbZlswU27Ed5qRNw9Qm5Xbbpu12C9vtdn9tt7vF3W27W0phs0kaZmZmM6MsybZsi3F4Pvr98c17536jEYwY5jyPnygalObqfve873nPEeDz+RCPx1mGtsfjwdsN5ue6okiApJndZ1ov0WiUzfdT3BdJxvk8doqgo+47mZ5RYYUUDDzRJvIRiCpsVnnj3Dy8ePt6nLOofFh7Gqk5gMykvqONdCR7KO9tuHPa/PgAqWD4sRLaj/hiIl+EE0UR+TYVsgjENKAjJiSJsNuLlw6Z19cL5notpmQ0k00FGFpXRJhJIUTy8pycHITDYVYUImUPP+dPai/+vfO/o1Qomo7/9+Q+/OCp/dB0A9euqsD9XzgTRb7exRheMp7pdZbvZo/k9ZlGQFLHmMYLE+Mva4RAhJkRmtLlAASg5xRW5ZsbysE0hmj9uZJPZWw91oEfP3OAbRQeh4yzFhSO3gue3gU89ElAV4FlNwIX/jDt3Zq6o3hhrznz/KkhR3odh2EA51cVYU7h6ElFy3OcKPI5oOkG9p/uHYkkCEJSPs4M0RId7UTEV6/bJwge2daAQEzFyc5I+k2wH9n4zhOduP2+neYmvboC372sagzecXoYBuB1yPA5ZNz1mXWYkTcKngPjiFRZryiKeHx3E/7xmVo8c7DTErsEAHmJjnab6oAgJLuUJH+cm29eTPefHvx+GIvFcPF8Hx69dT6+fu4s1rWhw5KqqmhpaWEXesrXJoL0QZO5By3xhCAK5gEgJyeHdedpdg0AcxInQkeyz1gshlBcwz+9cBxP72uFKADnLixkFf8shoe+5h4pseN0dwwxvbfzOG/KU5wg2u2q00Ky6EDJd61p7hpIRn/Ra5NzMx2o+HikroiKg90Jol2Y7GrSwcvj8cDlciEajbLukcfjYfP9vCycd/omkm0YBl7c34TP3rsHHWEFlXlu+Jy2XnO5mYCUGCQTpY7UVESqgeNgIUkS3HYJa2flIM9ttxBt+prILZD0cLDZbCiw65AFA4ohoDViVUlomsZ8IzweDyRJsihjPF4f3jpm7plnFOhMikpFQIoB83q9bE6WjPaIZIui6WpPMYder9digkbFJRq3ob8ZURRx13v1OO8/3sShUx2MXBXmDj9mNV182HiDSDbfrR3q38Fw57QlScKB5jAe2dmEpu4IGwPg5/oJdI3l15wgCBAMHeUe835NUZGR4O2NEXRFNfgdAs6ocMPv97MiC61JSuaw2+2WBAcyXyQ5vdPpRE9PD7ue8s778XicjU8RwR6MbPy5PY1s3O8fL6vCf924Im0Ma6pkPJOuNP2uAIz4+psos9mEKbWTs0xsIswOr2k+BWCN7bj1Ng50UEjnSj5V8fiOk/jEXzbjzvfq8fC23nFpI47OY8B9NwBKyJQYX/V7oI8/8vs2H4eqG1g3J39IbvDBmIpHEj/TUIn6YMF3pPua0+5liEYd7dbDgKZg5czE4ydQR1vVdDy63TT26TM7+9g7QLgdcOUDs89h3+4IxfG5u7chomg4Z2ERfnHd8nElOi67hD/ftgaPfWVjWtnTVADvCi0IAtsLj7ZF2QWQLv65QhQidMQNCV2qxEgIdezm5psXp8PNwUF3nMjtNMftQKnfwSJE6OAZj8eZzJcMf6i7GDMkHOwyL+KLXAFWOCgsLGTkiQ4FdHGmmTkiZfF4HE09UXzjmePYfLwHLpuIP9yyAp8+qw8DvywyBt8J4ddFrtuOshxTLni8W2VdBN55nAom5DzepjkssW9k/kXPT2snVWZM65Q3vKOuIb3W9jYBuiFghltDuSf52vR8Ho8HNpuNZRFTN5Ei4hRFYUSXfg7qMqqqiv/7oAHffOwgYqqOC6pNt+cSv2PI3WzeIIuinsbTIXcsMJRuIz8Ow6sb6LMFwD5H3hBNFEXYZAnFCTO+xojI1gsRmFgsBlmWmZQ7HA5DVVX4fD7s7zDQHdPhtQHz3Mn78dJcmtemNenxeFiBh+5H643iCmk/ow4lycZptAaCiB88tQ8/euYA2kNxPLXrNIDBZxP3B1KE0PNNhEJkKskebrFpuHPaoijiF68ew3+80YBtxzqYIRmtXX798XsMKazodWeYwgWcCiVHnZ7dbxqKnTvLDZuU3GfI/yHVWIzWWKpfhdfrhaIo7HFEtKkYqes6G63i57OB/mXjV60sxyfWz8Qdt67BV86b3+f64AuTmRo2TpduNjDFiPbiRGe6vi2UnIdNyMfnxGsAAHX8bQlQR7u2NTjwTOokh64b+M+XDuObD+9GXNNx+dJSfGxFmmzkkUSoHbj3OiDUApQsA266N607NWDKfO/fbEbBfWaIJPnxHScRiKmYW+jBOaMU6cVjFRHlwRqi5cwE7F5AV4D2o1gzKw933LoG93/+zLSPHw+8daQVLYEY8j12XNhXDBLJxhd/DJCSm/Zj20+iIxTH/GIv/viJ1eNmZLf1WAerPsuSmN7MbYogdR6NiPaxjiggJg15ZFmGKBjIFcwqdDPnwqsoCkKhEOYlOto1bZFBzVEqioKT7UmCTMSYLp7xeBxdXV2sg0IVdrr/5kYVGgQU2+IokJLzsmRWRbJxOnzQoYbIdzgcRk1rGF976gSOtkVR4LHhb585A5ctnzGyv+Qs+uxEXlBdjMuWlMBpM/cBOhTyhzre/Tmo2xHRBIsEk4+Bow4ldcQBWDrdVLzhjYLogLW9w3wPZxQk5/OJzNO8NRVsaG3RKAMfpcNnvNOB8qcv1eLXbxwDAHxywyz8+bY18DjkIR/udF1nBMxutw8qumgqYCjzs0RID7eE8ccPmvDYnnZGZvniG3UXqVtM64fk4y1xe6+CEa0jkniTOZnf78erR80GzJpCHZJoEgOPx8PWIa0X6kbzEV2Aef9AIMBIeE5OjmXWly+C0mwuRAm3P7gX93xgdhX/4YI5+Mo5syxEbzigLiSf4jCeoA7uSHSyeQxXPl6VMN871BRgnWr+OWmfon9UCOS7yhUJQeWpkHm9i2gCPjxhqiAuq8qzyNHJhJSem/ZHWteyLLMoQ6fTCZfLhZ6eHuZ1Qso1VVWZwSPNd9Na60s2vvVYB0IJPyNBEPCTa5bh0iWlff5uaC8GMi/W0M8HjF43m/elGW9MKaJd5HMgP+ECfaTZaojm7diDPLcNmm70ys8t9TuR47JBTXPbVEJU0fC1B3fid28cBQB85bx5+P3HV8NlH8WNNh4GHrgZaD8K5FQCn3gEcPbdVXx2TyPaQ3GU5zhx8eLMI7103WDz3Z/aOHtYbpyDxZlzC3D1ynJcuKg47e3U8T7eHkZnKG528osTZlzN++F32nDZ0lKU5kycCJeHtpqKgGtWVcAup9kmNAU4+Iz5NScbNwwDDyXUBJ/ZNBueIeZ6DhePbj+JG+74AP/8xD7o+tSP9EslQJX5HngdElTdwOmAyi64dKhizuNRyeLSGwqFmHT8eGccgVB4wNfuDIRx0z0H8HeP16MrqrHOIXUANU1De3s7q/TTgYK6Tx80mu95qTfESHRubi47QBNBoueiw4QkSWYHUtXwo1dPoTWkYE6BC498cT3OmDv6BbbpiL7mtH9yzTLccdsZWJ6I16ROCj9LKIoibNDglxJRS3G7pVNN5JdINx2U+NgvIscUG5fa9T4dMnAyJEKEgTWJJUBrirqORKb4teR2uxGJRCzyS5L9klnau0fb8ciuZggAfvDRRfjxVUshS6LFOZfvpg4EwzAQCAQQi8WYsdZE6cCMNvh1lOmcdkNXFA/sbMVrtT1sbVAHj1cD8GTabrczot0UldiapGg3KkTS/9Nsti47sfmkuQeuKzLfJ70Gn2ttt9sZkSaDNH6Gt7Ozkxm28aZt9LPTDC4R9beOduLNI61w2kT8+trF+OyGSssYw3AwlKzj0QSNLaWae40EhmuIRmrXmpYQm9PmP1sgGV1JxJX2Anrtcpd5/jgVMtfKG7U9UHVgdq4N8wqSUm8aK6B9iJ/9pj2JPByA5Drs6elhZm28KzoAViykdQXAUqQm3Pvhcdz85w/x9w/uGtR5iZeM88WHwYJ31R/JERlejj5RZOPAFCPagiCwPww2b50g2sLpXahOdLQOpMjH+cdNVfl4VNHw8b98iOf2NMImCfiP65fjHy+rHl0iqmvAY58HTm4BnLnArY8B/r5dp81ILzMb8rYNsyEPoRP6ztE21LWG4HXIuG7N2HS01szKw29uXoVrVqV/vRy3jbneM3l4cUI+npjTnkhoDcTw+qEWAMBNa/uQjde/DUQ6AHchMOss9u2dDV042hKE0ybiyhXlY/F2e+GNwy347mN7AAB+lzwmxZbxBt+VIPJBOaDHulUmw0vnPA4ku4iRSAR5dg1umwBFB440dvX7uqqq4sV9jYiqBiKKjlynxObKSFbJz596PB5LRb0ppONEWIYAA4s8IdYRzM3NZR0eItlkaMUbbKmqCkPX8K+XzsamuXl4+IvrMbck83GTLAaHgQ6uFG1D9+XNzOgzI0O0NtXBnofINR0uqbhCa4B3G+c7iSTrJkJD3exFuTp89qQ7Lx3oKD6JOiqUN2uz2dDTY54LcnJyLAd9OrxV5rtw69oKfOW8ufjsWXPZ7bxLeSZEmaKe+Jnd6YLhzGkvLDa7jMc6Y1AS0nDAVB24XC5GXEjKS0SIdx4ngs6TD0EQmOM9APj9frx9LARFB8pcOsqcuiUykDcs4/O3KSKO1j/Nz+q6zrrZ9P7oZ+fns2VZxpN7TEPf29bNwIXVhaxINFzwypFMikKjBb6TLUnSiPtpDHdOm4wea1rDjGjzcZM8SaTPlF6HPudC2SSkrREDYUXHa3VmmsclC/yWdUIeKYIgIBQKWTwi6LOikSyenPPu2lScJoM9XmnBE0+eGO892Y1/eXIfNN2AzylDHQTRpr16KMUa3sx0tCK9RlqOPlxMKaINJP8wmOlZyVJAkIBgM9YVmhtMOjL96Y1z8B/XL8eZ45TxO9p4+0grdpzogtch42+fW48b+pq7HSkYBvD8d4DDzwGSA7jlQTYv3xe2H+/E/tM9cMgibu6L4A2AQq8dly0pxc1rK+Edp25qOqxINTwrSbjsN5tEu6EjjP9+tQb//WrN2L+5FDy+4yRU3cDKyty+5db7Hzf/u/gqi2z84UQn/IplZfCPQ0717oYufOXeHdB0A9esqsB3L60e8/cwXkg1RCPZW31nnFWd6bDGnMcVu0XmHYvFoKkq5uQlDNFOdfd7QInH43h+v1mUuWi+6eRMF3Ei2Z2dnWxWkg4pgHmxf/ekeWGc44rCacRZJ8nv97PDKR2Y6bBAMk9eunfG3CLc9Zm1KMrJZmSPJvhOZOq6MAwDrWENQqKDTASWCAmR7mKOaNOBFQBTQLhcLmY0Rc/LZx5Th5m6SPQ4UZKxo91ce+uLk4729H6pQ07PQ0SLnKJpjebkmIUaOtjSe5hT6MU/X74Q37ksGQ1IHgRAZvFI8XicEXua2Z1uGOqc9sx8FxyygKhqoKEjwoobREL42V7qmNtsNpQ6zX2nW5UQVAw2p82Ta34cwe/34+UjXQCANQUaRFGwjL3wTtGhUMhSMCFiJwgCenp6EI1G2VgAvT+ekNHvQdM0tEc0vHu0HQBw1fISiKI4IiQbSLri8+aY4wVVVZkKgD63kSZHw53TXpTwCDrVHUNPOMZc7fmRFlJH8IVFmqkWBAEOQUO+03wPm08rONwWgygA583x9Orokts6n6rh85nGd1SUo72VIul4o1BSadD3+LEKGr0ArHLtB7eao5qXLy3Fr25ckV7ByGE4knHA2vEfybGF0ZSjDxcTh4mMEK5bPQNnzi1gEjbY3aZMt3kf1jqOAyhM6y5+2dK+ZxGmAi5ZUornv3422oIxnDl3DIoJ7/4K2Pa/AATgur8AszYM+JD/S0i+r1lVMeT4pSXlObjjtjVDql4OB7puJGb8dSyt6N1RW1mZiyd2nuptiNa8HwDQGozh168eQaHXjq9f2Lf5xFjgimVlCMVULCztg2SrceDgs+bXnGw8FFPxzG7TsOXG0S7kpEF9WwifvWsrIoqGsxcU4hfXLZ8W3WwCdUjoYElEu7Y9BrnKx0iwKIrIN8wDTo9mQ1wXmbyMMmA/s6YAqqZiabmbEaVUaJqG5u4ItpwwC5cXL8xl84aBQIB1HoPBIHOGBpLdSgMCtrWan88yX4T9DDk5OXA4HJbZM36OnKrViqrhVHcc80tzGKnLYnRBhzV+5g8w97/1P3sNrYEY7rxuJgodsBBbIEmsyJSqTXWw4gl1rnnnbj43lqLnaIbRfE3dct/DXQZ6FAFuycCSvOTBkpeO06GYdxWnbhIARrKBZMGKij1AbzLNHxoHK5/UNA2dnZ3sMEwxT9MNQ5H1iqIIWRQwt8CNg80h1LSGsaAslz0PkVK73c7m6mmNOSUDubKGLlVCU0REntu6hvjxBI/Hg9aogENtcQgwsK5EgCgmXZ81TWNz2qSyoGx2IFkcIpMqVVXh9/sZQXI4HOjq6gKAXtnZLkPG186fi9qWIGYXuEeMgNL+Dox/ZjY//jFaJJtAioO+rmP9odDnRJHXjtZgHIebAtiU62PXUN6Ej9YyjZpQAZjW1AyvgI6ogfv3mtxjXaUXXtlg+0Y0GmXRhESoZVmGx2OS8Xg8zoo1pBpKVScAyVGE1G42zWkTuaXfdSSu4emEyd5tG2YN+BkMVzI+mvnW/Gz2REtsmFjvZgSwuNyPixeXoMTPVQDLVwIAFmrmbPLBpp4xJ2ITAYvL/Thn4RjMLu56AHjtx+bXl//C7HoOgMbuCF7c1wRgZJzCx5qo3r/lBC7+9dv4xYuH0t5Ohmi7G7rMtUfS8e4TQLQHi8v8sEkC2oJxnOyMjNG7To/KfDe+eUkVPrq8D+l3/VtAtAvwFAOzNrJvP7e3EaG4htkFbqyfkz82bzaB1kAMn7xzM9pDcSyryMEfb10zYGV2qiH14LppXgH+/SPz8e0LZrJKPF2kHYIGt2BemJpikqW7FAgEsKLcg+WlbshIutOmIh6P49m9jdANoKrQjrnFPkaaYrEYy7Wm2TO68JPcrKZLQ6ciwSHomOcIsVnK3Nxc1qWkajwdbOiw5HA4sONkAJ957Dj+5aWGaWEgNVGQbk5bFAWU+BOz/V1JWWCqXNGUjpuHww7NAUVNztgSIaEOIxFjAIwApa5FnqTt6DALLasLDUiCwdYi/eOJP60XPrqLcttJWs67Cv/+7ePY1tADisOjn5/ez2CJi2EY6OrqYuMPNCIxHTGUOW06QNNYzNG2JFmjM53T6WSfNR3saf8gM76mhAkkqRtovIBUDR6PBy8e6jRfy68h3yWxvZOkvABYvBfJnt1uNxt1oBl8IuH0vPxIBACWeUxrPt/rwOc3zMDPrqoesXxrPjN7vA3QeJJNHf7R/BsYzpy2IAhJQ7TmACsYp87gMw+KBKElcks/V7nbXN/tYfMzv2ie1zICRUSaCgLk2eB0Oplqhsz+6DXC4bDF4IzWHAD2O00tiAJW2fhL+5sQiKmozHfhzDkDN+BITUQFp0xBZJgKnyOF0ZSjjwSmx0k0Madd0L0fkiigK6yguSfW627bjnXg7vePmYZVUwhxdfBmI8PG0deAp79qfr3x68D6vxvUw+798Dg03cCZc/OZC3wmCMZU/PT5gzjeHsr4sSMBMjxjRDoF1WU+2CURnWEFJzrCgDsf8CXm1VsOwmmT2M/dl3v5hAFzG78KEJMXbJKN33BG5ZgfHnec6MTprihm5rtx56fXTqixgbFC6oFiZoEHH1lajFl5Tna44mdoST7eHLMxMkJdGLrYE/FJBV3Ynt/XCgC4cJ6fzYjRYyKRCILBIOsIUseZXmtzIju72hOBoCtshjYvL4+5StNBkzdFo47SC4e7AJhmllmiPXbo6+C6KDG2dawraeRD6426jaIoIs+mwybo0CCiXUmSaV6qTdFthmEgEomw9UZdbV4Crus6FEPE3kRE3JmlIuve8O+ZDsUkp+SlizSvTQdbMigTRRFHW0P407sn8IV7d6MjnPxbIOJCEuKBYBgGenp62BxmXl7ehOu8jCWGMqdNjyGiXdseZZ8l7RFUVKT1BiTHCIoThmg0pw2AOc/T5yJJEtweD16p6QIArOPGEKgbSLPZ1Il0OByMRBPRonxtMkEjgu5wOBhh4Ys/tL/R+xpJefdEMUCjcSIAbJRptM8Kw53T/vI5s3HHDVW4uCofmqYxYzICXwjmZepEJkVRZIZoAOBzSFhdamefL6VpULQgfUb0OrquIxKJsBhCuk7Tfek5eAd0ehxde/kxGn5NkentDWsqB1T/8YqIoXxuY9HNHmlztZHCxHtHI4D3a9vw36/WYO/JbvMbCaItNe3C3AJzFiqdfPy7j+3BD5/en5T3TgFE4hrO+sXr+OZDu9AdSd+ZGjE07gYe/iSgq8CyG4CL/nVQD+MjvT69cc6QXvqx7Sfx57fr8Pm7t42LWqG6zAeHLKInqqK+rTfZd8gSy3BmRJoZopnycZ6sjweCMRVfuW87Xt7f1LfzZB+y8drWILYd74QoANePkQkdj0uXlOKvnzoD93x2HYp808dUiAd/geENqOhgSF2VpPO4eeA5HRbYBYqyTFVVxWu1Afx5WwdOtQd6/U3FYjHUt4VwsCUMUQAuri5g2bGhUIgZu/AyON59OqYZ2N1pkuMl3hAjRrm5uSyPlg4O/BwudY56IgreqTcl6+Ox3qYz+iLa1RSv2RVn5IEKJXwWuq5rzBCtXXNa5q+pc01dPgCWbFlaQ6R2oMPevm4bFF1AicvAbB96ESzq+vCGRXQopXEEmpOmAyw9x5O7TWOqC6qLUeh1sJ890w5KOBxmM6l+vz876oChz2lTfGFzMBmrRgSX3Jf5NUCktiQxttAclVkH2eFwwOVysXXocDiwvyWG1rAOp2hgVZHE1oPH47HIhmOxGDRNg8vlgsfjYWSO9j4gWeTx+/2MKPGSXz5N4Z4PG/DSwVbEVX3E5rJTfQTGS0FBec9AUto8Fu9luHPaZ8zOx9rZefDYRFaQ4wsitPYAWDrdvHyc9jsAuHBBLgRdZWMrsVgMoVAI4XCYrS0qFgFgbvRut5t9LxaLWTxL4vE4u4a73W6mEOFl47T/0e9C0XR4HBJskjCgcTAvGaf3nSlI6cE7tI8EeGXRROxmA1OUaD+0tQG/fvUI3q4xuy0oWQqINiDcjo1F5uHyYFNvok0HhUNNU8d5/Lm9jWgJxLDlWAd8o9nl6zwO3HcDEA8Cc84BrvqDGWM1AFRNx789ewCdYQUVuS5c1EdEVn/QdQN3J+a7PzmIOZPRgE0S2Wx2X4WaXnnabE77QPrbxxjP7TmN5/c24ecvHEKfv8K6N4BYN+AtBWYmc78fTkR6nV9VbB3bGEXouoHucLJ4dH5VMWYXTm8zLJ4ESZKEmtYw7t3WiG2nIoxo08WaGaLFbewwomkau4g/vKcTTx8KYO+pLou0k7qLJV4ZPzi/BLcuz8GMwhxLfmc4HEYkEmFScXLVpQLA3nYgpgvIkVSUy+b7cLlcyM3NZV0iuiCT/M0wDHi9puTujdpuxDUDcwtcWDVrbMcUpjt4AsOvC0ruqG2LssMnGUClqhrIEK0lbmdrlYgSdd+o00OOzrw0ksgJfY/cxteXmESeOtO0rlM7knSb0+lk3Sc+G5m61DFFxTP7TKLNG4hm2s2mwzQwfc3P0mGoc9orZvjx9OeX48/XzbVEF1F3mQo8qaSn1Gm+TktchqLpbM8h9Q5g7kMvJdQyy/NU2MRkxjYV/mw2G6LRKKLRKCPqDoeDkZ5QKGSRENtsNuY4zncjiWirqoqYBvzu7eP49uMHcag1GeM0XBBBGk8DNJJGA2DKkbHEcPK0eZMzPkaLvz4RgSTlGN2XSGmeTYXbZh6qLpzrsRTCSflF75PWLo1ahcNhNq8NgM1y86agVCzkI774fY9P+iDYJBF//dRabP3+RajIdfX7O+Al40Mls6PlCE4ke6TN1UYSU5JokwSXda1lByM1G1wnErf1JtOLUx83BfDAFvPnvWXdzNEzhgp3APdeBwSbzaLGTfcC8sB/jIGogs/fsw33JbrZ37pk4ZAivd6uaUVdWwg+h4xrV49fd4s60sxZPAW9iHTxEvO/iYgvcibfe6obijaGcv8EHt52EsAA0u80snFF0/HY9lPssWOFn794CB/7/bs4lkZBMF3BSzFFUcSbR9rxP2+fxKs1Xeyin+xomwS3TbFDECUL2YlEIphbYHbvDjeHLAcUumCq8RjOKLPjE6uL4Pf7GTEKBoNMOs4bDfFkZ1ub+T6XeEPQ9aSJUX5+PgKBACiHmQ4idIhxucwDwfMHOwAA16wsy8rGxxh8t5cn2pT4cao7hpgmWJyZ6WBJB9OiRNRSm2Z1HiczPiIqNP9KRRo+Dow6kD2ajLqguQY2lEsWwzYg+TdBh2Ai7vT/tC5dLhfrQpL08t3aTnSEFBR67Tivqoi9R3ofg5HhxuNxBAIBJjudruZn6dCfi31fEEURDllEqd/MCCYSDYAVSSgvHUgWhGw2G/JsGuyCDs0Q0BpNOkXTvieKIgTZgXeOmcRnbaHOuoxUHKHOYTgcRiwWszhDC4KAYDCISCTCCIlhGMjJyWFyWzJp4+fKDcPAywdbEVF0zMp3YcP8kfHSoZlfAGNObgkkiwbAyOBYg9YHFVMygSiKePFgG37z5gk0dkcsqjBeScEX8gCw6C5BEKCpCv5+jRv/dsVczPImowBjsRi6u7vZHDWN2tD1jtQ8vOqCn7Wnay79Xql7zc9m8/trukJLrrv/szp11IGhScYBWBRII1nsocIWMHG72cAUJ9qWznRCPr5IrzVvS0OmSY40VbK0DzcFsP14JyRRwA2jJa9UIsD9NwHtNYB/BvCJRwHnwDm2JzvDuP6PH+DNw61w2kT88ROrh0yS70p0s29cWwnPOM7mrpyZCwDYRSMLKSAivf90jzk3X5Ig2s37AcPA3EIPfE4ZkiigoSM8Bu84iaMtybVy3ZqK9HdSY8Ch58yvOdn4G4da0BaModBrx4VDUCQMBX99pw5/frsOx9vDE3+mfQyRalRVVWoe6o+2ReByuSwZnD4hBgkaVIhoiybJsKIoCIVCmJfvYI+lqjHdTmYsgNmhczgcbP4uFApZ4pJsNpvFublHAY70mO9zscvca2VZZjOrqeZpdHDIyTHjw050xrCvKQxJAK5aOT5Z7dMd6TqR+R47M0RrCGiMzPKdRSI/JOFtV52MCBHpoC62oigsr5V3hCYJOR3cdnWaB6xF+SIKEjE6VqM2kRUHeKk4FW3I/ZsINL9mn9xjGnRes6oCNimZ1wwMzt1WURSEw2H2mj6fb0LOEI4X+KLNYEkQrT1ewk3PQ1+73W4m2xUEgXWQBQHcnLaNfS70mYqiiPdPhBDVgHy7jgV5EjOR5A31aK/jTdBISh4KhSzkn0ZiqMhEr0VqCvobemqvGZN4/ZoZI26AxntzjCVisZjlPYzXfPhQCjoEURRx14en8MDOFuw7ZfIG+n3SNZMntXy8JU+853lVnFXpZNFfkmRmrNPvx+fzsf3H5XJZDL68Xi8j1aT2crlcbETL6XTC5/Ox6zPvQwGgl2y8vi2Ek50DnzFT19BQO8a8I/hodLNH2lxtpDEld/xFCcJc1xpEVEkcBBJEuzR00LytLZS8jR6XIOhmTFPmEpOJBupmX7SoGMWjIefVNeCxzwMnt5jk+tbHAH/ZgA/beaITV//+fRxuDqDI58DDf7cBly8b+HHpUNcaxJuHWyEIpmx8PLEqQaQPnu5Ju35mF7iR67Yhruo41NRj5ooLkung3XMaoijg+a+fjT0/vARzi8a260Hd7POrilHs62Ot1L4OxHpME7fK9dxjTdn4tatnsMPoaOLp3afx78+Zf8f/eFkVrl7VR2FgGiKVAC0uM4texzqiECSbRQIpCkC+YI7SNMWSsR9k5DMn3yQwte0xdqGk//7+zTr8dXMT2sI6CgoK2BwgHRyILNFBl59D3NkuQYeAcnsMebZkpbyoqAihUIgdVgRBYGSe5IaSJOH5A+ZI0KZ5+ajIz3YHxwN9SX5vOqMSn980C3luG+to01wozUXLsowCOQ7AQNiwIcBZh9DhUtM01s1mhmeJgysf8WUYwI5Os0Ny7kwnK+5QYYe+prEJem4ivWTM5HK5mLTb5XJBURS0h+J4u8ZUTly/xlTqENkHBu5mkzIkFovBZrNZZiyzSCJT+TgRxq0nAvj+C8dx55Zm9n0iUjRHS8/Nz4aWcoZoNCZD0liHw4FXa81u9qq8OOx2G5N+A2BfRyIRRKPRXsWTUCiEaDTKRmUAsxBJsXEkE6diDs36H++IYNepIEQBuOGMmcP+nQKwFKnGo9tH1wFgfEk2MPw5bXIeP9Ji7hF84YJfd/x4DD+3LYoiYrEYgsEg8wZQFAU9PT3QdR1ut5uNu+i6zkg0rWUaS4hEIhaTNfJA8fl8Fnk8qStS3wfhV68cwdm/fAP/9159vz/3SEjGRyvferJ0s4EpSrSLfA4UeOzQDeBIc6I7nSDa9pbdyHPJ0HQDR1uClseV5Tjhd8pQ09w22RBVNDy+wyRPH18/CgTUMIAX/hE49CwgOYBbHgSKqwd82HN7GnHznz9EWzCGRWV+PHX7JixPSK6Hgns+OA4AuLC6GLMKxnc+d0aeC9++ZCHuuG01BPSu2gmCkJSXN3SZIw0F880bE/Lxynz3kOTzw4Gi6Wyt3LS2H+k3k41fzebvW3qieOOwSXzGIjv7/aNt+NbDuwAAn9owC18+d96ov+ZkQqohWkWeCz6nBFU30BjS2ZweHUDzEoZojRGJM6sySfPsHPPCfDqgoisYTs7Majoe2N6Eh/b1oC0usUMlycaJCPFyYf5wub090c32BFkFn+Yq+TlWks0BpnkUGWR9al0Z/v2KefjcxsoJO5M11ZFOOg4A37ykCv90eTXmFHrYzD9JbmleXxAEOCQgTzaJSKtiZ4dB3oGXDpHUQSSJJnWQdF3HqaiMtpgIhwSsLbdb3HX57hLN1YbDYSazJBVGujVqGAYau2OYkefC8hk5qCr19TrY9deZ0TSNkWwaixgv6e5Ex1AN0bqiKt6u68b2UyGLuzIVVvjuGT9GUESGaDGJzbuSUiIMO/Y0mx28tYXJ5yETLOqcU0GQOomAWYQhIsX7ABQUFLA1ycc38QqOZ/eb19CzFxShNGf464TmdoHxMUAjnw16/fHO7QaGN6dNyrAjLUHL7DV1ioHkGuOd5KnTLcsy29OYsiuRQEARZ1SY4RVAAFghhyTctEfx4yj5+fmsiEOjOvzIDr0vAOgKx/HS/iYYBrB2dt/+JiMhGQdGL996tMzVRgNTkmgLgoDqshQZeNEiQHJAiHbjnCLzMHcgRT4uCAI33z255ePP721ET1RFRa4LZ88vHPkXePfXwNa/AhCAa/9syVNOB8Mw8LvXa3D7/TsQU3VcWF2MR7+0AeUDmDAMhFy3DX6nPGS38pGEIAj46gULcEF1SZ8Zziv6NETbP/pvsA+8drAFbcE4Cr0ONofYC0oUOPS8+fXSa9m3H9txCppuYM2sPMwvHt3u4v7T3fji37ZD0QxcsawUP7hyybg5qE5k8B0iWZaxMPG5HO9OGrnQhYnmtJuiydlt6vB4JB35bgkGzH2UzGzeOtKKnpiGXKeIi5bPZESou7ubGaDx3Ww+rqYxIuJUWIQIA9WuEKvYkyERzZuRy6mu6/B4PLDb7ezA67bL+OjyUpw5b2TmGLPIHH0ZogHmPkifIWW/Umea5NuaplkM0Xjznkgkwkg2dcGj0ailI03d6l3dJinZUOmGEY8w0pQ6l8gb6tntduTl5SEcDrO4LzpQUnQcAKyZU4g3vn0e7vz0WkvMGP18fYHieOgg6HA4xiTGaLJiqHPaNOpX3xGDnlg/RG74iC+Coiim8ziXpc3nEUuShDfqQjAAzPGomJHnYqSJnMWJ8ITDYYvBGa2PYDBocXl2uVysm50qw6VudlxRmefESBWraa8mkjeWoDxoAL2isMYTw5nTXpRQhtW0RljRJZXIps4gpzqP097Ex7/xRnrUrXY6nZZ1QkU98q2ga2FnZycr5NAeRqofAGy/SZWNP737NOKqjsVlfmbgmwpd19kacjgcQy5oj2a+9WiZq40GpiTRBpKZnsxdXLYDpUsBAGd7zO5dulnsb11ShUe+tAGXLy0dmzc6SjhrQSG+c2kVbj9//siboO1+EHgtEd112c+BJVf3e/eYquFbj+zGf758BADwubPm4M+fPGNE5qm/cdFCfPjPF2LT/IJhP9dYYNUAhmiKpuObD+/CRb96C4HoKMexJeCQRSyt8OO6NRV9S7+PvgrEA+YcfsUZAMyDwyMJ2fiNZ4y+Cd2PnzmAYEzF+jn5+NWNKyGNlrnfJEeqIRplztZ1RJlJEN2HpOMtcbulOk9up/PyTSJTk6jkG4aBZxJzqxfOz4HP42akmEzQ6OJKhJ4utHw3e54rDDsURlry8/MZmSJiRSTL4/EwIxh633yxIIuxB79WUjtEnWEFO0+HoSdIU6oTLnXYihOEp011sM+WN+Mjok2HTjrIUqRSXNWxt9s8vJ1TaWcHL/7ASwdTKuIIgsDWEx1c6cBMpIqXgAqCgAKPnZExIk99HeyIcFFHkTrn2bXaN4Y6pz0r3wWbJCCs6DjVGbF0jfniBq0r+qxLnToAA0FVQkAB85Ow2Wx445hZeFydr8LlcrFZVyIJZFAVj8chSRJycnKY0iEajbJuNhUMiATR++JNs2itdMcMlPkdyHPbcNHi4Xuc0B4MDM6sbyQRiST9PCg7fKJgOHPaFM3a0BlFREnGTvIFR77bTMSWPABEUWTjVKkxhuQVQd+ja6YkSUwFwysU7HY7K+TZbDYUFBRYCow8qSbw+w+N+t3Qz5mNd6ofzmc4WvnW9LsaaXO10cKU3f0/tXE2blpbiTl83E/5KuDUdiwVagHMS+suvm7O1IiKKfY5cfv580f+iWtfB5663fx649eAM7/U7907QnF86W/bseVYByRRwL9+bAluPXNkpexu+8RZxlFFw7s1bahrC+KL5/SWNS+fYVYQ61pD6I4oyEmJ+LJJIjbXdeBUVwR7T3Zj42ioEVJwfnUxzq8u7t/pnGTjS65msvGtxzpR1xaC2y7hI8tH35TqD59YjZ8+fwg/uHIxnLasZLgv0BwrXYiqE7K3mtYwnHM97JAgSRLyDfNgGdRlRHSRzY5RDuztG8pgFw3kOU1JeXc4hnfrzX3zYyvKmCN0T08Pk7LRBZ+P5pJlGRAlbCe3cU+QdbOdTie8Xi9CoRA7gBK5KigoYHPlbT1hfPXxGly2qBCfO2t2VjY+zqDONHV4ADOuceMv3kBc1XHntZUo8QhsvfESQsMwUrK0Oywkl9aGYRhsnIB3Gtc0DfVKDiKagAKXhIW5QFenzrqavMyXSAd1Jd1ut0V+TqZUDoeDdahq2qKoLnfCLgmWTjYZCqYD3/WmmKnhHlSnC/hIpMEcnEVRhE0SMSffhSOtYRxpCWFGnoupHvgCBxVYVFU1O6yigXybhg5FRlNExJzEXnM8AJwKaJAFA2cUi6yDHY/H4ff72fvs6elh0XVut5uRp+7ubvY3QV1Hn89nKV7Sz0frT1EUFPvsePiL6xHWRDjk4e1p/HgDxUSNBajYykuNJxoB4j0b2DVpkCj2u5DvsaEjpOBIcxArK3PZKAr5iZAai8guEWsArKsdj8dZscbj8Vh8UXgneto36PlojblcpsqitbUVgiAgJycHDoeDmaSluqGnuo3vP92Nfad6YJdEXL0yvbcNjVMAw3OqJ2M2YPS62SNtrjZamLId7cp8NxaU+Kzzrok57RmRwwCAQ009GVe2pjUadwMP3QboKrD0OuCiH/d796MtQVzzh/fMDG+njLs+s3bESPauhi68d7Rtwn1+UUXD5+/Zhp8+fwhd4Xiv2wu8DszMN2cW95zsAooTRLvtMKCZmxKLAesjj3u00Gc3W4kAh18wv+bcxh/aalZGP7q8DN5RcnvnP98CrwP/deMK5Lgm1gV8oiG103hBVTHuuW0pfnnlfEuWtiAIsAk6fIJZvW6KyuwCrWkaQqEQyn0yCtwykzm+vL8Zcc1AZY4dq2cXMpdwirShiytf6QfMC21tUEaPIsAlapjrjDDZLsnG6TARj8dZJ5I3kHq1pgtHWsJ44UAbHBPsEDcdkW5OW5ZELEwYBx3rUtmhkTprZAQkCAJzHu/UHIhrOjsY0iGTSAN1i4iMUddwd495CDx/rgfxRJeb71zSwZpGGAzDgMvlgsfjQTgcRjweZ7fbbLak2Zpu4FN3bce6n7yKfSfaejlZ94VoNGrJtCX34MlwEBxvZDo/S2tvYbF5LT3aFmFFGt65OTWKjrrJ5DzeGJGYxP/dk+b1elmeDr/bLO6RioHWMPkHCIIAv9/PCjuhUMjigAwAeXl57Oei4guvoCDXcjIMzPcMn4yMhHlVpkgl2UQGJyIyNd4jCIKAqsQI1tGWoGUumDweeGJLf/+0J1HkHJ9+QKoLwDSO46M3+axxTdNYEofT6bQY8eXn57POOb+38u+b73A/kjC9vXhxCfLSrDdyzgeGX6ghMszHoY0EqCgBTHwTNMKUJdppkSDanva9kEUDnWEFzT2xXnd7bPtJ/Osz+9EW7H3bREdU0fD5u7fhmd2noY5kFnPnceC+G4B4EJh9NnD1H1lnMx3eO9qGa//wHo63h1GZ78LjX96IsxeM3Ezlf718GJ/462b88a3aEXvOkUCu285UFH3FTrE57RNdQO4swO4FtDjQbv4sK/nbRxGGYeCx7SfRM5BEveYVQAkBOZVAxRoAZgb683sbAQxgoDYMqJqOv/vbdjyYcM/PYnBINUQr9juxYkYuHLLAujz8RT2PnMejSUM0yuukC5okSYjFYnjxkDlLePniQkaGenp6EAwGWSebCAvv/izLMra2mhf7ancI0DV2WMnPz2cHEgDsIEuz2dQ1f/5AOwDg6hWlk+YCO5XBH1r5ghjlaR/vVhjBpUMmHcYlSYJHUOAUNegQ0B63dib4wouqquzzpm5LxJBxOGAe5s+pdLC1So69/HwiT7JJqknEiDrUfDTUO3U96I4ocNkkzMwzC1Nut7vfQycRDd7tfCw7ipMdmcp6qXhC/hO17VH2mdNzkBKGd5ymz4eKPI1RUz0BUcJ7J83z3hkFKtsnI5EIW7t2u53NH9vtduTk5DCzOxpDICWPw+GAx+NhZIxPXaCuu6IoqO+MQxFHZsaUzLCAscvMJhUHT7In8pjEcOa0/+WKhXjpK2vwkcUFTPZNnxsVTwAwRQ0/DiHLMrue0fgMfUaCIFgKFVTUI08SAKxbzs9q+/1+eDweCznmf/epbuO6buCVA6ZDf1+y8ZGSjGe72VZM6avAY9tP4psP7cKWevNwiMIqQHZBiAdxdp6ZdcxmuDn84c2j+L/3jmHfqfR5yBMZz+9txKsHm/HzFw6N3CIMdwD3XgcEm82Z4pvvMx2z+8ADW07gU3duQU9UxRmz8vDkVzZhQYlvZN4LzMznd2raIAjAlWMgWc4URJR3N6RfP+z2k11msaJ4kXlD8z7z9pnc7aOIzfUd+NYju3HBf77Vf1GGl40n1tSzexoRUTTMK/Jg9cy8EX9vhmHg+0/sw8sHmvHDp/ejsTsy4q8xlcGTID5Plg6fFH8DJA3RToeTnW5VVVk8y4N7OvGvrzejoSuGMp8Mr13ElctLGRkKBAIIBAKMrBBh4TuRmmjDng5z7Sx2B5hMzuv1Ii8vj0nfqDLvdDrh9/sZSa9tC2NfYxCyKODK5aVZAjMBkEpgCGQoWt8ZZ4e9VPJrdlmAIpt5GGtRrIdKmpul71HHiFQTNTE/dANYkG9HsVO3kH0qJPHdJE3TmPM3dSWp60kyTyo+PbbjFADgY8uKYbfJA5JsWrd8N12W5WwxKAPwnedMutpVJV44ZMHyPVLk8IZotB/RvlOS6Gg3Rc11dbBbQiBuwG8zUJ1nxiXRXsbHewWDplcFyX6BZJGFupJ2ux0ej8eyx/IdRyJGgiDgJ6+cwLm/eg9vHG4Z1u+PH7fhUyVGE7wfATDxSTYwvDntBSV+lOW6e7mL8yA1BY0H8H4lDoeDja14vV52f/rHF6X9fj9bJ7SP0Z4WjUYhyzIbS+Ddxkl6zqcv0NoVRQEv/8M5+PVNK9I2vUZKMg6A7YcjPUPNR4VNpv11Sp9W3q5pxeM7T2HrsQTRlmSgbDkA4Hy/eTFNN6dNB4VDTZPPeZyys29eWzkyZlFKBHjgZqC9xjTCuvVRMzM7DTTdwE+eO4DvPb4Xqm7g6pXluPfz61HgHVlDjrvfNyO9LlpUgsqEDHsiYUViDntXQ2fa21dyhmiGYSTl4wlDtKXlOZBEAc09sVElmA8npN8XLy7uO1IsHgaOvGh+nUY2ftPaylGpKv761Ro8tK0BogD8zy2rUJYzPHf66QaeaIuiiA/qO/Efb5zAG3UBdiCi++QnIr6a49buD81pf3AihA8bQth/ugf/cHYZnv/Ccswu9LJ5ReoOUpeGj7Yh1+Xd7QIUXUC+rKBQMIm93W5Hbm6upVNEc5Qulwsul4sdVl44ZP4tnTUvHyU5E+9vfroiHTlalHCDrm1PKsLIhA8AI7+GYaDYbnYnWpXkfDRvhsbLsPlM6t3dSdk4ZSHzs7F0wKXuIq138gIg6aXb7WYHVVmW0RZS8O7RNgDANavKB5R+K4rCCA4v08xGeWWOTLuNoihi3Zw8vPbllfjxpTPZwZ4nyLyqgAg47zzeGhPh9efgvdPma67KV+F0mPFv5HwvSRIzYyQJr9/vZ8/FjyEA5lr3eDyW1AV+BpfMyuo64zjUEoIAASuHEXEKWM2hxsIALZVku93uCU+ygeScNpC5fJy/NgJgUZn0Nc1gA0kSTkVrUompqsp8Iuj1iZSSXwQVcej+5JZP96VCNN2P0jnSFVdSjdE8DhnXrJrRixuMpGSc3icwet3skTZXG21Mnnc6BJCEzUKmE/LxFZIZ1J7OeTwZ8dWbhE9k1DQHsPVYJyRRwA0jEROha8BjnwcaNpvk+tZHAX/6DnIopuLv/rYdf3nH/L1+8+KF+PVNK0fctKo7ouCxRObzZzbOHtHnHimsTHR4GZFOwZJyP2RRQFswjlNdEaAk4TyeMERz2SVUJRQAu/uQnw8XPVEFz+8zpd/9rpWalwElDOTOBMpXAzCz6Xc1dEEWBVyzauTdxu/98Dj+57UaAMC/Xb0Uly6Z3AkA44HUucS9pwN4bHcrPjjWYyHakiQhP0F82xU7VCNpVqUoCkKhEOYVmKThaFvElMC5nawzQ91sOuCS8RBV2qmrs7U1YYLmDkAQwA6ERUVFCIfDrHKvqircbje8Xi8jTnFVw/OJnNmrV5RM2Pm/6Qi+Q0SoTlw/T3XHEFGtXWa6Lx3AKOKrTXWykQO+C0jrhOJwAKDbcKMhJEASgI0Vdqa8oPvySgqKN6J16HA4mJmV1+uFzWZj3UVBEPDY9pPQDWDNzBwsmlHQL8mmGDzAOq6RjfIaGjKdnxVFEbIowG6T2f5Dv3cyuyLSyXe1RVFErs2AU9ShGQKOdBnY2WSuQ8rOplEZcn52OBwIh8PM0ZzPSg6FQizuiyTBvNM8LxuncQjDMPDiYVPx1te87GCRSpJGe+3pum5x4R/Iu2CiYahz2pIk4Y53juPbT9WguSdqSTYg4sfP9NM1kvYiUm2QUz0VhKhgQXP1pPCizG3ypBBFEeFwGJIkwefzsdEt+uzJ1JEH20u1vjv4NGNPP+NwyTEVlUa6mz2aUWGjjSlNtBclsrTTEe1ZsSO9b+vvcZMAD2wxu4wXVBejNGeYFXXDAF74LnDoWUCyAzffn5Q4p6CxO4Ib7vgArx5shl0W8T+3rMLXL1wwKhv+I9saEI5rWFjixYZ5EzPSa1GZD3ZJRGdYQUNH74600yaxYs6uhi6uo53M0l49KxcLS7wYyTF7Hs/sPo2oomNBsZdFjqUFk41fw2Tj1M2+oLoYRb6RrZ6/tL8JP3jKlNB//cIF+MT6kXWony5IPUxQl/FoW4QdAuki7BXisEOFDgGtkWRXjojEvHzzovbc4W5GWGRZRjgcRiCQzNcGekvyJElCQLPhSDcAGFjgMA+XNLOWn5+PSCTCnKVlWWZuvlQk2HYyiLaQgjyXjHMXFk6qSvZUR7pDa77HjhK/uS80dJsHo1RzJjLtKUrMyrZrDqiqxg5npIYgCTYdPGVZxv6Q6YFxRoULbkm3SGYpn5g64S6XixV83G43gsEg6xD5/X5W4KFD75N7zBnGm9bO6vf6pWkaIpEI+x3wctLJ0NmbiOCNwwYj6+XJHT8qQISH1gMAi/TW9IaQUJxYe48ejkHVgRkeAzN8IlsXVBCi4k13dzeb9Sd5MJFvIkJer5cpMFJl40TeAcAQJLxwwCweXj/MaEx6Tr7DOhqgNR8KhQblwj9RMdQ5bUEQ8PLBNrxd24WDTQH2GdNcvs1mY8/Jx3xRV7qgoACVlZVwuVzMGA8wPz9FUeB2u1mnmpI/qABIhUzaE6mbzUfG8YqhVLfxP71Vi8t+8w5eSPjq8CATR2BkZvtHa4aanpf3l5ksmNInFjYr1hZCVEkcBBJE29+5HyJ01PG3JUCd8NrWEGJqZlWv8UJU0Vin9+PrZw7/Cd/7DbD1LwAE4Jo/AbPPSnu3vSe7cfXv38OBxh4UeOx44Atn4mMrRmduWtMN3POBKRv/9MY5E7Zr4JAlLErkLvblHL6i0pSX727oSna0u04AMVNh8W9XLcXL/3AuPrK8bFTe48ODkX7HQ8CRl8yvE7LxuKrjiZ2n2GNHEsfaQvj6AzuhG+bowz9ctGBEn386gSejmqZhUZm53o51RCHZTBJEFyxBAPIS8vHGqMQu7iSVnJNnXqx7ohp++cZJ9tyhUAiBQIB1EEkCR90jkrORCdpMRxReIRk9k5+fD13XWf62YRjw+XyMZBOBKct14/LFhbh2VRk8zrHNhc2if/Q18/jV8+fjR1csQHmOg60nMvPh3XEL5DgEGIgaMnrUZBQXdYgcDtPojGKzJNmGnV3mejx/tptJt3Vdh9ttjhREIhFWDPJ4PGxNejwe9PT0QFVVRoh42e/RtgiOd0Tgskm4op99l7pQ/M9PrzHWucVTCZnOadN9Xz7ciU8+cBi/ffc023uoC0jdabo/39WmOe3DbUkTNJvNBo/Hg0DAvA5T9CB1cKlgRJ2/np4eRCIRRqp4d2ki9hQnRT+TYRjYfDKMroiKUr8D5wzDJHYsDNBUVUU4HEY4HGavRQXRyUZ4gOHNaVclojIPNZnqGhqBoeelrymekE/xAJJu5FScppQNXdfh8XjYSEI4HGa303ql66vD4bCY9dHz0t7JG7SZ12EDD287icPNAYTj1r+rVLf44RaxR2uGmjdXm4x77JQm2sU+MzJBN0y5KwCgYD5g90JUI1jlaoGmGzjaErQ8rizHiRyXDZpuoKY5mOaZJx5e3NeE7oiCilzXsDZuAMDuh4BXf2R+felPgaXX9vmaN/7pAzT3xLCwxIsnb9+ENbNG3hiL0NQThU0SkOOy4epVE88Ejce/fmwJXvvWufjosvQHtpWVSXk53PmANyGPbjkIAKNaRDjU1IPdJ7sT0u/0WYoAzNlsNQLkzQHKVgIAXjvYjI5QHMU+B85dOHIu8gAwq8CNr10wHxctKsG/X710whZSJgv4A0VFngs+pwxVN9ASFRjJZoZoCfl4UzRp4kSdwXJuJHrFDD+76AeDQXZgIOdUOiwnI2Yc2JLw+al29rDbnU4nCgsLWUecDqY+nw+yLLMupCRJqCr24OdXVeMb58/JdgsnGIhEA1ZydNuG2bhpbSWK/ebhnz5zAhVSHLKIAtk8QLWpDtZZ5olSLBZj3exTqgddMcBrF7C61I7u7m72XB6Px2IMRN1svttEMnGfzwdVVREKhdjM4/KZBXj9W+fiP29Y0WdcIW/IRl0kvhuU3bOGh0y6jWztCQLq2qM40trbeZzynPn4MJJxlzqTryEKwOoC07EeMLtnvFN0MBhELBZja8lut7PRGuqeu1wuJiunn4Ok4tTNpmLMU3vMTfHa1b3nZQcLXvJLBG6kwI8O8bPYVIgYCVI2XhjOnDaN9NW0hllsFZFp+syp80qFRUriIBJOa5MiNGlEyu12IycnB9FoFLFYjHWmaa+h16ACB11zAXPvob8ZXl0DAFuOdeBERxheh4zLlyXH8KiTTo8fiWtrtpudHpPzL2WQEASBycDZLLYoAWUrAAAX5ZwGABxIkYgLgoBqklq2TA6ine+x44xZebhpuCZotW8AT33F/HrDV4ENX+l1F8MwcMdbtfjyfdsRUTScs7AIj35546gbk1XkuvDKP5yLp27fBLd9Yh+4V1bmYl6RF2Ifn8XKREd776luKJrOzWnvt9xP0fReiovhYvvxToiCaSbXr1FdOtn4NrMTfv2aGX0bqA0RgiDgqxcswJ9uWzPizz0dkeo8vrDYlNwe61Z7HQjJEK0pKrFuIzvIqTHcsKIQZ83NxUcTF+pYLIauri42j0UHB5L+EvlpCItojgA2Qcc8ew+bo/V4PPD5fAgEAggGg2y2ke9A8TNedKiZrIe7qYx0c9pAUi5O6ggiPUByTeq6jiJmiGa3ONaTZDcej7PM4X1Bcw2fNdMN6Co7kJKbL8loyXCId/wNh8Osc2Sz2dDR0cHM94hQzS3y9qkiMgyDPQdfBADMLstkPABONAxlTrsqkdte2xFNa4hG6gieuMiyzDraALA4V0eO0yz0Ufea72bz4wkOhwNerxdtbW2Ix+Pss+ezj6nTSYUf6mxLkoSIJmDzMdPccTheOqQCIrXISID+3sgwkNY6Oak7nc4psQcPVT5OfOJoa9Ioj5QLqftgqiEaEWYyegRMF3tS2NC+RM72JA2n37+iKCxqUJZlpuSh90Gg5ybi/HDizHblijJ2bqZkByC5d/EjNJl2+unnHo0Z6tGMChsrTGy2MgKoLvXjg9p2NPck5whRvgo4/h7W2I4BWJ3WEO2n1y6Dzymj2Dc53EPPWViEcxYWQdcz/wNhaNwDPHQboKvA0uuAi/+t113iqo5/eXIvHk4E339ywyz84KOLx4wYiaKA2Ymc6smMuYVe+JwyAlEVR5oDWFKyGKh9zUK0f/T0fjy49QT+9WNLcNPaERgHSOAT62fhgupiROL9HGZiATM/G2Cy8cbuCN4+Ys6VjYjZHkxzu1+/cgTfubQKnkQXaUTc8rPoZYhWVezB9hPdqGuPYkGJy5Ixm5eI+GpR7ND1MCNBiqIgHA7jm+dVs0gScoWmWT0Alq40PdbhcGDrafM9zHeG4JDACIrf70c0GkU4HGYHkLy8PPZYkv7es/kUNswx/Qqy3eyJCZpD5MmRphvYfbIHO+o6cXaFxA6LvHMvHRZL7AoOhs2OtqqG4Xa7WeZ1OBxGNGoSKF2yY0+HuZ7OqXSw7HbDMODxeJgpmtPpZPJePm6HTPvcbjdzMBcEIbHuBl5bvMmP2+0eUQOhLEykzmkP1BWTJAnzijyQRCAU19HUE0eRJ0k6iBiHQiG2P1FnsNihQYABAwLWFmqw2ezwer1oaWlh+5TH40FLSwvrSLpcLtY9DAQC0DSNER+Hw8HWAT8zTtJgKvg4BQEvfXU9djaGMWeIZxmSHAMjo6SgvZ6eEwD7m51MecWDBW9MlwkWl+cCAI53RBBTdaYK4+ekiVTzcVukpiEZPhUFiTzn5ubC7/ez2+n5+E45PR8RYzKHJOVO6s8nCAICUQXP77Wa3vJJCRT3SR4p6cCrlujr1P8HwH4+KjLx5oTDWT/8SNpkPQNMznedAb52wXx859Iqq/t1Yk57rmI6G6czPZtX5B2T9zfS6KuDOiC6TgD33QDEA8Dss4Gr/2hmPHPoDiv40r3b8UFdO0QB+MFHF+PTm+aMwLseGNuPd2BJec6Iu5iPJh7ccgLv1bbj9vPnsbl/gigKWDEjF+8ebcOuhi4sKU50tBMRX4BpmhZVdOxq6BpRog1g4LisIy8BahTInweULgMAPLrNdORdNyd/yAcEHlFFwxfv2YbN9R042RnGXz+1dtjPmUUSqd0hmi9rDSlsxotkdHl6BAIMRHQJ3XEDNlmGoihQFIXNcVG1W5Ik1s2m5yai7XAkY5oEyYZtrQYAAVUJEzSSXebm5iIQCCAUCsFuN+N0KM6LMnDrO2L4z9fqIIsC3vzGmSj3TP4C21REui6kbhi49c6tiGsGFl4zAyXe5Mw15bWmGqK1qU42MkDdbMMwGEmqiXgQ14Fyn4wF+TKam8NMtstLhsn1mQ6p/JwkGWXRP5/PB5fLhc/ctRVuu4RvX1rV57Wf76rQIZ0IWRYjAxotobnmgQ7WoijCJomYk+/C0bYIalrDKPKYXUee3NL64J2hHbKI84siCIluLM41STTN35NZHqkp4vE4IyU+nw9tbW2IRqPMuI/mZun9i6LIiAftnV6vlxU/i/1OXFs2dDNXIkq8qeVQQEkRtLbpd0Q/61Qj2IRMCzqEslwXclwyuiMqjrYEMTfPVExQ55lSDHiDNCA5hkVScV3X2XXV4/HA6/XC6XQiEAj0koDTnkkO+PRe+UILXyABkrLxZ/c0IqromJ8wveWTEmifpbUEgO2VPGgf7g+0TwMm8acZcx7pyHl/xJ2+5qX4kxWTXwMyAHLd9t7kLEG08wOHIEPFoaaeIUklJgKiioY7361HRyg+8J37QrgDuPc6INhkOmDfdC8gWyXFx9pCuOYP7+GDunZ47BL+91Nrx4xkd0cU3PrXLTjzZ6+hoaP3H/BExfP7mvDM7tPYWt+R9narIVrCebx5v+n4jqS8fOeJrhF7T+3B2MB3AnrJxnXdwMPbEwZqI9DN1nQD33x4FzbXd8DnkPHNi6uG/ZxZWMFL/HRdx0eWluHNv1+HH182h0m0iWzLggG/YF6Am6LJTjddmIkcUQRXV1cXO5zRbdQBoQPykYANYVWAV9JQaTf/bikjm49Zoi4RvV/qQD6zz1RPnLsgH/neqSFZnIrgc4qZbFISMb/YJDz1XUrC6Vlmh3f6f0EQWJZ2t25HTDNYx4dihCj2a2/AHE06d6aDdQlp/QBgZIgOpLQ+bTYbMzyj59U0DS6XCx6PB6e6onjrSCte3N/UZyGXN/nh83JHInM2CysykfXS735Bkbk2jraFGXGiIgxPTvg1IEkSzi+O4uNzVTjtMstYp7GFvLw8Ju01DIPJpzVNs3SzqVOeTjYeiUTYXupwOKDpybi7oYLvxA7VGIp3EKe/E/I1IAnzVCXZQObGe/zjqku8cNpENHZH2GdP64mP9KL9jm6PRqMIhUJMAUTE1O/3M7UY7Xe8wZrD4WDvkfLZKTe9r3WUKhu/8YwZFhNHMu0Dkn9nNCrh8/ng9XqZnJ1SQOg6TUUlUjvwo2L0/+nWDhF23hyQTFRJyh6LxRCNRhGNRhGJRNi1gK4XkxXT8wqRNwdw5EDUYqiSTqMzrKC5x0pADMPAf718GJ+9aytaAtE+nmj88dL+Jvz42QO49g/vDa1YoESAB24B2o4A/grgE48CrlzLXTbXtePqP7yHurYQKnJdeOwrG3F+dfHI/ACDwCPbGhBRNJT4nJiRN0AndgJh5QyTKO9q6E5/O2+IVlgFCBIQ7QICjZbbjzQHEI5nNkuUDqe6Ilj/09fwyTu3IK72kxsW7eklG/+wrh0NHRH4HDKu6MPgbbAwDAM/fmY/nt/bBLsk4k+fXIPF5f6BH5hFxuDnxvxuO/I9DnaQpAtjck7bJMONkaR7Mj8jSzK3QCDAYpFIAkddHb5jtDlhglbl7IFNTpqvud1uxONxJgmmizh/uIAo4Zl9ZtTSVctLJ/VFdqqDP7Ra87RNon28O9mh4eOWiIB4RA1uUYMBAe2qgx00yfXeMAxERXciIg7YVGGzzEpT15pMhXjySx1uKhjROiLzKpvNhke3m2NQG+cVoCI3/fWFJyN8NzGb6T7yyGROmz5n8p+obU8aopGhHvkEUKeZlDn0/+T/4HK52Pys1+tlHhVkxOdyueD1etHd3c08Ayh+jt9HST5M3WLa40RRxL+9UIPP/G03dp8emvcP70MwlCJPfw7iJIGfLhjqnPZvblyOD7+9CefOz2eKBgDsukp7EQC2LkiaT0Ubuv5RbrbL5bKox6izTN1q8ieh56euNE/CU93GDcPA1y9cgI8sK8NVK8otSQlEsqm7DliLP1QMpb8NWuukSKN9ls+Md7lcyM3NZR16n8/HSLvH42Gk3eVyWUg7PR8fHUo/L1+kmsyFn2lBtH/3eg2u/cN7eKfG7JBAFIFy0xDtAp95kT3Y1NsQ7bm9jXj9UAsOppnhnii4b/MJAMA1q2ZkvhB1DXj8C0DDh4AjxyTZOVYX6ke3n8St/7sZXWEFKypz8cTtG3vJoEcTmm7g7g+OAQA+vWn2pPpjWzkzFwCwq6Ez7e3U0a5pCSKoy0DBPPOGZlM+XprjRKnfCd0wY9SGi0e3nYSqG1BUHXa5nz/9Iy8CWgwoWMBM2pihxspyuOzDk+//8a1a3J2IafuvG1dg47zCYT1fFn0j1RCNLp4kDeQdefOFhCFaLNl1BMAOBXQ4pW42HSjIcIp3Po3qEvZ1mMR5kdPcW6na7Xa70d1trmc63FGnCDAPDx8e60FHSEG+x4az5uVlCc0ERzpytJjiNTvj7DDKH5jYiAHX1W6Jm+7gdruduY3ruo6DEbPjs7TIhgKXaDGCoi4SvQ8aX6COjyAIlvlBl8vFHieKEiPaN6xJr9ThzXj42cOsZHx0kEn8Eu1n1aVezMl3osSb7KZRIZAO8bwhGk+0iSBR19HhcMDn87E5fiBZmKE893g8zqLj6Da+a07dbJ4wheMaXjjQim0nugEM7RxD5n+k+hkMBuMgPh2N/DI13iMUeB3MR4b2L16NRUVCnnjz+xEpxHTddLn3+/2MPNPcNhFOm83GRl744jddc+l2+j6QlI0LgoDzq4rx21tWwiNpbJSGX6t8sWWoZ+uBZqj5IhcRdp60U4ecxsfIyJLIudfrnfTX/2lBtGtagthxogt7eLKSkI+vc5hENd2cNuVwp7ttIuBoSxBb6jsgCsCNa2dk9mDDAF78J+DgM4BkB265PylfBqDrBn754iF8+5HdUDQDH1lWhoe+eOaYm8O9fqgFDR0RM9JrZT9RVBMQK2bkAjDz2HuiSq/bi31OVOS6YBjAnpNdpmwfAFqShmhMXt5HHvdgoesGHiHp90D51ymy8e6Ighf2NZmPHaZs/LHtJ/HLFw8DMGf8rxylzPUsTKQaoj2ztxnfePIoXjgSYJ2e1I52c0xmzrxkuhOPx1knmkyoaO6MSLzT6WSEZ0+XDZohoNgWYzO4dGGVJMmSHUqHFfpnt9vx1B6zm/3RpcVw2qe2jHEqIN2hlQqy9R3JqBpeWkjz2ABQbE9GfFFhh6K3JEnG9g7zALexQmYHu1gsxuYMiZRR4Ygv2lAGN995JOK19XgXTnWZSp1LlySjb3gQyabDMgDLYTWLkUWm8UuiKGLj3Hzcf9tifGlD8jPkHbmpyMiTIiLBVDRJlYgTMeXVD+RATsSE1hMpNYho8AogIluvHGpDOK5hVr4La2dnHoNK+y0wOAO0/hzEaSZ4Oo89pM5pDxZ8KgatJyr28WRTURRLIZtGrCga02azwefzwel0su9Tp5oKKXwuN+9hQmMRBH4t8GQ3NY4wdd/ix2uGCj7SK4v0mBZ/ZWkJc4JoV+lHASCt8/iiUooGm5hE+8EtZpHggurigc2tUvHefwNb/mx+fc2fgNlnsZsicQ1ffWAH/vBmLQDgq+fPx29vWTUuRmR3vV8PALh5XeWwO6ljjQKvA5X55ueypw/5OBHpXQ1dQMlS85vNSUM0i7x8GHi/th0nOyPwOWVctjT9gRIAEO0Gjr5qfp2QjT+96xRiqo6qEh+WJ+TwQ0VVqQ+FXgf+7ty5+OxZYzPjP52RSoAau2PYfLwHe5vCLOKLDgwU8dWp2qAaApNv0WHNMAyWnU2dbKqs89nbAFh29mJXwCIHo9lZ3qiIOkVEgIIK8GZNOwBTNp69gE98pJOOUxTOqe44Yloyro3WAkEQBBTbzMNam+pgckYiyB2CDy0RAQ4JWFtqzlsTSaI1TOuQMmbpPtRdBMz5RjoQE0F6JNHN/uiKvpU61D3nO0bTsQM4lshUPs53FHkzJerikfqA/p/+S+vR6XQiHA4zkk0dabofb+IXjUZZF5iKh/SasiyzwiRviCWKIh7fZY6EXb8mc/Uhn5k90PrTdR2xWIxlf1MxgWLsJrsMd6QwnDnt7z11CNf97060BmKsU0vPQddCPj2DCos0E09d69zcXLYnkZyfiiE0+wxYlTqpMZo8qKD0Tk0rfv7CQRxoaGMFllSSTV13etxQQEVPej9ZpMe0INqUiX2oiSPTCaJdGKqBHcoAHe2JJx2PKhoe22EeEj6+PkNH6j2PAK/+0Pz60p8CS69lN7X0RHHznz/A83ubYJME/NcNK/DtS6uG7mY+DNQ0B/DeUdPh/LYzZ435648EiCj31ZFeWZlr3p5qiJbAujn5uGhRMTYMU15N+ddXrSzvv2By+AVAi5sz48WLLI+9cW3lsC/QSyty8PzXz8J3L60e1vNkMTjwB09d19meVtsetTiPS5IEFxQ4oMCAgOZocu5MVVXmTEuycSJDZHzmdptmRKqqokORcTwkQoCBKlfQEnXCG6fQAZUOtoDZKaxtC8HnlLG41IuFxZ5pNTc4WZHOEK3A60CR1w4DZleb1BP8gYwKPcWJTON2zQlRlJhJjmEYLDv7jFIb3DaRdbPpQMqvQyLdfHeSXpe6TXSojKgGXthH0TfpFWH0PBS3Q4Qli9HFUAzRRFGEAQGBaNIYllQOtM5oLyJ1gs/nQ16eOZpCpnsul4uRVCI4ZEBFJIfWHmA1JJMkiY07EOmRJAkNXVFsP9ENUQCuH4IqjIqT/a0/3nCLuoyiKLKYMr4gkIWJocxpi6KI/Y0B1LVFcKgp0KuDTHsSeUIQ0ab9gzxNPB4PfD4fI7xksEfXZVqnQFLBQB1tKt6kEm3aW+9+/xjueKsOj+44DUEQmEcAD+pmD0c2znezs2urb0yLEwzNitW1BhFVNJNo5M4CXHkQI51YKDTgYJs9eVsC7FDaGkRM1eCQJ04V+6X9TegMKyjLceLchRkYk9W9CTz5ZfPrM28HNtzObjpwugefv3srTndHkee24U+3nYF1c/JH9o1ngPeOtgEALllcihl57nF7H8PByspcPL+3EW19uH1bOtYfSRDttsOApgCSDWtm5Q079qorHMdL+0n6PUBRZt/j5n+XXgsIAvaf7sa+Uz2wSQKuWTU06X59WwgdoTjWzDJ/1mJ/drZxLEEGZTzRPtYZhSDnsIMAGfjkixE06jacjogoy3Wwjgh1SEg2zsvtaO6VqvU7O83Pd64rCo+kARAZySFXcpLCUceRLvYOhwNnzHTirW+ehdOdoSkdMTOVQISCZI10qPvxVUsg6wqKJXMsgYo6dGikQ2qBTYEEA3FDQlvUQH57u9khkmTsTGRnb6qwMUdfRVFgt9vh9/tZJ8jnMwvqZKDGz9Cmc6612Wz4zqXV2FrfgVWJgmcq+G72VDDlmSxIndPu73dO931gRzPueO8UPrIoD1/bVGqJdOPn6fmcX1EU4fV6LaTD4XCgq6sLmqbB4/EwFQ6RJCK6TqeTEXfqqlPHmwgTEe4ndppNkU3zCjJWH1KHGkDa9UfjPTxZpEJmtkjZP4aap11V4kN9uxknd8YMDyO9fGeXdyLnI+vi8Thk2XS5p6IN+QHQvkWknHfzpvdIiQl0/aW9FDDXb0sgijcOmX5UV68oZdfZVNB6GWonmgz/gMkdvTUWmBYd7SKfA/keO3QDqGlOuD0KAutqn+k8AU03cLTF6gRZluOE3ylDTXPbeKOhIwybJOCmtZXMmGFANO0FHrwV0BVTFnzJv7ObXjvYjBvueB+nu6OYW+TBE1/ZNK4kGwA+vWkOXv/Wufj2pZM3+ummtZXY96NL8cMrl6S9fWmFH5IooLknhiaxBLB5zI5ye+2IvYend59GXDVJ1tKKfozsIp1A7evm14uvBgA8ss08IFyyuBT5nsw309ZADJ+8czM+8dcP8X6icJLF2IKXYc7Id8PnlKHpQEtUZF1AOrzRnHZTNNn5ozmvrq4uZipFh1ggmeUajUZhQMC2NvOyssgVYIdQ6gzxF2QyQIlGo5a8W5vNBkkwUJHrzB4UJxHSyX0vW1qG9XPy4HbIlk4gfU2zg5Jgkm3A9Agg06YGNQdhVUCeU8CSQokVfQzDgNfrZS7g1CFSFAWxWIy5+ZJkk3fOpffqc9rwubPm4I7b1qQlcnQwppncTAyoshgeMpnTps8u121HVNVR255MiSH/CJrT5me1iWyTczMVUihiiWTlZCbGrxHKaednpWVZZpFNVCCUZRkQRDy5u3/lRH8gkp2qBsk6iA8fQ53TprGYmpZkMZj+8YVE6j7zZJv8IqgwaBgG+wzJqJSMRvkRB1qDRMJT3y+97iNbjkMzDKyo8GNJZUFaWThdw3mPlkyR7WYPHtOCaAuCwP4w0s1pb3SlN0QzH+eHxy6huWdiRXx99YIF+PB7F+LTG2cP7gGRLuC+G4B4AJh1ljmXnXBI/N936/GFe7YhFNewcV4BnvjyJswu9Izm2x805hZ5Mb/YO95vY8jwOuR+Z8vddhkLS8y1uetkN5Nr84ZohmHgdFcER5qHNsJw7eoZ+OV1y/H1C+b3vyEeet4swhQvBoqrEVU0PLHzFABTNp4pgjEVn7lrCxo6Iij2ObEg8XNmMbbgD6ySJLEonIYejZFkuniT83hzTLbE4cTjcUa0qTtOHUmv18vmEk/GHOiMi3CIOuY6Q4xIUVeJXoekcXa73WJI1NAZASCkjRzJYmIj3Zw2HQypwJJqTsUfFnnncbp9d4/ZidxUYYMkihb3e6/Xy2TiJBmn2Wyfz8cknPF4nJmm8Z2fgUCdLlrDWZfxscVg57RpjVWV9I74IgJN3V3eGZzP86XnsdlsLGLJ6/WyAiI/9w0kpby0fwHWzjMpdyRJAgQBf3/+HJy/sACXLMksGpPWN5Ak9+SZkXUQHz6GOqddnVCGHWkNWUYE6FpGz0njCHy2Ou0lFLFJ2dFUuCFVBRFrfuyB/CUA9CLatHYf3ZE8s/W1zw3XbZz+doBsN3swmBZEGwAWlfpRkeuCqnOLM0G0Fxlm9zDdLPafbzsDe390KS6oLhmT95kJCrwO5LoHucj3PGTmM+fNAW6+D5AdUDQd//LkPvzbswegG8At6ypx92fXIcc9vlV7TTfQ1D2xChujiZXMEK2bm9NOGqI9uv0kNv78dfzrM/vTPXxAeB0yblxbicsHyr/m3cYBvHygGd0RBeU5Tpw1P7MZ8biq48v3bse+Uz0o8Nhxz2fXociXnW0cD/AyTEEQUJUg2se6FEZ46SBAHe3WuA2KorKLPMXakFkLL/l2u90IBoPQNA07Osy9o9odhk1I7rVEyOni7HQ6mWyPHYIlGZ+4axcu/M27ON4RycrGJxl4YkSHwJiq4dl9LfhLIlSdDqRU4KFijSiKnPO4SWijhowDXebnf9YMOzPmU1WVuUAT2bDb7cyAyu/3Iy8vj5lX0eu6XC72/4/tasTD2xoQiqWfzaQuJpH0VAO3LEYfmc5pzyvyQhKAQExDWzgpa6XCHpEOnggBsMxnkxyWut+0Dngne75DznfHY7GYJVKO1rZNEnHlshL88eMrMzKUTTVAIzMtep2sg/jIYChz2ovLzDNbXVsEqp4k19SxpvECGjWgvY7UNjTWQsScMq75WepU3wmKDuP3IfoeYF7ft9a3o749ApdNxMf6SOkhwg8MvZBN3Wzau7PoH9PmN/S9KxbhvX+6wGocliDaJdF6OBBPa4iW47aNixFYX4ip2tBk7Dv/Zv73zC8Drlx0RxR89q6tuG/zCQgC8P0rFuGn1yyDTRr/JfHawWZs+sXr+P4Te8f7rYwInt1zGlf97l38x0uH0t5Ohmi7GjqB4oTEvCVJtJeUm5v6noZu6Prg5U0ZIdwB1L1hfp2QjT+81TRBu37NjMGPJ8DcyL/72B68U9MGt13CnZ9eO2EUEtMRvQ3RfPA7ZRY9Y7fb2Qx1jhCFCB0xQ0KXYnUo5eWTRLjpQKEoClSI2NNpHgIWuwPsQEAz3Ha7nUnWiLzQIdZut+Od2k50hhXEVD0rG5+ESF1nACAKAv7f04dw744WNAeTh7t0RZQk0TY70YciXuiGgNl+ERVekRFnMvdJna+k7k9OTg7L4Y5EIpY1DgC6Afzm1Rr846N78PaR1rQ/C3XHiThlDdDGHpnkaUuSBJddxqx8s0hT2xa1PIZ3/yYCQ9Je/rOmtURFQdrzeAUGuTfTDDY9J5Eh3gWfvqb3kAlovZNaiM+OzzqIjxzoc8mkoz0j3w2fQ4KqG6hvC1vmsgEw9Us8Hofdbmf7DxUZqdDMmz6SJ4DdbmcFFnocFYJ400kepNx5crfpxXPFsnL4nOkbZlQITfWsGCx0XWeeBtlu9uAw/qxqjJCWKPgrAE8RREPFIuEEDjX1ZDSnMR54aX8zLvrVW/j6AzsH/6DTu8z5bMkBLLsBJ9rDuO6P7+Odmja4bBL+dOsafOGcuRNmw77r/WPQdAN+19SYh4vENew+2Y2t9Z1pb1+RINp7T3ZDK+7tPL6wxAuXTUIgpqKubfBFlqii4cY7PsCd79Yjpg5wETn0HKCrZsRY0UI0dITxbmKm+oYMXVLfr23HEztPQRYF/OETq9nPl8X4gZf1XrOyHG9/Yz1u31TOOnXMkVkwkCuYF/mmqGyRrZHZlSAIbIbR7/ezvOOakAsxXUCurKLCnoyVkSQJPp+PdYhSZ12J8D+dyM6+cmkxZHFoh4AsxhepMkybJGIeU1AkuyD8zCKRbor46tbsUCBhV5d5iDtrho11Fmn9kGw8FAqx13Q4HEzuS10bmpF0u92M8Gw+3o3mnhjy3DZcuCi9Ui0Wi7FuNk/Ssxg7ZDKnTfebX2iapta0hdl5hgp7VCzh3eoVRUEgELA8Dz8LTR1JMqaiMQjaw3hjSFVV2WsQmX9hfwvufP8E2kNKRvuZqqoIBAIIh8OsgJV1EB8dZFLQIQiCgMVlPswvciMUt7qA8wSWzPiIYHs8HnZfwFQqBINBKIoCt9vN1h0Vsin6i4/h4s0B+X0OAAq8TuS4bLixHy8A3vhvKKDHk+oji4Ex7a4e5pxD4o+JM0RbIdWjM6yguSfW6/5ff2AnLvjPN9EyAea0H9hszpPPyaRDSN3sRR/Fthbg6j+8h6MtQZT4HXjkSxtwyZJ+cpXHGIebAni/th2SKODWSRrplQrqWO891Q1V03vdvqDYB49dQiiuoU6cbX6z6zgQMw8AsiRiWQUnLx8kXtrfhC3HOvC/79bDNtBBkcnGrwYAli+7aX4BKvMzc3x/fq9p/HLzukqcV5WBI34WowZe1uuw2xi5JiLBX3TzEvLxxohoMXqhgyZ/mJBlmeXNbms3X2OpNwzA6vjr8XhYJZ3icigKRZZlBBTg7aMdAICPLS/JysYnKfhDK2FRaSL1oyOZbc2TB/qcPTbAK5lk+GDIhZNhCZIAnFlmrk3yB3A6nbDb7ejp6YGiKJZ5R7fbzWTklM1OHSUi2k8kuj5XrayAXe69L5JzNK3PbNdm/DDYOW0iLguKzGtVbXuMzbSSFJxmnPl1p6oqgsEgWxtEsqmbzEt1VVVl+xW/P/FmZdTdBkwS9Zd3j+FXr9fj5UODNwIlkk1qH4fDAZfLxUhadl8cWfCjBJnIx+/+9Bo88cUzsKoyhyUbEPh9jUYIaB0RmabXpehMt9vNHO7Jd4Iivmht8b4W1BGnGDGbzYZ//ugSbP7nC/s0MuZl40MxdiSPACDbzc4E04pof+/xPVjz76/izSMtyW+mGqI19TZE23+6G3VtIRxIIy0fS9S1BvFBnZkrPWhzKiUC7H0EAPC+/3J8/C+b0RGKY0m5H0/dfhaWJgjcRMFd7x8DAFy6pAQVuZnFYExUzCvywueQEVE0HGnu3ZGWRAHLZpifw45WAN5E4aPlILvPCjbHnb4rng4PcdLvfscfwh1m7BsALL4Gmm7gUcrOHkLm54+vWor/+8xafGbTnIwfm8XogO8M0df8rCFfZecN0eiwQBd1igEj8zKqtgdUEUd6zMcvdgfZYYDm0UjKS90kAMx91Waz4fn9LVB1A0vLfZhf5Mm6O09SpCNGFClX3xm3uH8TieGJD8nHXz5trpFlhRK8KUvB5XIhFosxt3G73c7mIKlwRM7RRMIB85DYHVHw2kFTLt6XA3Q0GmUkh2TCWYwPMiXaK2f4cc7cHKwsNxsRJMmlPY4vKPJkm4gNkWiSjdPsMz8TTQSI7yTSXC65RYuiiLrOOA40BiCLAq5eNTi3cUVREIlE2Prz+XxZB/ExwGDXWbrH8B1sUurw0YVUoOGVEFRwplQDUunIsmwx1KP1y89C07VVVVVEIhG2tkmu7rRJfe5Z/JjNULrR1M0mBVwWg8O0ItrhuIaOUNxqepYg2suEOgC9nceBpMPgoaahuT6PFIg4nVdVPHgSevBZINqNuHcGbn3Dibim45LFJXjkSxtQmjOxXFS7wnGWN/npjVOHpImigOUJorz7ZFfa+6xgc9q8IVpSPm7J2x4ETrSH8X5tOwRhEJEiB58BDA0oXQYUzsd7R9twujsKv1PGpUNQO0iigPOrijGvaPK6xU81pBqi3fVhA679v314pibCpG3MeTzR0W6O25m0lwgNEWtJkhjhMQwDuzplGBBQ4YjBLyZNgYho85mgqYddu92OpxKy8auXlwwrciSL8UU6GebihMdEfWeMqSP4riBvClSSINo9Cpmg2diMIj0/uetSd5sn2LSGqetCpml0wHzxYDvimo7FZX7mfcGDonYAsOfOYvyQzmCvv/ueMSsXP//oXFy9tIARHho34NcH3Z/k4zR7TXJwek0q+BHx5We9iWjz2fA05y3LMh7feRoAcP7CAhT5Bz6vKYrCXPWpkJntGo4NhjKnzbrgmp42RYGKidFolBVxqNhM6ygSiSAajcJutyMnJ8fiQ0EmfYDVsI3WNRmoORwOdEQNbK5rH/BvhJ4v280eW0wrol2dkLBZyHTZSgBAafw4XIjiUBrn8cVlaR43xoipGpPz3rJu5gD35rDzHgDAO95LoBsiLqguxh23roHbPvEOEA9tbUBUMQ9Ba2fnjffbGVGsmJELANh1oivt7asY0e4y47UAiyEadbQPNQYQVQa+GDyy3SzKnDW/EDPyBpB+p7iNP5ToZl+9qiJjl9R00vgsxh+pUjZFAxp74qjvSrp+E9nOF80LeLdmQ0xLyuqom01fU4SNqqrY0W7uJ0u9IUs0l9vtZoQcAKvm8xm09Z1xHG4OwSYJuGxxUVY2PolBRBpIHlqrE9GaJ7viiCjWsQO+EwQkI74AwC0DywuTDvexWMwi7SX3cSJQLpcLDocDgUCAqSVobdO6HSjPOBKJsMOsx5M1cBxv8PvWYLratFfx4y50GxX5eKJNagp+hpu62URGSA7OrydBEFjsF188pHUmSDKeSqy161aXD7ifxeNxZoAFJIs8WW+AscFQ5rR1A7jlzp3Y8J/vozOssPVERSFSi1GRxuv1sj2FPEsCgQA0TYPP54PL5bJkuBNxJ9JN4B3uRVGEz+fD/VtO4KY/f4jvPranz/c7XLdxPns7W4DMDNPqr5iytC2daX8Z4CuDCB2LhePpO9qlicelIeFjhZf3N6MjFEep34nzq4oG96DOY0D92zAg4OeNawAAnztrzoRyUScYhoHHdiS62ZtmT7mDNs1pD9TRPtIcQKyg2vwmF/FVkevC7efPw69uWjnga2m6gUcTRZkBpd+hNqD+bfPrJdegMxTHK/ubB/fYFOw/3YMNP38dv37lSEaPy2JswMvHaU871hlnZmQs71pQ4YZJeBojydgScr2l7g/NQDYEDTRGJUgwsNAZZBdjkvQSMeKdegEwuVtViRePfXkDvnfJfOS4bNmL+CRH6px2odeBQo8dBoDjXTEmq6TPmTqOgiCg1JEkU2tLRDhtJtmgg6XbbRYN+RlGOrxSsSgcDlvcoYkoheMact12OGQRV6WJvjEMA8GgOdrDx+xkMb4YbLeRJ9rtYRWtQcVCnFLXHG+IRi725D5Oz0Vrh7rYVNSh9QhYZ25prOa9YwF0hRUUe+04d2H/PiXxeNxSiEyd5c1i9DGUOW2bLKE7qiCq6qhti1hk40Ayo5qfiSbljcfjgaIoCAaDLCmBita0d/GdbbruUoec1qjX64UBgZ33+vPEofdBRadMwXezp9r5fLQxra4kNCtW1xq0dgUT8vHlYh3q2kK9Oob0uNrW4MDuzaOEp3ebMqQb11ZCHmwE1877AADNhWeiJpaH2QVubJhbMFpvcVgQBAGPfGkjfnjlYnxsRfl4v50Rx8rKXJTnODG/2Js2oqssx4USvwOabqAGCRO4lv1AYtMWBAHfubQaH1tRPmCX+e2aVjR2R5HrtuGSJQPkvx982pSNl60E8ufiiZ2nENd0LCn3Zzy//9DWBrQGYqhtHUL8XBajDp4ALS4397TjXTEYQjLXmO5D8vGmqMwurHw13Ol0svkxys5e4I7AZpiHWzpUkAkaPY7eBxEril5aUeHHDavLsrLxKYB0845/+PgKPPd3K1Fd5GIdEb6jSP/y7RqcoklgNpXLFmMzUkhQHBPNy9I6Ijd8kt66XC5L/rHXacO9nz8Tm//5QuR7eksfKZM7282eWMh0TvsP753G1f93AA/uarWMJhDJ4c2kiPT4fD7WiaSZWj6pgR9PINkuGawRyHiNl41fubwETkffMlvyGgDAOqDZruH4YChz2tUlZsH6SEuIScWpcEjPyUfAAWCeJYFAgOVq5+bmsnGY1Fg48kKhfY/WB40WvF3TyqUoDEy0h9rNTi0sZTF4TCuiXexzIN9jh26YnUOGBNFeYzNjpVJzqstynPA7Zahpbhsr/PaWVfjvm1filnWD7DLqGrDrfgDAvbFzAAA3r5s5IbvZhByXDZ/ZNCcjufJkQbHfife/dyF+9/HVfX4GJC/fHCgEBBGIdAKBpoxfq8Bjx2VLSnHDmhlwyAP8LjnZuGEYeDghG79psGZ7CUQVDU/uOjWkx2YxNuAPEhV5bvicMjQdaIkKlk4KLx9vikmM/JJrL3Wi4/E4wtEYdnWYF+4lnhB7HSLQDocD8Xi814y3y+VihiqpWbPZavnkRroD66qZeZiR72WfLRVa6B+pI0QB+PisML6w1IZFxWYxp7u7G5qmwe12w+FwIBgMWg6auq4zUp3akSbTKiB5wMx19yY+hmEgFDLXr8fjyXazJxAGO6dN95tTYKoe6jpilscRsSZQMSY3N5e5PQPJ2Vr6L3lL0HqLRqMsJ5uej/cRsDsc8DkkOGQR162u6HM/owg5wJyzdTgc2XziccRQ5rSrEsqwwy0hVoThi4dESvkud25uLhRFQXd3NyvqORwONrZC5JyPxyTvCFrHpECTZRmPcKN+fZ33hus2Tus063o/NEyrq4kgCOll4AmivUo+BqD3LLYgCFhRmYvFZX6E4+PT0XbaJFy1sgJlOYM0Qat7A+g5Cc2Rg7+0LoJNEnD9msE5X441OkLxCZ9fPhZYOTMXALDjdBQomG9+kzNEi6s6Pqhtx98+ONbv8yyfkYs7bluDf75iUf8vGGwBjr1rfr3kauw91Y1DTQHYZRFXregtrewPL+5rQiCqoiLXhU3zCjN6bBZjA75DI0kSqhL5xqdCAiPCdNjIE8yOdkvczi7u1IEkmaWu6zjYoSOoiXCJGiptAfbcNpsNXq/X4sJLJJpJ1J1OfP+ZI/jBU/txrDURZZft4kx68O64/Iws/SOJJd/1AZLyzbkeBWsKzc4g3+Xx+XzQdZ3NapMbMz0XHSZpXhsA62jXt4fRHu5bEsrPZpM8PYuJgcHOaVPRZmGJua/VtkfZGiTinGqIRvsQSXZpFps/j5Cih7rXJBsnjwkCkWSX04mfXVWNt75xJhaU+NO+12g0aiHZ5HfBR4NlMbYYypw2GT0eaQ5aXMJp36P1oaoqcnNzUVxcDI/Hg0AggEgkGHW2fQAAcelJREFUwog3362mog/vUB6JRNhzkhO+LMvoDCt45YA56nfDmr4bHLxsPNMiIr8uswWgoWFaEW0AWDcnHxvnFcDv4jayhCFauXoSXoStruQJ3PPZdXj+78/G2tnp8+lGC5pupJUaD4gdZnb2Ft/FiMGOSxaXotDrGOBBY493alpx7n+8gat+/x62HusY77cz6jAMA23BWNrbVqY1REsS7Yii4Za/fIj/99R+tPfxHDwGrDwefBowdKB8NZA3m7naX7akFDnuzC701Am/4YwBosSyGDekGqItLDFd4RsCVjdwvqPdqtgQi5tGL+Sm63a7Wfbn9oQJ2iJ3CCIMdjiw2Wxwu93swEBRJkCyY9QTB57b14x7N59ATNWzcskpAn7ekQ6HYUXH7986hp+8ftoiHaeRBToAkokZHT7J1Z4yZgOBAOtmk0STl43z2ey86/SvXqvHWb98Ew9tPdHr/WqaxpzGs93siYlM5rTnF3kgCkB3VENnVLMkJdC6oDVKYyxEtPnbUjvhdrudjReQjJzWN60zWte6rsPjkNPuZxQfB8DiLM531LNdw7HHUOa0aQTraGsIomyzFBQBsAI1jboUFBRAVVWEQiGoqgq32w2v12tRSfDjLk6nE6FQiKnCeO8IWZbx5M5TUDQDSyv87L2kw3DcxqkglDXnGzqm3W/tGxctxP1fOBOXLeVii7xFQE4lBBhYIhzHoZQsbWAQpGWU8MK+RlzwX2/igS29Dwh9ItQOHHoOAPBfresAZOhUPka4b/NxfPr/tiIQVeGQxSkfB3W4KYBV//YKrvztu2lvX1aRA0EATnVFEMytMr/JGaLluGyYV2RW69OZqhmGgb+8XYf6ttDg3tD+J83/LrkGkbiGp3eZc2WZSr+tUWJZ2fhEBm+ItmJGDpaWeVHklVm3h2RqfiEKCRpUQ0SnIrEZbafTyQ4OncEIDvSYF+6l3qRsnCTjJKekwwYfs2O32/Hy4U5ouoEVM/yYW5jNip1KSJWPO2QJf32/Aa8d7UZzICmP5aWVRHKooENRSXTAJEJMBmgkOacZRjqMUp4suY23BeN452gHdANYM6t3mgV/yKXHZjGxkMmcttthQ2Wu2VSoa4+x2WkqAvKGaES0qQtJa4kku3Tuo+41xS+5XC6LWoPmrFsjwKHTXew98+dG6kzyJJtf/8MhQ1mMDDKd056Z74HLJiKuGTjZFesVo0nqLnKy13UdoVCIRXNRpBypJPgZfXIsVxSFjc7wxR1ZlvF+bTuA/o1rqctOj8kENBsOZLvZw8G0I9p9onwlAGCZWIeDjT19SkdUbfCykpHAA1tO4Fh7GI1dkcE/aO/DgK6gI2cxtsVmYGa+GxvnTRwTNE038G/PHsD3n9gHTTdwzaoK3Pv59WkNaqYSKvNd6IkoaOyOorkn2ut2n9OGBcVmseGokCiMcB1tICVvOwW7Grrwk+cP4vL/fhuh2AAV2UCzRTb+wr5GBGIqKvNdGRvm8VFig853z2JcwB8Erl5Zjvs/swo3LC+0dHtsNhtEAcgTzDXaHDPNz2iOkAjOjhYDqiGgQI6jWI4xokRd79SMWd7ozG6348k9pv/AVctMw77sAXPqIPXAapdFzCsyJdn1XXG2FuhgCVhllpFIxGJa5XK5oKoqVFVlTvZ0iAWSB0KHw2GJDFNVFc/ta4FmGFhZmYv5xT7L+1QUhXXNac47i4mHTOa0RVHE/ELzOlTXEWdEg4/i4p+DlBB8l5s63PR8DofDkpvNrxMqPALA/20+hSt+9wH++PbxXpFMVNABkgSLfw8Aej13FmOLTOe0RVHAuQsLcWFVAfSEogFIzmRTd5sIcyQSQSgUQiwWg8vlgtvtZkVCWpvkXJ+q0uHXC6ke/nzbGjzwhTP7HfXjs7gz7UjTuqa9OouhYdoS7Z6oktZ5fIVYh86wgpaAVZqr6Qau+t27WPyDl9A6CNnuSOBYWwjvHTU7hTcOtstoGEw2/oh2HgCzmz1R5LyhmIq/+9s2/O+79QCAb128EL+6ccXApl1TAG67jIUJl8qdfeRpkyHa1nCZ+Y3WI4CWJM2WvO0UPLzNjHi4bEkpPI4BLtYHnwZgABVnALkzk9LvNZUZr5WPLC/DpzbMwic3zM7ocVmMPfgDKxFjMjjhZ7QFQbA4j1O3j6rz0WgU29rN5zK72UnZOGXAqqrKOuWKojASLooiajsV1LSE4JBFXLa4KOs2PsWQKh0HgKrE3lfbnowySp3bJlA3m8gzdYJ4IyBas0ReSE3BF3Y0TWMFndTsbMqjpdxa3kE6i4mFwc5p0xpakCjq1HYkC9pEWFKN+IhMkJqBn6/lVQ7U9U6VdhORUQwBz+8119ra2TkW0kUeAADSFnSy3eyJAb4Qze9d/eG/b1yO31y/BAtLfBaFAu9HQqQ5EAggGo2ywh7FeNEa5F3y6T3QqAyN1gDJgoAoCtgwr6DfUb+huo3zKotsN3t4mJZE+5N3bsHyH72M92vbkt9MEO3VtmMAgAMphmiSKCAYUxHX9LQz3KOBBxMzs+cuLMKMvEEatJzeCbTshy458Pu2lZDFiWWC9s9P7MWrB1tgl0X87uOr8LULF0yreaRVCcOzvvK0yRDt7RY3YPMAWgzoqE3eXmlKH3c3dFmq8uG4ime4CLgBwbmNH28P4cO6DggChrRWqkv9+NerluLixQNEiWUx7uAJEPtakKCLNguJAYC8BNFujtssVXFFUXCyM4LjETsAA4s9YfY3TB1FOjDwh1KaX7TZbHjugOnHcPGiIviccvaAOcWQzhCNjEjrEuSHVznwMTjUveEPiCTPJWUFGZdRd1JRFEvXhwo9+xuDONoahkMWcWVKbGQ8Hmedy9SOURYTD4OR9dK6WzcrF7esLsaF83Ms+dayLLP0BIPrQJI3gCzLLEqOZvzJ5IpINm/eJ0kSk42/XR9AKK6hMs+JdbPz2R5Ic91AepLNm2dl1+D4gp/THmxXmyfnVKzjr6+0jkg+TmaOtN74SEIqDvJjCdTppj0SAAxBHFTUMBUsgcyJdlZlMXKYlkQ7L1H9sRDmhCFahd4IP4JWV/IEqhN52qmu5KOBuKrj0YQkN6P56p1mN3uv/xz0wItLlpSgyDdxKvXfvqQK1aU+PPjFM/HR5VMvL3sgUMd61wAd7V0ne2AUJ1zDOefxqlIf7LKI7oiCY+1h9v3n9zYhGFMxM9+NM+cMIP3uaQSOv29+veRq1s0+e0ERyrPS7ykNvjMEAP/xai0u+dNevHY8brmgSpKEAmaIZmfdaaqqf9hkXrxnOaLwy5pl/pqMz9JlJQOAINvx3D7TKfXKpWbuZ/ZCPrXAKxTooLcocf2s64gx6TetRX4mVlVVKIrC8oxJypsq/SXTIHocHz1Dtz252+wwXra0FH5nksSQXFNRFOb6PJ0KvpMRg5H1EllZMcOPr51VgbPn5fWKNkrNvqb5fHo8PT/v+szvm/y4Ax/r9fTeVgDA1ctL2ePC4TCTrZNLfir4bnZ2DY4/MpePm0S6qTvC1hZ1tIEkeY/H45bMdN7Fni/4kIycDPfoOfiIsBf3N2P9T1/D79842u9749U+mcjGDcNgXfZsN3v4mJZEu7o0DWF25wN5swEAS8Vjacn04sRB4dAYEO1XDjSjLRhHsc+BC6v7DqG3IB4G9j4KAPhtx5kAJoYJ2vH2pDlXZb4bz3/9bKye2duUZjqAOtZ7TnZBS+MmX13qg9MmIhBT0eNfaH6TI9p2WcTShLvkroZO9v2HE+qHGwfj+n3gKQAGULkeqrccj243Jec3ZWhk1h6M4duP7MbmuvZsPNskAl+xz3XboRnAiYDOqud0kCyQzM5jQJMR0QQUFBTAMAwEAkHs6jIPCUu9IQvJJsdxismRZZlV8IkoibIdt545E6sqc7B+di573SymFlKJNkXhnOqOI66BOY6nIy7U5QHMgx6tIfII4F3ydV1nxJ3vIsXiCl4/YpoFpUbf0Fw2EfZsJ3HiI9M5bSA590+fNR9TKAgC6yRSZGE4HGaFHLovvS4lL6Rzp24OadhyrBMCgI8tL2HPRc/vcrnS7nFZE7SJh0wN0eKagbN+9QEu/J/NiBnWz5gvzlCEF5Fo2vfi8Thbi9FolO2LFPnGK34AsOzsrrCCmNq/vJ13ss8EpPTJJoGMDKYl0V5UlsjSbkrpWifk48uFurREm6RvYyEdJ5fxm9ZWQpYG+TEdfAaI9SDonoHXYlWYme8e10xjwzDwxzdrccF/vYWX9jex70+UefHxwIJiH9x2CaG4htrWYK/bZUnEsgrzQFovzjK/2XLAcp/vXbEIT92+CR9ZZioC6lqD2HKsA6IAXN9PliIDJxt/u6YVzT0x5LltuGjxIAs6CTyx8xQe3X4SP3n+YLYSP4nAS90WJYqOx7tURmTooGqDBp9gVuAbAgaTve1rDKBDkWETdFR7Y+yCTLJzkvXSDC5/aHU4HCjO8+E7l1bj/s+ugSRmL+RTFalz2sV+J/I9NtgkAU1BxSKL5KXmANjhk0g1rSFSS9Aa5uN0eNm4ruuQRAFPfWktfnn9cosZKJmqUTc7a/QzOZDJnLYoiuiJqth1KogTXTGLgz2RGABMCUHkJxqNMlkvAEv+NpFqKixSEREAnj9oFr03zs1DWY4T0Wi0F4lPB16em12DEwOZzmk7bRK8CU+co61hy+dI64eKebTfkFKHXoNk5ZSi4Ha7mRKDV5IBQFNAwbtHzbHXG/oZ9ePff6ZFHL6bnT3bDR/TlGgnJGytwbSGaMvEOtS1hay3cY+rbQ0Oaj5iOPjaBfNx1cryfm37eyEhG39GOA8GRNy8LnNjq5FCXNXx3cf24BcvHoKmG9hxvHPgB00DSKKAm9fOxJfOnQeXLf2FleTjO6IJQ7Rmq/P42tn5WFGZC7ts/vkebQnC55Rx7sIilOYMEE/TfQpo+ND8evFVLDv7mlUzMjKkMwyDPTajNZrFuIOv2FP25skeBRqShmhEtilPuzEiIhKJIBKJsOzshe4IRF1hB08yQqOcWXodvkNERmmpcs4sph5SO5CCIODhz63BG7evxpz8ZAQXdRj5r0kqToSHom+oq0iz/7RO+S4mdY8AIN/rxI1nWK+DRI4AWAh6FhMfg53TFkURf93chNsfP4oXj/Swx5DyhgqADoeDxSZRPBzN19LcNq073g2aQCaP79aZ55urlhdbZm753ON0yHazJx6GMqddVWKmxRxuDlqUNvRctG4oFo7GBKigGAwGWfHG7XazDjddWwmyLOOxHSdhGMDGeQWozO/bu4n3VcmELKuqmvUMGGFMy1ZCsc+BfI8dHaE4apqDWDbD7CAS0V4p1UNTDBxtCWJporsIAGU5TvidMnqiKo62BLGkPCfd048I1s8twPpMYpY66oBj78CAgN+2rxtXE7SucBxfunc7Pqwzu6w/vHIJPrVx9ri8l4mIH1y5uN/bSV7+WkchPgsAXceBWABw+NLe/5Ilpdi6sAgdofjAL37gKfO/MzegTSzAawd3Acg8O3tXQxdqWoJpTYaymNjgO43luS74nDICURVNYSCfi0wyDAP5YgTHtVw0Rc0Im/bObuwLmHP8SzymIoOv1NPzUwRTJJKcW5MkCR+eDMPd1oKNc3LZfTONHMlicoAOmGQkJUkSynNdiESAeCzKzKV4Z15SRjidTiiKwmK9eFMqek7etZxmYgHzMBoIhiAKvSWT8XicdZDosJtVVEwekMldfwSI9iFyHq/riLHCHhVveGk5GZT19PSw7iOpJmiWljeV4vdPWoePfXkDnt95AmdUuNhaHohkZwnNxAWZ4tE+MRAWlfnxxpE2HGoK4OLZBYjFYqwbTXsW+U7QXkXjBfF4nBFqn8/H9jdShlFxEQBEUcIjiXSZgRocQy1kZ7vZI49pecIRBIHJxw82cRLxshUAgAq0Ig89veTjgiDgosUluGJZKcSJtgB33gcAOOpbh9MoxMWLS1DsG6C7OQqobwvhmj+8jw/rOuB1yPjfT6/NkuwMQR3tzc0CDE/CybvlkOU+T+8+je89vgeHEuvXaZMGZ2TGycaf2HEKqm5gRWUuqkrTk/i+QAZqVywrQ44re0iYTOAlmIIgYGGxBwBwKpTs8BGBYRFfMRnBYBC7WzVEdRE+SUOlPcLIEX9AJaLNz0HSofU3r9fjc3dvw+M7zMNCluRMbaR2hlIN93gTKlqX9H1esktf89navOFaMu7GfL2/vncCN9+5A68fTiaL8AY/9JpZA6rJhcHMadPnWZXY1+oScXJEtMlHAgAjNxSxRMSZ/ksKHJL10l4myzKiUdPDwul0QjR0bJrlgdMmsa7kQAXErAnaxEWmc9qkdj3cHGRxcAAsexpgklhepROLxRCPx2Gz2eByuSxmarTv8fPZW09041RXBD6njMuWlvb5fnjn8kyusZqmsZ85W/wZOUxLog0AFy8qwS3rZmJ2gSf5TWcOUDAfALBMrE87i/2rG1fiD59Yw/6wRhqvHWzGj57ej5rmDObAdQ3YdT8A4E+BDQDGxwStuSeKq3//HurbQqjIdeHRL2/A+VWZzf1OF3SHFbx9pLXXeAIAzMhzodBrh6obCOQkDNFarPLxx3ecxANbGnDfhycGb0TW1QCc3AJAgLHoSjy0LWmglgnMKLHGxGOzsvHJCH4OrTohe2sIGBYiBIAZorXFbejs7sGubvMgsMRjdgx5ks13GqkKT4cEm82Gum4dta0hOG0iLliYDyB7MZ/q4NcZAHRFVHzv6cO4/Yk6y3w2b2JG0nGaU+SLN7y5D8U08TPeRIqe2tOE/Y1BdEcU9l7IAI1/X9n1N7kwmDltKtrML/JAANARUdERViwxR3a73TIbS6SZXMcpu5hIE62d1NdXdQOCKKKnp4epLgZDsrOjMxMbmc5pL0qMYB1tDUEQkySd1oqu63C5XPB4PGzMJRwOs3Xgdrt7ueFTUYdX6jySMK69amU5nH2MHgLW7OxMijhUiKRiexYjg2n7m/z0pjn42bXLsG5OvvUGmtMW6lm3cCxx1/vHcNf7x/DUrtODf1Dt60DgNGK2XDwdXYUZeS6cNX/sTdBK/E5cs6oCKytz8cTtG5m7exa9celv3sYn79yCvae6e91mxpPkAgCOy3PMbzZbDdFWVpq3/+3D47jwV2+hJ6pgQJBsfNZG7Oh04WhLEE5b5tJvihKbVeDGmXPzB35AFhMOvPxx/Zx8XLG4CAsLzAMfzSUKggCfEIcNGjQIqO02UBM0q/FVzm7WHeJdmyVJYlJMOigQGX/xcBcA4LLFJfA6rAQri6mJ1M6Qz2XHywfbsL85grZwMgIutSNNs7QUv8TLd0kdQQdIm81m6d5sqW/Hic4o3HYJVywrY6/PG0/RfbPrb/JhsHPaHqcNM3JN8lLfGbcQbSISsVgM0WjUQjBo3/L7/UyRQzJvIi60Fp/a145L/vt9PL6ryfKYgcDPz2ZN0CYeMp3TnlPohUMWEVF0tEbMvYhmtIFkgYjk49TNJh8AXmUBgEXOUYIHYK7br10wH188Zy5uXtt/I20obuO0zoFspNdII3uVSQU5j4um83i6bqFhGDjZGR7xSKMT7WG8U9MGQchwZnbHPQCAV2znIg4bblk3c8xM0HTdQCimsv//l48swoNfPHNcZOuTCcsTvgB95WkTkd4dT5DgFEO0FYnbASDHZbNkxPYJTjZOcWBXLCsb3GM5yKKAmflu3HhGZVbyNknBH1YvW1qKX1yzCOfN9bMLPpEQQQDyJdMQ7ZVmN3QIKHMoKLKrvYyoePdxwLxwK4piHk657OyPLTfHIbKdnKkPvjNkGAZcdhmzC8wRl7oOU9LLz2hTh9rr9TIDKlqPdBCkfFkaTaB1RIfjx3eaReorlpXCk3ADJgM0XoaZXX+TE4PJOaY9aV7KWiP5OKlwVFVlWdf0nKIoWrrZNBNO87pE0DVNw7P723CqO4aYZvTrLp4KnthnMTGRSZ62JAq4flU5Pn3mDLgShWoy1KN5bOpex+NxRmh5PxM+io6um7zbuCzLmF/swz9fscjiHZUKfqwiE6JNazLTzO0sBsa0/m1GFQ17T3YjwHcDOaLdGVbQEohZHhNXdaz88Ss46xdvoDXltuHiwa1mpNfZC4r6dRO0INQGHH4BAPC7zg2QRQE3ZCgFHioicQ1fuW8HvnDPNihaYjOQxH4lLVmYIKK862RX2tvJEO3NriLzGy37Aa6wszLR8QaAqwbTke48DpzaBkBAeN4VeHaPeRjNNDsbAK5eVYE3v30ePnfWnIwfm8XEAN/Rpgs8zVXzruOCIKBANGWVDRHzor3YHbDM1PKycTIPosOFrutwOBzY2hhHIKqiIteFNZWmH0B2Pnvqg3dpJhJDDr217VHLeuPzYulgqiiKRTZO3WzqPPLSSFmW0ROO4qWD5lz2jWeYXR9FScqG+Y55dv1NTgxmTpuKNwuKTKJd32mSiHg8zsYO6H5UEOTHXXJykkSGZrf5PS8Wi+FQUwCHWsKQRQFXrawYNGnOZhRPDtA6I1I8EH545SJ868K5KMtxsEIgycf5zGxat3S95ePkAPQi50BmEvChyMb5PPdsN3vkMa2J9tW/fw9X/u5dbD3Wkfxm6XIAAsqEDhShCwdSDNHssogCr7kQD6bmcA8Diqbj4YSb4MfXZUB+9jwE6ApOuatxyJiJixaNjQlac08UN/7pA7y4vwnbjnViTx+EMYv0WEVEu4+O9vIEkX6nqwCGIAKRTiCQzCLP89hxzaoKrKjMxfWDIcskG599Fp6t1xGKa5hd4O49OjFIiKKQLahMYqQaomm6gaaQgR7FKtsVBIEZogGACAML7D0WkxfqZouiyOYTabaWDpPP7TfJz9UryyByj8ti6iN1TpuIdl1HzEI2iBzx0V2KojATNDIN8ng87LlIUg6YB8vn9zQiHNcwK9+FtbPzYBgG62bb7fas0c8UAL939TU/S3vLOfPz8J3zK3HzyiKLwoZiDFMzjElW7vEkvXuoA0ldx1gshnA4jJeOmGNf5y3IR77HPmjSzMt6s4qwiQvat8gEbyDwxWueaPNqHX798coaeizvNs7vV7VtEXz1/h1472hb+hfnMJTIOOpmZwuQo4NpfdJZWJJwHudNzxxeoKgKALBUrMehNIZoZISW6ko+HLx6oBltwRiKfA5cuKhkcA8yDGCHmZ19Z/gsAMAt60ffBG3/6W5c/fv3sPdUN/LcNtz3hfVYMys7q5sJls3IgSAAp7oiaZUROS4b5hZ5EIMdYe9s85sphmi/vmklnrp9E7yOQWyM+x83/8vJxm/IUPqtajpe2Ns46hnyWYwNeAL0/acP4zOP1uP90xpzHqeKer6QJNpz3VG4pWRONj9fK0kSywClQ4XdbofN4UJH2Lz4X7nUNEfMXsynD1JnahclEg6OtkUtigh+L7Lb7azLSBJyMtqjbiQ9ljc4eywhG79u9QyWU8t3I7Oy8amBgbqNRFyqS7y4dnkRS1bgCy2UkkBGaKTI4eesaR/TNI0Rn0AggLiq45Uak2hfs6LU4izdH7JzsJMHmc5pS5KErrCC7cc7LeNT/HiVw2F2u2l/MwzD4lJORJuXngPA47sa8eyeRtz74fF+3wN1ywe7Hukx2W726GJaE+0+CTPJx4W6tGR6ceJxh0aQaN+/xZSN33jGDNikQX4sp3YArQehiQ48El2PilwXzh5lE7RXDzTjhjs+QGN3FPOKPHjy9k1YOztLsjOFz2nD/CKzs7O7oSvtfUgefsqe3hBt0OioB07vBAQR9UUXYtvxTogCMs5Zf/NwK7583w585H/eHXF/gizGHnwFfl7iIHoyYDDHXRbxJUUhwPy8Fzl72PfpH3W+HQ4HI010wbfb7SjIy8FzXz8br37zHFTkmBfyLNGePkgl2tWJ6+fJ7hg0iJwfQNI4iLrZNINNX3u9XhiGwbqPvGxc13Xctq4C5y8swPVnVELXddapcTqdFpfnbCdxcmMwhmipahvAOqNNSoloNMrWA7mGE4hkE+EhA6vtjTF0RVQUee3YOC8/4252VtEzOZDJnHZPRMXZv/4An7xnNxRIrODMj1W5XC6LWow3EiWSzUfMAYAuiHhi5ykAGHAsNBO1BPkTkPs5FdizGHlM67/06kSW9qFUCTg5j4t1aZ3Hq0vTdMKHAcMwsLQiB4Vex4BughbsNE3Q3rVvQg88uGVd5aiaoD28tQFf+Ns2hOMaNs0vwONf3oRZfDxaFhmBGZ4NMKe9T60wv9EyRKJ94Enzv7PPxoMHTGOr86uKUeLPbMSA4sDOryrKHlSnAPjDKhUPG4LmgZLIDgDYRGCVsxWLfVHMtgcsRlS8vM7v97MuUTweZxV8kmHOTDgAZw+Z0wu8LFLXdZT4nSjy2jErz4muqM4KNqlSTZrvJ5dem80Gt9udVjZOXe8Lqgrxh1tWoDzXZTFAE0UxG6c0hcAToIHmtOvbI3j2QAcOt0YssUk0I6tppvu90+lkHUdCLBZjRR5ahwDwco15LvzY8hLIojDoNTUUWW8W44dM5rRz3DaU+BIu94mxGFqbqbnsVNxJF+lF3ydy//bRTnSGFRT7HDhnQVGfr89HxvVX+FEUBaFQCJFIxKLwcLlcA/6MWQwN07qtQIfLutYgooqWnDllhmj1qE29DclOeG1rEDFVg0Me3qyqIAj47mXV+NbFCyEPtpsdDwF7HwMA3NGzAZIojHqm8YrKXHjsMq5cUY4fX7Vk8J33LNLiujUzsHpWHjbMLUh7O0V8vdNTgmuBXs7jg0bCbVxdfDUee8n0AbgxE1d7AC2BKF4/1GI+NpudPSXAd7RpTzsd0ADJbnEe1zQN65zN8PsjUBQwuTgvraNqvSzLiMfjUBQFXq8XccmJUFyD1yEPKXIki8kPXrZNJOflr61HJBSEqqqIRg0L2dY0DZFIhN2X1iC5OvNEici0LMuIRCLsa1VV2aGTz9/OxilNDfBzr7Qe0t1HFEU8uqcNT+xtw43L8rCoxANFUVi6gsfjQU5OjumI73LB6XRaisiKoiAWi7HXIxL0uY2VKM5x46rlJYOW6WZN0CYfUot/AxWIq0u9aA7EUNMaxsZiicnDAViUO1QgovVGKh0y46MIOQB4gsZh1szolx/wsvHU9cU7nvPz5mQsmS18jy6m9W+32OdAntsG3QBqmoPJG0qWwhAkFAtdKNQ7cLQlaHlcWY4TfqcMVTd63TYcDJpkA8CBp4F4AB32cnyoL8JFi4pRnGGHcjDQ9WS1uKrUhxf+/mz89JqlWZI9AjhzbgFuWTcTswvTqwIWlflhl0VsjyZcxVsPA9rgHDAZ2muBxt2AIOEd6Uy0BeMo9DpwQXVxRk/z+I5T0HQDq2bmYkHC2yCLyQ1erluW44TPKUMzgOZwMv6GP0TS7Bj9Px/p5Xa72f1586k7t7Rg3U9exQObj2fnY6cxePWEKIqQRashHu90T91pWl9EpGiWMfUgKYoith/vxG/fqMPJrghkWWZrkA6R2U7i1MNg5rT7cx6ntUF7WmpXzzAMBAIBRKNRRkjovmvnFODfP1aNOQXuQZNmPtIrqwibHOCvf4ORj1eXmgXrIy0htr7IFDR1JCbVeIyIMv+9joiGN4+0AgBuGGDUL103m0wkQ6EQotEo65jb7XZ4vV44HI4syR4DTOvfsCAI6ee07W4IxYsAJPO0Ux/38fWz8OXz5mWcQZyKHSc68daRVguhHRR2miZo98XPgQERt6wbeRO0E+1hfOS372JzXTv7XmW+O3uRGCPYZRFLyv1oMIqgSi5AiwEdtZk9CcnG55yD+/aGAADXra7IqFBiGAYzUBtKHFgWExd8J6YqMafdEDRY5AjvTA6AHTb5Do9hGPD5fMzgJRaLmdV7mxMv7G9BOK5hBicbz+4f0w/8YZXWDRmZ8YZoQLLzQ3OKFOPFyyn5r2VZxt8+OIY73j2BuzefgqIoFglmtpM4NTEQAaLbFxabXij1HTE2t08dbZKJk1qCL8QEAgGEw2HmDUBjMaT2GYxMl0Du5kC22DPZkAnRXlRu8onDzUE2mkB7EXWtqeBit9stxUR6ft5P4pm9LdANYO3sPMxNePqkAx/PRfsmEexYLMb2PxrloveWxdhgWhNtwJTBfu/yaqxKzMMylK8EQHPavWex/+nyanz3surB5133gd+8WoNP3bkFf3wrAwLVXgscfw8GRNwX3WSaoPUzuzEUbDvWgav/8B4ONvbgR88cyLwQkMWgcLQlgL99cAzb+Ig5Ditm5MKAiCYHGaJlKB9PyMZ75n0UbxxOVEYzJMvbj3eiri0El03CRweT2Z3FpAHvqlpVal7ITwaSVW8AFulbKvmmPFA6fJJs3G63Y1uzimBMxYw8F1ZWmM+dPWROT/BjCgDQEozjU/fuw3V3H7SQaj7XmOYaaT6b1h4VgegwGlENvHTAHGu5blWF5SArCILlAJo9XE4dDDSnTQWd+UXmGa0trKIzrFhm9R0OB1wuF1NM0PqIRqMIhULQNA0ejwdOpxOGYWBfYwA/e6UOBxoDGbk7Z03QJi8ymdNeXG7mr9e0hCAlioe0r5F3CUnQ+WspGe6RYoL2ydJcF+YXewc8s/FFAFVVEQwG0xJs/jWzGDtM+/Lu1asq0t9QvgrYeS+WC/X48wi6i/No6AjjnRqT/Fy5PAMCs/Ne8z/21WiKFuBbayshjaAJ2pM7T+EfH92DuKZjWUUO/vqpM0bVZG0644EtDfjfd+vxyQ2zcEYa9/ZVM3Nx1/vAQX0GZuBAwhDt2sE9edtRoGkvIEh4JLwSmt6MNbPyML+478poOnxQayoaPrK8bHBRYllMGvARXxdWFcMtAUV6B4AYk4/TAYC6PnSopQu2z+djpi6xWIxd2J/fbhaPrltdYUYRIjufPV2RaohW6HXiYFMQmgG0R3S4OJUESX4BWLrf9P9891sQBDy3rxkxVcf8IjcWlbjZwZbimLKdxKmJwc5p+5w2VOTYcao7jmOdcRT5k+uBTM4cDgcbTYhEIlBVFbFYjBnw0Yzr0/s78OSeFkRVA//+0YWDcnfmu43Z+KTJh0zmtOcUemCTBITiGpqDKuycCSMVhPh9jq6l/B7FF7avX1OJ61bPwEB9rlgsxq69BNoDs/ve+CN76ukLnPP4wdPdrDLEoy0Yw5GmADbMKxhSleihrQ0wDODsBYWYWTDIzrimArvuBwD8OXiWaYKWobFVXzAMA79+5Qj+5/WjAIBLl5Tg1zethNueXSajBXIe39VHxBcZom0OleJiCZlFfB0wu9nG3PNw727TS2Ao0u+vXbgAly0tzc7lT0HwRHvT/AKsmeHBgQMRdHXFLCYpJOflDx30eI/HA7fbjXg8jnA4DJvNhhAc+LDezPy8clkJe45sNX16gjp/RHyddhlzCt042hpGXUcMywslRrD5eW0i1rw7r9PptMjGH0mkIXxsWTFbl0SaeAO+bCdx6oHm+ck/IhW0puYXunCqO466zjjWVOpMAk6Zxna7HZIkMZKt6zoMw2Cdbl3XEYzG8fIhs+h89fLknjYQsqMLkxupe1d/+4hNEnH7uXPhd4jIddsR08yZbOpo89GE/LWUyDgvG+eLi1Ifl01d1xGLxdDTYzYDSZ1ht9uza20CIXvlgeke/szu0+gMxZPfLFkKQ7ShQAjAHWlESyBmeUxU0bDuJ6/i43/djNZgDJlC0XQWl5TRfHXta0CwCSE5F6/pq3FhdeYxTekQV3V8/cFdjGR/6dx5+OMn1mRJ9iiDiPbBxh5Eld4zQLMK3Mh127BfSxDklgyk4/ufBADUl1yK+rYQPHYJH1leNqT3uaDE16dpWxaTF9QxpK9JxssbBNH3/X6/5bHkmupwOCBJEsLhMDRNg91ux1vHozAMYMPcApT5zIp69sI/vZFqiLYw4QlQ1xFj640OpABYzjF1Zug5bDYbO4we64hiV0M3JAG4rNpMb6BDbOrcYhZTD4OZ0yaiDQDHOEM0IteAudbi8biF5FCXnLwEXjvSgXBcQ2WeC2sq/ZbX7w/ZNTj5kcmc9lfOm4sbVpch32t1FCeFGM1m07qiQgwVsnVdRyim4uk9zYjE078eJTNQTBdgri+v18uMSbOYOBhxov2jH/2IHd7oX2lpKbvdMAz86Ec/Qnl5OVwuF8477zzs3z/E2KIRwpfv3Y6vPbATOxs6k9+UHRBKFgMAlon1OJAiH3faJMxJEI+h5Gm/drAFrYEYCr12XLSoZPAP3GFmZz+uboICGbesHxkTNJskQAAgiwJ+ed1y/NPl1Vm5+BhgRp4LBR47FM3otcYAk/ysmJGLw3qCaHceA2KDcLpvPQI07wNEG+5sXwIA+OjycngylH4HokpG989i8oGvrLcGYtjTpqM9JrAuIHVj6NDAR5CQc6lhGIhEIhAEAU6nE88faAMAXLu6nM2bZS/+0xv8nLZJtM0Rltr2KOv2UaGHuox0X767zefTPrGrEQCwaW4eihIZttT9JoKT6u6bxdTBQHPatHYuqcrHf18zH19YV8SMoijXmIz1iGS7XC7mEcA//7P7zW72tavKeo0w9IWsCdrUQCZz2nRffk/jncf5WEzALPrw5pAA8OqRDnzrkd246c8fWJ5b0zSEw2GEw2HLe3G5XPD5fNl9boJiVDraS5YsQWNjI/u3d+9edtsvf/lL/OpXv8Lvfvc7bN26FaWlpbj44osRCGROVkcKSefxlPfA8rTrcCgNma5OPO7QEGa4H9hyAgBw/ZpK2OVBfgzBFuDIiwCAv8XOQUWuq98A+0wgCAJ+ef1yPPKlDSMmRc9iYAiCwLrau/uQj6+szEUH/OiREjPcLQcHfmLKzp5zLh47YBLzG9f2Hw+RiqMtAaz591fxjQd3pj3EZDE1wBOgX75ahx+/2YrtLclIJZLNRaNRC9kmgxWn04l4PM7cxn0+H+77/Hp859IqXFRVCCArG8+id1eIOtq1bRFLbJzD4WDZxmSIRgdUkvECCTm4AHjsEq5YlMckk7Ses53EqQ8+opDPB+ZvB8zZ2XUz/Sj0ORnRTi0kAkn38XA4DACsiHi8PYTtDT0QAFy51IzGHAypIWO+7OjC5EbqnHZ/0Axgz6kevHCglalryNCRV0rQmksnG39iVxMA4PKlZew+RLD5sRmXy8UUaNl9buJiVP7yZVlGaWkp+1dUZJJBwzDwm9/8Bt///vdx7bXXYunSpbj77rsRDodx//33j8ZbGRQo+y41xovNaQu9I74AYFGpL/3jBkBU0dDcEwUA3JwJqd3zEKCrqLFV4YhRiZuGaYL25uEWfOeR3cxR3GmTsGpm3pCfL4uhYcUAc9orE474R5BQLwxGPp4g2lvd5yGiaJhX5MHqDD/bh7Y2IK7qCMW1LEmawuDntKsTe9rJgLknkEtpahyTKIpwOp3sQh8IBJhsPC8vDxV5btx+/nzYhGw3OwsTPCkyDAPVCZf7E10xqIbAOtE0E0lZ2mQQRLJLOoxKkoR/uHAeXvzSKpwzL88iMac5WyBLtKc6+pP18spKuq+u62xtUUdblmVGslVVZV1GWjvP7DNNazfNK0CJz1xjA+1p/Oxtdg1ObmSSp90dUfGJu3bhn548hLgOlqTArwci3CQbB8ASFurbw9h+oguSKOBjy0uYPJxXRng8HrhcLvZY3kAyi4mHUflkampqUF5ejjlz5uDmm29GXV0dAKC+vh5NTU245JJL2H0dDgfOPfdcvP/++30+Hw378/9GEovKzMNlrxgvS0e7O83j/OkfNwCcNgkv/P3ZeOkb5wx+7tUwgB1mdvad4YQJ2jAyje9+/xg+e9dWPLL9JB5MZCRnMT6gjvaek73XGJA0RNsZSzjTD2SI1nIQaD0IiDb89vRCAMBNayszIstxVcfjO06Zj81mZ09p8ES7qsTcCxuCJkmhOUYyXSEJnCzLltibaNQsHHq9Xrhc5jwkL+fMEu0sAGucXInficWlXpw1JwchxRptQ+uJDpA0K8vPcFOcnCzocDrslmzYbKTX9MFAsl6a095yvBt/+rAJexrDTNLtcDhgt9uZiRRgdqFpPIbWY67bjmKvHdesNMcgB6PQyZqgTS0MVj5e5HOg0GOHAeBEt8pUEzSewBetY7EYU+LQtfLpPWZU4Vnz8uG3JTvodrudXXNTVTvZ9TWxMeJEe/369bjnnnvw0ksv4S9/+QuampqwceNGtLe3o6nJlEOUlFhnkktKStht6fCzn/0MOTk57F9l5cge/Ikw17UGrYZURYtgSA7kCGEobfW9zKpIOn60JYiYOrBJAg9BEFCV6B4NCie3Am2HoYgOPKttwAXVxSjNydwETdV0/PCpffjh0/uhG8D1a2bg+jWZSYqzGFmsmZWH+z+/Hk9/dVPa2/M9dswqcOOwQYZoAxDthAlasPJcvH9KhSwKuHZ1Zp/x64ea0R6Ko8jnwHlVI5vRnsXEAt/xoaJjU8iAaiQN0ugQQHJeu93OZsIoWkSWZXxwWsUX/rYTbx5usVTvs2QnC8Ba1JEkCQ99bjV+ceU8FHqsBkFiIhaHSDZ1H4lkB2Iadp/sRigUAgBLjA11iuj7WUxt8J3G/ua0Xz/ahXu3t2D76QhbI263G16v12JqFgwGmYJCEARomoZPb5iJV7+xARdxhnsDIRvpNbWQiSFaVWnSf4I62vSPX2uKorCRGEVREInF8eRu03fimuUlEAQBdrudeaHwXWsi70BWMTHRMeJE+/LLL8d1112HZcuW4aKLLsJzzz0HALj77rvZfVIPXemis3h873vfQ3d3N/vX0DCyHdhinwP5Hjt0A6hp5oymZDtQuhQAsAS1ONpiNaEqz3HC75Sh6gZqW0KDeq2TnWGE4wMbKvTCTrOb/aJ+JgJw4+OZOJUnEIgq+Pw923D3B2bszj9eVoX/uH754GfEsxgVeBwyNs4vhM/Z92a5YkYuDpEhWvN+lkvcC4bBZOOvihsBABcuKkah15H+/n3goYTK4brVMyBnY72mPOjiX+Kzw+eUoRlAc1iwOI+TMZUsyxbJZTAYZN2hF2t68OaRVuw92Z2dkc2iF1KdxwFYOtZ80QcAm2uUZdniNv7c/lZc84f38S/P1UIURaaiAJIEhwh6FlMb/LxrX3PaoihiQaEZoXqsK87mtFOhaRpiMTNFhggyPbddltmBeSCinc1vn3rIZE6bxlFr2yJsZCaVaGuaxiTluq4jGAzizcMtaAspyHfbcNGSMng8HotShwdv9pjd5yY2Rv3T8Xg8WLZsGWpqapj7eGr3uqWlpVeXm4fD4YDf77f8G0kIgsBmEw82WWXpAp+nnTKLLQgCvnHRQvziumUo8Q+OyPzLk/uw/iev4aX9fXfweyEWBPY9DsA0QSvPceKchZl1GcNxFTfc8QHePNwKp03EHz+xGl85b3620zRJsLIyFzXGDOgQgUgHEGxOf8eWg0DbYRiSHb86Pg8AMh4xaOqO4q0jrYnHZtUO0wH8hboqYVJ1MmQeEonsAOZBlirsNDtLxkEhOLD1eDcEAbh6ZRkroA4mAieL6QG+o03XHlEUEYjpbK3ws4x0OxmiJc2CzK7PsnIPM+wDYIn0ynYSpw/66zbyWdoAUNcRt6wTHrFYjJEhSZLQHVHwbl0nVD1Z2OaJfV/gJb3ZM9bUQCZz2ovLTY5S0xZhqjAaV6A0BZq7JiNRwzBwpNUs8lyzega8bme/ayc7/z95MOpEOxaL4eDBgygrK8OcOXNQWlqKV155hd0ej8fx1ltvYePGjaP9VvrF3507D3fcugbnVxVbb6A5baE+7Sz2Z8+ag5vWzkTBIDqGJzvDeOtIKwIxlc1CDgoHngTiQTRK5dhiVOOmtTMzNkH7oLYdh5oCyHHZ8PDfbcDly4aWp5zF6KC+LYSfPHcAP3shvaP4ispcxGDHCSSi8pr7MERLdLNbis/CibANxT4Hzs2wKPPYjpPQDWDd7HzMLfJm9NgsJifSGaKdCvV2fSbDKY/HA5vNhlgsxqJy3m4wO0Sb5hWiyGMS8+xB8/+3d9/xcZVnvsB/Z/pIGo1kSaNiyQ3LltyLXDDFBmwDoYZiY7PedHYDJLAJyw2bfC6QAmySC8mNd29CkiWQBGyIIaEkBhMbm4DBwr1IbnJR79JoJE07894/js7xjOrMaNRGv+/n4w8w5cwZ6+XoPO/7vM9DwYJXrIUQuNDUidX/dQDrXzqurVyrq4pqxV69Xg+z2aytIp2sbceJ6jYY9RKuL0hDQkKCdnzuix2f+ts/q04izshUJhDr2/1o6fRpK9fB3G63lm2h0+nw12O1+MZrJXhg67Gw2xRysid+hbtPuzDbDgA4Xa9MQquZYOp4cLvdaGlp0TLBAoEAzGYzHv3cLOz592vwtaum9Xv84LZxvM6NfjH/CT3yyCO45ZZbMGnSJNTV1eGHP/whnE4nvvCFLygrwA8/jKeeegr5+fnIz8/HU089hYSEBGzcuDHWpxKRPoORrkB7ju4cNle1DOozXi0uhxDAFdPTwi+CBgAH/wAA+L37KugkKeI2TQBwXWEm9vz7NahxujGvq7gWjR7OTh9+/eE5pCYY8Z0bCnoEJ7NzkmHUSzgu52KKvkoJtKdfF3qQoLTxN7xLASh78CNN/V6/JA8mvS6yMUpjWnCgfeu8LExKErB5GqDTCa3yuLpvUQ2ydTod2tra4PP5kJiUhPdOKcX87lqcG7I/myiYWtkZALKSzXB5/JAF0Ngha6szXq9Xq2ivBuDqe/5yRMnmuWqaHRnJCSFjjNsVxqfu+7SDf3+qE4Q2ixHZySZUO7041+RBZkroa9VVRvU6p9fr8ZeuwlRX56eHHdgEp/Qymye+hLuifZkjEQadhDa3H42dAdiNl3pkd3R0wOv1apkTycnJIR0SJqUNPDkT3HmBaeOjX8zvgioqKrBhwwY0NDQgIyMDy5cvxyeffILJkycDAB599FF0dnbi/vvvR3NzM5YtW4b33nsPNlsEK7zDKX0mAnoLbHIn2qtPQojLQy7ifjmAwxUtOFPnwrqivis7++UAtn6m7HvdEMn+6obTwMW9CECHbfJVuLYwE9l268Dv68WktARMSksY+IU07AqybTDpdWju8OFiUwcmp4UGuRajHoXZyThZPQk36ff1XhCt9jjQeBpCb8bmqnwAkaeNA0B6khlfu7r/GVWKL+pKoxACcycmIy8xgNLSZrjdkpY+rtfrYbVatf3Zatq4JEk465RQ2eqBzWzAdTPTIWQv08apV2qgLcsyrCYDJqdZUdbQibImDwpTlN6wSUlJWpqlGmy73W745ADeOqpsu7pldgasVqv2O5f7YscvNZ1b3e/a/bpzaZ+2FdVOL8qaPFg6JQCfz6etMqrBj5oNcaquHcdrXDDoJNwyN1P7nIECG072xK/u+7T7Ggtmgx7fv6UAGYkGpCYEANmnFTZTr1NWqzWkoGibV8BmCy/7i9XGx5aYT4Vs2bIFVVVV8Hq9qKysxLZt2zBr1izteUmS8MQTT6C6uhputxu7d+/GnDlzYn0aUdl1sg6bd55GgysopUhvALLnAQAme06hri003cgnC9z9y734X9uOot7VMxVJtbO0DrVOD9ISTVg7Kyv8k+pazf4HFqAWE7BxWeSBU7sniuJrNKzMBr22r6evftrzc1MuVR7vLXX8uLKPvyxlBVzCimVTJ3BVmsKm3kSoVVDVm1c10FaDHrXfrLq3zGg0YvdF5dp38/xsGHWXWnoxbZy6614QbYajq0Jvk1sLZNRJGqPRCLPZrK1U7jrZgJZOP9ITjbgyP73X1Wy1DRiNL+Hs076sa592RasvpDo9AHR2dobsz1YzJ1bNSENqghI0h1MEjf3b41ck+7TvLsrD8qmpSLSYtN+jiYmJWoaYyWTSqo0fq2rD1c9+hG+8crDXyvnB1KJqAMfYWMHfRkGeeqcEP33vFI5262esm7gIADBPd65HQTSrSa8FMyXVfffTfmXfRQBKWmXYVb5lP3D4FQDAH70rkW23YOUMxwBvCuXy+HH503/H1176DK0dPYt/0Oih9tPuK9BekJeCUjXQrj+pjA9VUNr479uU7Q7rl0Q2KdPa6cOm336KbfsrEAj0f7Gn+BOcPl5S24G/lwdQ2Q6ttZLBYEBCQoIWyLjdbvj9fphMJqy4LB2LJqXgzkVMG6f+qUGwekOpFt8ra/RoxdB8Pl+v1cZ3nmoAAHxuVhospktF+rgvlvrbP6tO4Nw+Jx1/+kIhHrw8IyTQDgQC2oq2TqeDLIC3jylp43cszIk4bZz92+NXuPu01etc8JhR/13t0662M3zjcC3kgIBBJw04boLTxjnGxgYG2kHUftonugXTCKk83jOYVt/XPQhXNbo82HNauUGIKPg5/R7gqkWrzo6dgYVYvyQv4iJobx2ugtPtx5k6F5KtvPEdzQYKtOfnpeCicKBDmAHZAzSVXXqy5gjQVAZZb8arzjmwmQ24cU5kBe/eOlyFD0834Fd7zoLX7/EnOAD6/b5KvHi0HceblJ7GSUlJSE5Ohslk0oq3eL1e6HQ6mM1mbLh8Gl6//wosyE1mMSrql7pnVjUjU+0526llTwCAxWLRtizIsgyfz4cnbpyOzXcX4p6i3JAbTe6LpXBWtDOSjJiYYoXBYNCuYYCSNq6uRhsMBnx0rhXNHT6kJ5pw5WWpIcfoS/BkD1ca41e4K9rtXhnvHKvDHz6r0VLN1eKh6nEkSUKnT8bfTiiTOneH0eWFY2zsYaAdpCBb2Sfeo7q4WhBNOo+T1c093lfYVaW3tI9AOy3JjA8eWYWn75gbWRXnrrTxrd4rIUuGqPbbqivpG5b2vX+cRof5XYH28SonvP6efRqnpSciyWLCKTFReaAuKH28azX7aMIydMCCWxbkwGqK7Ibz1a4aAv3VGqD4FbyiPbPrmlbhgpb2ZrFYYDKZtDZLbrcbRqNRa/UFgKvZFJbgvY4zula0LzS54RcSEhISYLFYYLVatVoAfr8fXq8XJqMBV142AXkTEkICat58UvDES/cgqPvqok6n03ppCyHgdru1/dk6nQ6flSv3gLfMc0DfdcyBxhYne8aHcPtpd/oC+M5fSrH5w3L4ZKFlUARPUPv9frxf2gCXR0beBCuWT03r97OD08b5O3bsYKAdpM+V6bTp8BsSkSB50F7Zs/3Spff1nTqeNyEhsiJobbXAqe0AgFfllbhmpgM5KZEVQTtW2YojFa0w6iXcuYj9kEe7KWkJsFuNsJkNqGrp7PG8Tidhfm4KSgNd46i2qyBaUNr4Cy1daeMRTsqUVDu1sXIHx8q4FNx6SU3nrXSFbiGwWCwAlJtKv9+PJo+E7Wc70drp44oOhS34ZjXTZsI1+am4Z1Em/AFljNlsNq0Imt/vh8fjgSxCVxXVG02/3889iwRg4FVtSZLw1vEGPPl+JYor2rXgx+fzaem8Op0O370hH1u+tBD3LskNO7Dh1oXxIdx92g6bGSlWIwICuOj0aRM7Pp9Py9wRQuDPh5XijncvzoNugIxV9mcfmxhoB5nVFTCX1bvg9gX9D6TTI5CpFERLaTkW+hyAgq73na13weMPfU6Odq/r4VcAIeMI8nFG5GLjsgiC9C7qavb1s7PC6vNNI0uSJOz89kp89r3VfRYxW5DXS0G06kNA83n4dRa855uPgiwb5uXaI/rsrcXKavaaWZmYkMgbhfFKvYFQV7SrOwT8IrQPqCzL8HqVquJ7Knz4yc4L+Leth7SbDlYbp4EEb1PQ6XR47s5ZeGjlJNgTTNqKoMlk0oruHa5oxa2/OYL/9+FFbUJIHWPcF0uq/gIgNYg+Wt2O3WVOnKhTemarvbOD981KkoTZOTZk25WJxYHSxoMne7jSGP/C2actSRIKspQM1nNNl7YoBAIB7VpV3tyJfRdaIUnAnYsHXuBgxtjYxEA7iMNmRmqCMgN1utYV8pwxTymINhtlOFMX+lyO3YJkiwH+gOjx3L/+YT+++uJnOFXb92p3D0JoaeN/9K3qKoLWR5/vPrR7/PjLoSoAiCpIp5GRlmTu92ZRKYjW9fNUU8e7VrP3GorQCUvEqd8ev4w/H6oEoFTKpPFLvYHItJmQbNEjIICadmj9s9Xn3W43dHo9PjivZF58flEuV7MpbMEr2gBCghiTyYSEhARtxaejowNvH29EY7sPFS1uAJduNIMLWnElkfoLgNRgeXpX5fGyJiXo8fmU1UZ10scv6XsE6iyCRsHC3add0DVhfb5ZCbR9Pp82iSjLslbZ/srp6Zg4QMZqcEV7BtpjCwPtIJIk9Zk+LmmVx8t6PidJeObOedhy33JMS7+0B7uypRN/L6nF+yW1MERSxKz8U6DxNNySGe/Iy7CuKA8GfWQ/qrePVMHl8WNKWgIun9b/vg8aO+bnpeBkoCsYbj4PeNq0QPtl12IY9RJuXzgxomO+d7wWLR0+ZNstuDo/sgkdii8hRaq60scrXAIGg0Hrbaz+KW0KoK7dD5vFgLWFDs62U0SCg21JkuB0yzjTqKwuqnUBPB4PXG4v3j+l1Ea5bZ7Sz1gdY2qAE05/Y4p/wZk0ve3T1ul0yM9QAppzzR4t0FZbzR2v6cCqZ/fiqXfPQJKksAIbtYYAwEnG8SLcfdqFOUpm4dkmtzZO1PZxQghsWjoRT946C/ddPW3Azwz+/crJnLGFd0TdPHZjIYwGCZd1L1rWVRBtlnQBf6tqBhC68ve5uT0rPL9aXI6AAC6flhZhEbTfAwDe8i1Dh5SAdRG2aQKAG+dmw+sPIMnC/ynHEp8cwAN/PIDDFS147+GVsCeE/uLOsJlhTclEfacdGVIrcOgVoOUiPDordgUWYO3crIhTv9MSTbh8WhqWTEmNuKo9xZfggmgFWTZ8dtGJyg4JsizD41F6ZavBzZ5yZZb+1vk50EsCPjBtnMKnVhMXQuBkbTvu/u0BpFgN2HH/IpjNZuh0OnR0dGD3mRa4vDJyU60ompSsvZctvag36r5+NRVcpfXSTlMC7VqXH85OL6zWS2njfy2tR4dPRrvHD0mStEmg/q5pwZM9vPaND+qYkGVZa3HZG3Xh7kyDW8uYMJvN2thKs1nxhRUTwvpMZoyNXQy0u5nb197W1KnwGmyw+NvQVnEUwLx+j+OXA1oV5w2RpG572oBjygrlVnkVVs10DJhS0ptkixGbLp8S8ftoZBn1OpTWtKHW6cGRyhZc1csK84K8FJSW5iFD3wp8+H8AADsDi+CGOapJmRXT07FierqWxknjl7r/VQiB9YtzsDAtAFNHA3Q6HQKBAIQQ8Hg8cMsSPqlQ0njvWpzLFR2KWPAK9JQ0K3QS0NLpR2OHHykpErxeL7xeL94paQQA3D4/G7quG1xJkrSUX7aSo2B6vV4LtIOpxdBSE83ITDKi1uVDWZMHGSlKJWehM+K90iYAwO3zs7TfhwNd09R2Tbz2jS9qoN1f+viMTJt2XWvz65CVqLQsjLR4ozohqX4ujS3MtQqXTgevYy4AwFp/pEdQ0umVsW1/BX767kkAwAcn61Hd6kZqghHXz84M/3OOvwH42nEeOfhMzMTGSCqVU1zQ+mlfbOnzea0gmkupWPln71Lk2C24cnp61J/LzAcCLv0ivywjCfNybEgw6UNS5Px+P/ZV++CRBaY7kjA/1860cYpYcPql2aDD5AnKhPLJWhdkWUZnZyeqWz347KJS3+TWuQ4Al8aYGuBwNZuChVN5fHpX+vj5Fp/22AdnW9DulZGbYsHiSXbtHq+/a5rf7+dkzzil/rz7C7QtRj3+558X4W9fL0J2itK20Gg0orXThy+8dAhb91ciEEbBZNYAGNsYaPfixY/P45HXDqPO6Q553DK5CABwme806to8Pd737386jM27zqCuza1V/L5rcS7MhghmoLqKoG3xXY2sZCtWzYxsz2yH1497nt+Llz+9CJ/c994RGr3UftqHK1r6fF4riAagU7Lig8B83FWUF1HqdyAg8LuPzqGuzT3wi2ncCAmAulJ4hVD2aau/8BvcAgadhLsW52o3GuwfS5FQAxx1L2x+RgIA4HRdu9Y+7m+lTRAAlk+bgOxkJaA2GAwhhYG4kkjBgq9ffe3TvizNCqNOQrtPCXIkScI7Jcpq9m3zMqHrCmbCTRtnADT+BHdO6G+f9hXT0zEx1aoVQQOAd47V4UC5E3/85OKALb0AVhsf6xho9+KPn17An/ZX4FhVa8jjhlylINpc3bkeBdGsJr3WkmlXaR12nawDANwTyYp0/Umg/FPI0GGbfBXWLYmiCNrhanxS1oTn95yFnhf+MUlb0S5v6TWde+5EO07j0rh6178QHphwdxjtIYJ9dLYBT7x1Ajf+7EP4OSlDXYJvID6+2IGXT/pxqlGp0KveuH65KAMfPboSG5ZO4k0ARU0NtoUQKMhU6picqu8AoKwUrS7MwKblk3Dv0jzt9Tqdjv1kqV99rTaq4+cLS7Lw7n2z8U8L0xEIBFDj8mN/eRskXCq4F3yc3gRXvOdkz/gTPAnTX5svdauL+h6ld7ZSbXxdUXgtvcKpFUCjFwPtXhRkqZXHu7Xk6iqIVihdwMnKxh7vUwsfVLa48eRtc7Bx2aSeRdX601UEbae8AA1SKtZHsd/2j10r6fcsnRTWTBmNPrNzkmHQSWhweVHZ0tnjeatJDymjALJQfr7vyMtxxfQ05E1IiOhz1N7Zn5ubHfGEDsWv4BWhXWdbseO8FyWNSu9sv9+vVSDPTElU2hryZpOiFHzjOLMr0D7T0KkFSIXZdjx562ysKVC2xBgMBhZBowH1lT6uVqe3GnUw6nXaf797SllUWT41ReudDfQfaLPiPYXT5quh3Yv/t+cCfvGPKphMJpTUuFBS64JJr8NtCwbuEMNq42Mfrw696KvFF1Imw22wwyTJcF483ON9s7reV97UgU3LJ+Opz88N/0NlH3B4CwDgVXkVVs3IiLgI2vGqVhwub4FRr6R00thkMeq1MXiovKXX1xROysR/ybfhLXk5PggswLoI+1+3dHjx3nFlVjWaCR2KX2o6LwBtlbHGrYPFYoFfltHQKZCcrIxP9SZAXSkiikRwlfsZmUpG2IUmN9o7Pdq2BZ1Op40zvV6vBTjcqkB96SsAUseTJEnQ6XQwGAzQ6XS4fZ4DD1w9Gf+0ZKKWRdbfvuvgyR5OMI5f4ezT9skC//3hBWzZX432Tjf+fFipq7NmViZSB+gQw9Zx8YF3Rr0oyFaazJfWdFvRliR0pCvBs6mmZ6CtNqfvEaCH49S7QHs9GpCCXYEF2BBFEbQt+5QVyrWzspCeZI78HGjUWD5tAhZNSoGpj5XmhXkpeNa/Dt/wfRMJViuun50V0fH/fLASXjmAWdnJmDOxj0r7NG6pN6ozu65p5W1Kv9nDtR58/a/1ePTNMwDYcoQGJzhQdiSZcG9RNh67fjq8Qo8n/3oG+8udWuqk+noWQaOB9LVPW51E1Ov1eGFfLb74Sin2nG3GpLQk/OtVk3F1fpr22v5Ws9Uq0CyCNr6Fs087x26BzWyAPyBQUt2Gt48p20rvDiNtPHiccVJx7OIVohfqynRZvQtunwyL8dIAN01aDNT8A1ntJfD45ZBCZ+oqZGlNG1o6vEhJiOBGoCtt/E/+K5GWnIhrCxwRnXOH148/H6wEAGyMpJ0YjUrfvWlWv8+rBdMA4PYFOSFjdCBCCGz9rAIAV7Opd2qLnBkOZZWxyhWAq9Oj9c7OtFtCbmJ5s0nRUAMftX3cI9dNhcFgwBuHavD64RocrHTibw+mArhUBI0BDoUjuP1ScJCi7pmtbvPgdIMbZxq9uKGXbJz+xldwSy+m845f4fTTliQJM7OS8NmFFjz/0UU43X5kJVt6bd3aXXAtChq7uKLdC4fNjNQEIwICOF3rCnkucYpSeXyOVNbjuWy7RUv37q0qeZ+c1cDp9wAAr8krsb4oiiJoR6rR5vFjcloCLp+WNvAbaEyb7khCWqIJkoSIe2cfq3SipNoJk0GH2xbkDNEZ0limztQ7koywmXUICKCk3o3iKuW6tq4oj3sUKSbU8aP2aRdC4M9HlPTKuxbnhUzmMMChcA1UEG16mnKv9vzHFdhRUo9A19hTx1VfK4jBRSGZyUPh7NMu7Kr71NThw1XT07BuycAdYpg2Hj84TdILSZJQmJ2MvWWNON/Yjrm5l1JrpYlK5fEZUgXeqqwPSbuVJAlb7luONrcfMzJt4X/g4VcAEcBngRkow8SIAycAmJKWiGtmZmD5tDQWQYsj7R7lQptoDv1fVa+T8OKXl6K5w4vZOZGlfpfUKEH29bOzIsu6oHFDvXmQJAn5GQk4UOHCH4844ZWB6RmJmDvRjs5OpVAfZ9tpMNRAW5ZlQGfAu8dqcaDcCZ0EfH5BDgKBS+3jGOBQuAbap622kwOAX/7jItYUXlph7K/wVPAqIycYSZ0A7C/QLshRAm2b2YAXvlgUVhq4GmQzbXzs4x1SH35693zYrcYeAQ6SJ8JlSEWSvxnNZQeBpdNDno608jOE0Hpnb5VXYeWMDOSmRngMAEunTsDSqUt7bQdFY9Njrx/B1uJy/PD2ub1uB4h2b/W6ojysnZWJdm/fvxhofAtO583PSMSBChdONSm/+O8uymXaOMVM8E3kmYZOPPbmKQDAldPTkZFkhNst9yiIxgCHBhK8fzY4fVzrpZ1+qdjs2sJ0rZ+7JEl9TuSwCBp1132fdm/XJnVb6cm69pB2X/3hanb84G+rPuSkWHsG2QAgSXBOmAMA0FUfHPwHXdwLNJ1FByx4R14eVRG00NPjana8mJBoQkAAh8qbY37slARTxFXtaXxRbxi+duVkPLNGqRmhl4DPL8pl0EMxEzx+goOfW+bn9FptnEXQKBzBK4HBq41qoJ1iNWB+ThIykky4e2F2SJDU1wpicE9jTjASEF4/7ZldGa6TJiSg0zfwAkdw2jjH2djHO6Qo6LvSxye0Hh/8CvIBpQjaW/7lSLLZcV2ERdA6vTJ+/v5pVPXSb5nGtgV5ShGgw+WtMTtmeVNHzI5F8U29eXDYzDhSp/zSv/KyCXDYLLwJoJhRsyd0Oh1Megn3Xz0Ft8zPwS3zs0NuXBngUKR626etjje9Xo/f3jsX2x9chrSgLi3hpI1zlZGCDbRPO9FswBcunwybxQhjGPWXgttmMm187ONvrD4IIfD9t0/gWGUrfrFhEbLsFu251OnLgIPAzMBZ1LV5kJls6edI/XA7gRN/BqCkja9fEk0RtCo89/4p/PlQJXZ+eyVXtOPI/DwlNfxUXRtcHj+SesuwiMCFxnas/MkHWDw5Fa98bTlMBs6zUd/U1R1JkvD1ldMwM9uO6TlpLAZEMRe8T/vBVVORkJAAv98PH5Txp443rmZTJPrbpy1JEiQImPTKPZO6aNLXRA6ve9SXcPZpP3nbnLCPx2rj8YV32n2QJAn/ON2A4vPNPfpim/KUFe18qQIny2ui/5DjrwO+DpwNZOMg8rGuKPIiaK/suwhA2TfJIDu+OGxKFXshgCMVLYM+3mtdLb0SzQYG2TSg4Jn0CfYk3Fk0CSvyHSHpvLzmUCwEVx5X+9GqN63q3lmAAQ5Fpq8+x2oGhfpYcNp4X8GNWvGeRdCou+71AAYj+Bi83sUHXi36oRYwKKkJDbSRnI0WQzr0kkDjmf3Rf0BX2vhWeRWuzndEXEittMaJAxdbYNBJuGtxbvTnQaPWgq5+2YNNH5cDAn/arwTa64o4VmhgaoolAJjNZiQlJUGSJKZPUsypgY/aJzt4j2LwTScndigSfe2fDZ7YAaAVQetr8pBF0Kg/fdUDiEZw2jgndOIDf4r9KMhWChiUVLf1eK7ZPhsAICoPRHfwuhKg8jP4ocPr8tVRFUF75VNlNXvNrEw4bFGmr9OopqaPD7Yg2p5T9ahxupGaYMSaWZmxODUaB9Rf9OrNQ/CKI9PaKFbUAEddvfb7/VpfbRUDHIpGfwXRgle5gb7HWHDww+se9aavvu2R4oRO/GGg3Q9tRbtb6jgAiOwFAIDk5mPRHbyrpddOeSEkmwPXFUZeBO31g5UAMOhK5TR6LZ+Whs8vnIjrZ2cN6jivflYOALh94USYDSyuQeFRb1LVG9LgvWNcXaRYCt6nrabpqiuNLApE0eotAFIDbUmS4Pf7w04bZ/BDfYnFinZwHQBO6MQP/iT7UZilBNpl9S64fTIsxku/6FOmLwWOAVO8p+Dxy5EFL34vcPgVAF1F0IrywqpEGOydo9Voc/uRN8GKK6enR/ReGjvm5abgufULBnWMRpcH75fUAgDWL4m8DgCNX91vHlhtnIaKuqodnDWhrmizCBpFq68+xzqdDlarNaSlV2+Th7Iss0YADaivvu2RYNvM+MSfZD8yk81ITTAiIIDTta6Q51KnLwUATEM1zpZXR3bgU9uBjkbUiRTsFguiCn6a271IMOlxz5JJ0Om4skR9e/NwFXyywLxcOwq6Jo+IwhF886Cm8wIMtCn2uqfzqiuNbOlFgzHQPm1VX2OMWTwUjljs0+ZEdnziT7MfkiShICsZ5xra0dThDX0uyYF6vQMZch3qThVj1tQICkwdVIqgbZOvwor8rIiLoAHA166ehg3LJg2+jzeNenJA4EydCx6/jHm5KRG//95lk5GVbIHFxNRLioyathsIBODxeADwhpOGhhr4eL1ebVXIYDCwCBoNml6vhyzLPdLHg/UW3AQXQWNWBQ3EYDD0GGfhYvu4+MVAewC/+/KSPtPC622zkNFSB1/5fgCfD++AziqIM+9DAvCqvAr/a2n0qbyD7atMY8O2/RV4dNsRLJ82AVvuuzzi95sMOtw4N3sIzozGg+5tlzjbTkMheB+23+/XJpF500mD1Vuf4+BAu69UXTXIZo0ACsdgVrTZNjN+MXV8AP3tvfZnzgcAJDYeDf+Ah16GJALYF5gJV9IUXFcYWQVot0/GofIWrmSPI/O7WnwdrWiFHODPnYZX9xtMBto0VNSx5vV6YTAY2LOYYqK3ftqRpI1zsofCMZh+2hxr8Yu/wQbBNnUJACC3szS8wDcQ0KqNvyqvwrqi3MiLoB2pxu3/9RHu+/0g+nfTmDLdkYREkx7tXhln6lwDv6FLh9ePG362Bz9//zTcvsG1nKDxKzjQZto4DSWDwQCTyQS9Xq+ljRMNVm/7tNX9/0DvgTaLoFGkot2nzYyx+MZAewBCCHz5d8VY8qP3Ud3aGfJc9iwljXcSatBQXzvwwS5+DDSfg0tY8I68DPcsiaJ39j6ld/aCrlVOin96nYS5uZH3037nSDVKa9rw+sEKmA38X52iE7zywxtOGkp6vR4mkwkWi4U9iymmeguAEhISkJiY2GvWRHBLL04uUrii6afNgnvxjXffA5AkCeVNHahv86C0ui3kOUtyOqokpb9xZcknAx/sgFIE7S35chTl50ZcBO1UbRs+u9AMvU7C3YsjKL5GY56aPn6ovDXs96i9s9cV5fHiTVGTJAkmkwkGg4H7FGlIBY8vTupQLPXXT7s7tcsCwHFIkYlmRZvVxuMbA+0wFGYrLZFOVDt7PFeTVAgAcF8YIJXb3Qpx4i8AlLTxjUujX81eXeiAI9kS8ftp7FqoBdotYb3+bL0LxeeboZOAOxdxUoYGx2w2w2q1csKGhpTaykun0zHAoZjqbZ92X1gEjaKljpdw92kHb1FgoB2fGGiHoSDbBgAorWnr8Zw7Yx4AwFx/uP+DHNsGyd+JU4GJKE+YjdWzIi+Ctm1/BQBgQxRBOo1t6or2yRonOrz+/l+MS6vZq2Y6kGXnpAwRjQ1WqxWJiYmc1KGYimT/LFt60WBEkj4evJrNa1584vRJGNQV7ZJeVrStk4uAMiDbVdL/QbrSxl+VV+HuFXkRF0H769FqON1+TEyx4ur8jIjeS2Nftt2K79xYgJlZNuh1/V+MfXIA2/ZXAlDSxomIiMY7tZ+23+/vM2PC7/dzhZEGRa/Xw+/3hxVos9p4/ONVJAyzugLtsnoX3D4ZFuOlVKLswmXALiBL1MHjrIM52dHzALXHgaoD8Ak93pCvxBtRFEHbcUIptrZhaR50AwRaFJ/+deVlYb3ug5P1aHB5kJZowrUFvYxHIiKicSacFe3gwIcrjBSNcDMnZFnWOhZxi0L8Yup4GBw2M1ITjAgI4HRtaHulzAwHziMbAFB9oo+CaF0tvf4eWIRZ+ZdhUlpkRdAAYPPGRfifLxZh3RKuUFL/Jk1IwN2Lc3Hv8skwsdo4ERFRyP7Z3vZpBwIBFkGjQQt3nzarjY8PXNEOgyRJWDY1DU0dXvi6XZwlSUKFtQBTOqvhOlcMLL819M1+D8ThLZAAbJVXRb2/Wq+TcG1BZPu6Kb64fTL2nKrH6ToXHrhmep+vm5llw0/unj+MZ0ZERDS6qfu0ZVmGLMs9Ko6rgY9er+cKIw2KwWDQ0sf7Gkuc1BkfGGiH6ZebFvf5XHvaXKBiFwy1h3o+efJvkDqbUCNSccJahNWFkQXLPlkJ7CPd003xxycH8C9/2A8hgLuLcuGwscgZERFRuPrbp839shQrA+3T9vv9EEKEFOmj+MToLQaMeUoQntF2oueTB5UiaNvkq/D5oikRp/K+faQKK57Zif/5x7lBnyeNbTaLEfmOJADA4V76aQsh8Ox7J3G0olXb90NERESKvvbPBgc+LIJGg6WOM3XVujtWGx8/GGhHyOXx9whiMmcsRUBISJMbINpqLj3RWgFx5u8AlGrjG5ZGvr/6lU/LUd/mQbtn4JZOFP8WdLX5OtxLP+3PLjTj/+48g/XP70WHd+Bql0RERONJX/u0WQSNYkmv12vjqPukjhAiJNCm+MZAO0xyQODa//MB5jz+LmqdnpDnLsvNxBmRAwBoPVt86YlDr0CCwKeBAuRdNgeT0xIj+swzdW3Yd74Jep2Eu9mmiXCpn/ahXgLtrcVK7+yb5mYj0cyLNxERUbDe+mmzCBoNhb6yJ9Rq48yeGB8YaIdJr5Ng6Gqr1b2ftsWox3nzDABA85l9yoOBAERX2vhWf3RF0F7ZpwRO1xY4kGXnflwKWtGuaEEgcCmzos3twztHqgEA61mZnoiIqFfd03qDi6B1L5BGFK2+Au3gauMU/3hFiUBBltJPu6TG2eO51tS5AACp+qDywPkPIbVcQJuw4lPLVVgzK7IiaG6fjG0HKgAAG6OsVE7xZ2amDRajDm1uP8oa2rXH3z5SjU6fjGkZiVg8OXUEz5CIiGj0Cg6AhBAsgkZDord92sFp4xxv4wMD7QgUZNsAACXVbT2ek3IWAgBSW44DQmi9s9+SL8fNSy6LuAja9mM1aOnwYWKKFVfPyBjkmVO8MOh1mDvRDgA4UtGiPa6mja8vyuP+MiIioj4E79P2+XxM46Uh0ds+bfWfrDY+fvCqEoHCbGVFu7S654p2xvTF8B/UwS43AfWlECfe1Hpn/3xJ5CvSL++7CEBJA9brGDjRJf/75tlINOsxpWvP/6naNhwqb4FBJ+GORbkjfHZERESjV3A/bY9HqbnDImg0FILbfOn1emZPjENc0Y5AYVfqeFlDO9y+0D0XM/IcOC2UICew/T8gyW6UBvKQNG0ppqRHVgQNAB6/ZRb+afkkrGMRNOpmbq4d0zKSoOuagKls7oTDZsa1BQ5k2MwjfHZERESjW/fVRAY+NBSC08dZbXx84k86ApnJZqQmGNHc4cOZOhfmdKXwAkBWsgWf6C5DIS5CV7YTAPCavBIblk2O6rNm59jxw9vnxuS8Kb5dU+DAx9+5Fi2dvpE+FSIiolEvONA2GAwsgkZDIrgegBpk63Q6po2PI7yyRECSJNw0LxvrinJh7rbnWpIkNNlna//tFXp8YL4Ga2dlDfdp0jiwtfgiHnj5AI5VtgJQ9m6nJ3E1m4iIaCDBgQ5Xs2moBO/TVrcpcDV7fOFPO0L9rTIHshcAStyD9wOLsXrZ7IiLoP3taDV2lNTiC5dP0XomE3X33vFa/L20DnpJwrPr5sOg55wZERFROCRJgsViQSAQYOBDQ0rdpy2E0pKVEzvjC+/OYyh1yiJ4hHLBflVehXuiaMv1u4/P4/UDlfjgZH2sT4/iiNpP+83DVbjyP3fB6WbaOBERUbiMRiPMZmaC0dAKzp7Q6XTcpjDOcBovCl5/AGfrXSjIsoVUqZyZm47v+b+MXKkevinXYGqERdDO1rvw6bkm6CRg3RJWj6a+LZiUov37pAkJSLZwhpSIiIhoNOE2hfGNgXaEfHIA8558F25fAJ88dh2y7BbtufzMJGwLrEJAAL9YNiXiY2/paul1bYED2XZrrE6Z4tC83BTt329bmDNyJ0JEREREvVL3aQshuE1hHOJPPEJGvQ55qQk4XedCSbUzJNC2GPV4ePUMnG9ox/WzIyuC5vbJ+NP+CgDAhihSzml8sVuN2LR8Ms41tOOOhcx+ICIiIhqNEhISAIBp4+MQA+0oFGYn43SdCyeqnbimwBHy3Devy4/qmO8er0Fzhw/ZdgtWzXQM/AYa935w+5yRPgUiIiIi6gcD7PGLP/koFGTbAAClNW0xO+YrXWnj65fkQa+TBng1ERERERERjVZc0Y5CYXYyAKCk2hmT4wkhcFV+Bqpb3VhXlBeTYxIREREREdHIYKAdhcIsJdAuq3fB7ZNhMeoHeEf/JEnCA9dMx/2rLgupYk5ERERERERjD1PHo5CZbEZqghEBAZyudcXsuAyyiYiIiIiIxj6uaEdBkiR86Yqp0OskpCWZBnWsvWcb0djuwdpZWTAZOO9BREREREQ01jHQjlK01cW7+79/P429ZY14ZO0MPHhtbI5JREREREREI4dLqCOorN6FvWWN0EnA5xexFzIREREREVE8YKAdpUBA4FxDO7Yfq4EQIqpjbC0uBwCsmunAxBRrLE+PiIiIiIiIRggD7Sh55QBWP7sb//qH/ah1eiJ+v8cv47X9FQCADUsnxfr0iIiIiIiIaIQw0I6SxajHtPREAEBJTeT9tN87Xoumdi8yk824ZmZGrE+PiIiIiIiIRggD7UEozFb6aZdURx5ov7LvIgBgfVEeDHr+GIiIiIiIiOIFI7xBKMi2AQBKq9siep/bJ8PrD0CSgHVL8obi1IiIiIiIiGiEsL3XIES7om0x6vGnr69ARXMHclMThuLUiIiIiIiIaIRwRXsQCrOUQLusoR1unxzx+xlkExERERERxR8G2oOQmWxGSoIRckDgTJ0rrPecrXehud07xGdGREREREREI4Wp44MgSRIeu7EANosReWGuTv/vvxxD8blmPLd+AW6alz3EZ0hERERERETDjYH2IK1fEn4P7PMN7fjoTCMkCZifZx/CsyIiIiIiIqKRwtTxYbSluBwAsHJGBvdnExERERERxakhD7SffvppSJKEhx9+WHtMCIEnnngCOTk5sFqtWLVqFY4fPz7UpzIkvP4Adp2sw6/3lEEI0e/r/rRfCbQ3LA1/FZyIiIiIiIjGliENtIuLi/H8889j3rx5IY//+Mc/xrPPPovNmzejuLgYWVlZWLNmDdraIutHPRoEhMBXX/wMP/prCWqdnj5ft+NELRpcXjhsZlxb4BjGMyQiIiIiIqLhNGSBtsvlwr333otf//rXSE1N1R4XQuBnP/sZvvvd7+KOO+7AnDlz8OKLL6KjowMvv/zyUJ3OkLEY9ZiWngig/37ar+y7CABYV5QHo54Z+0RERERERPFqyCK+Bx54ADfddBNWr14d8vi5c+dQU1ODtWvXao+ZzWasXLkSH3/8ca/H8ng8cDqdIX9Gk4JspZ92SU3v59Xo8mDfuSZIErB+Sd5wnhoRERERERENsyGpOr5lyxYcOHAAxcXFPZ6rqakBAGRmZoY8npmZiQsXLvR6vKeffhpPPvlk7E80RgqzbXjrMFBS3Xvqe1qSGR9951rsLWtE3gQWQSMiIiIiIopnMV/RLi8vx0MPPYQ//OEPsFgsfb5OkqSQ/xZC9HhM9dhjj6G1tVX7U15eHtNzHqzCLGVFu7Sf1PEMmxm3zs8ZrlMiIiIiIiKiERLzFe39+/ejrq4Oixcv1h6TZRl79uzB5s2bcfLkSQDKynZ2drb2mrq6uh6r3Cqz2Qyz2RzrU42Zwq7U8bKGdrh9MixGvfacxy/DbND39VYiIiIiIiKKMzFf0b7uuutw9OhRHDp0SPtTVFSEe++9F4cOHcK0adOQlZWFHTt2aO/xer3YvXs3VqxYEevTGRaZyWakJhghBwTO1LlCnvvqi59h/a/24nhV6widHREREREREQ2nmK9o22w2zJkzJ+SxxMREpKWlaY8//PDDeOqpp5Cfn4/8/Hw89dRTSEhIwMaNG2N9OsNCkiQ8t34B0pPMmJFp0x6/2NiBD083QJKAZItxBM+QiIiIiIiIhsuQFEMbyKOPPorOzk7cf//9aG5uxrJly/Dee+/BZrMN/OZRatXMnr2xtxQrLb2uys9gETQiIiIiIqJxQhJCiJE+iUg5nU7Y7Xa0trYiOTl5pE+nVz45gMuf3okGlwe//KdFuGFO9sBvIiIiIiIiolEpkjh0yPpojzcdXj9+99E5PP6XYxBC4P0TtWhweZCeZMZ1hb0XeSMiIiIiIqL4MyKp4/FIJ0n4wTslkAMCX181HS/vU9LG1xXlwqjnfAYREREREdF4wQgwRixGPaalJwIAdpyowYenGwAA9yyZNJKnRURERERERMOMK9oxVJidjNN1LjS2e/HzexbgRJUTk9JYBI2IiIiIiGg84Yp2DBVkK1XTy+rbcduCiXjsc4UjfEZEREREREQ03Bhox1BhtlJ5rqTaOcJnQkRERERERCOFgXYMFWYpgfbpOhfqnO4RPhsiIiIiIiIaCQy0Yygz2Yxp6YnQSUC7Vx7p0yEiIiIiIqIRwGJoMSRJErbctxwdXhlTuiqQExERERER0fjCQDvGHMmWkT4FIiIiIiIiGkFMHSciIiIiIiKKIQbaRERERERERDHEQJuIiIiIiIgohhhoExEREREREcUQA20iIiIiIiKiGGKgTURERERERBRDDLSJiIiIiIiIYoiBNhEREREREVEMMdAmIiIiIiIiiiEG2kREREREREQxxECbiIiIiIiIKIYYaBMRERERERHFEANtIiIiIiIiohhioE1EREREREQUQwy0iYiIiIiIiGKIgTYRERERERFRDDHQJiIiIiIiIoohBtpEREREREREMcRAm4iIiIiIiCiGGGgTERERERERxRADbSIiIiIiIqIYYqBNREREREREFEMMtImIiIiIiIhiiIE2ERERERERUQwZRvoEoiGEAAA4nc4RPhMiIiIiIiIaD9T4U41H+zMmA+22tjYAQF5e3gifCREREREREY0nbW1tsNvt/b5GEuGE46NMIBBAVVUVbDYbJEkK+31LlixBcXHxEJ5Z9HhukXM6ncjLy0N5eTmSk5NH+nRCjNa/M4DnFg2Otejw3CLHsRYdnlvkONaiw3OLHMdadHhukRuOsSaEQFtbG3JycqDT9b8Le0yuaOt0OuTm5kb8Pr1eP+r+B1fx3KKXnJw86s5vNP+d8dyix7EWGZ5b9DjWIsNzix7HWmR4btHjWIsMzy16Qz3WBlrJVo2rYmgPPPDASJ9Cn3hu8WU0/53x3OLLaP4747nFl9H8d8Zziy+j+e+M5xZfRvPfGc9t7BuTqeNEgJIeYrfb0draOqpn1Wjs41ij4cKxRsOFY42GC8caDZfRNtbG1Yo2xRez2YzHH38cZrN5pE+F4hzHGg0XjjUaLhxrNFw41mi4jLaxxhVtIiIiIiIiohjiijYRERERERFRDDHQJiIiIiIiIoohBtpEREREREREMcRAm4iIiIiIiCiGGGgTERERERERxRADbRoxTz/9NJYsWQKbzQaHw4Hbb78dJ0+eDHmNEAJPPPEEcnJyYLVasWrVKhw/fjzkNc8//zxWrVqF5ORkSJKElpaWHp81ZcoUSJIU8uc73/nOUH49GkWGc6wBwDvvvINly5bBarUiPT0dd9xxx1B9NRplhmusffDBBz2uaeqf4uLiof6aNAoM53Xt1KlTuO2225Ceno7k5GRcccUV2LVr11B+PRpFhnOsHThwAGvWrEFKSgrS0tJw3333weVyDeXXo1EkFmOtqakJ3/jGNzBz5kwkJCRg0qRJ+OY3v4nW1taQ4zQ3N2PTpk2w2+2w2+3YtGlTn/d10WKgTSNm9+7deOCBB/DJJ59gx44d8Pv9WLt2Ldrb27XX/PjHP8azzz6LzZs3o7i4GFlZWVizZg3a2tq013R0dOCGG27Af/zHf/T7ed///vdRXV2t/fne9743ZN+NRpfhHGvbtm3Dpk2b8KUvfQmHDx/GRx99hI0bNw7p96PRY7jG2ooVK0KuZ9XV1fjqV7+KKVOmoKioaMi/J4284byu3XTTTfD7/di5cyf279+PBQsW4Oabb0ZNTc2QfkcaHYZrrFVVVWH16tWYPn06Pv30U2zfvh3Hjx/HF7/4xaH+ijRKxGKsVVVVoaqqCj/96U9x9OhR/O53v8P27dvxla98JeSzNm7ciEOHDmH79u3Yvn07Dh06hE2bNsX2CwmiUaKurk4AELt37xZCCBEIBERWVpZ45plntNe43W5ht9vFL3/5yx7v37VrlwAgmpubezw3efJk8dxzzw3VqdMYM1RjzefziYkTJ4rf/OY3Q3r+NHYM5XUtmNfrFQ6HQ3z/+9+P6fnT2DFUY62+vl4AEHv27NEeczqdAoB4//33h+bL0Kg2VGPtV7/6lXA4HEKWZe2xgwcPCgDi9OnTQ/NlaFQb7FhTvfrqq8JkMgmfzyeEEOLEiRMCgPjkk0+01+zdu1cAEKWlpTE7f65o06ihpnRMmDABAHDu3DnU1NRg7dq12mvMZjNWrlyJjz/+OOLj/+d//ifS0tKwYMEC/OhHP4LX643NidOYM1Rj7cCBA6isrIROp8PChQuRnZ2NG2+8sUf6HI0fQ31dU7355ptoaGjgys84NlRjLS0tDYWFhXjppZfQ3t4Ov9+PX/3qV8jMzMTixYtj+yVoTBiqsebxeGAymaDTXQpPrFYrAOAf//hHLE6dxphYjbXW1lYkJyfDYDAAAPbu3Qu73Y5ly5Zpr1m+fDnsdvugfhd3x0CbRgUhBL71rW/hyiuvxJw5cwBAS0nLzMwMeW1mZmbE6WoPPfQQtmzZgl27duHBBx/Ez372M9x///2xOXkaU4ZyrJWVlQEAnnjiCXzve9/D22+/jdTUVKxcuRJNTU0x+gY0Vgz1dS3Yb3/7W1x//fXIy8uL/oRpzBrKsSZJEnbs2IGDBw/CZrPBYrHgueeew/bt25GSkhKz70Bjw1COtWuvvRY1NTX4yU9+Aq/Xi+bmZi3NvLq6OkbfgMaKWI21xsZG/OAHP8C//Mu/aI/V1NTA4XD0eK3D4YjplhhDzI5ENAgPPvggjhw50uuMpSRJIf8thOjx2ED+7d/+Tfv3efPmITU1FXfddZe2yk3jx1COtUAgAAD47ne/izvvvBMA8MILLyA3NxevvfZayEWe4t9QX9dUFRUVePfdd/Hqq69G9X4a+4ZyrAkhcP/998PhcODDDz+E1WrFb37zG9x8880oLi5Gdnb2oM+fxo6hHGuzZ8/Giy++iG9961t47LHHoNfr8c1vfhOZmZnQ6/WDPncaW2Ix1pxOJ2666SbMmjULjz/+eL/H6O840eKKNo24b3zjG3jzzTexa9cu5Obmao9nZWUBQI+Zpbq6uh4zWZFavnw5AODMmTODOg6NLUM91tQbzlmzZmmPmc1mTJs2DRcvXhzMqdMYM5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./usr/share/doc/python-statsmodels-doc/html/_sources/examples/notebooks/generated/gls.ipynb.txt
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Similarity: 0.9997807017543859% Differences: {"'cells'": "{16: {'outputs': {0: {'name': 'stderr', 'text': " "['/usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430: UserWarning: " '`kurtosistest` p-value may be inaccurate with fewer than 20 observations; only n=15 ' "observations were given.\\n', ' return hypotest_fun_in(*args, **kwds)\\n']}, 1: " "{'name': 'stdout', 'text': [' GLSAR Regression " "Results \\n', " " […]
    
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234 ············"cell_type":·"code",234 ············"cell_type":·"code",
235 ············"execution_count":·9,235 ············"execution_count":·9,
236 ············"metadata":·{236 ············"metadata":·{
237 ················"execution":·{}237 ················"execution":·{}
238 ············},238 ············},
239 ············"outputs":·[239 ············"outputs":·[
240 ················{240 ················{
 241 ····················"name":·"stderr",
 242 ····················"output_type":·"stream",
 243 ····················"text":·[
 244 ························"/usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430:·UserWarning:·`kurtosistest`·p-value·may·be·inaccurate·with·fewer·than·20·observations;·only·n=15·observations·were·given.\n",
 245 ························"··return·hypotest_fun_in(*args,·**kwds)\n"
 246 ····················]
 247 ················},
 248 ················{
241 ····················"name":·"stdout",249 ····················"name":·"stdout",
242 ····················"output_type":·"stream",250 ····················"output_type":·"stream",
243 ····················"text":·[251 ····················"text":·[
244 ························"···························GLSAR·Regression·Results···························\n",252 ························"···························GLSAR·Regression·Results···························\n",
245 ························"==============================================================================\n",253 ························"==============================================================================\n",
246 ························"Dep.·Variable:·················TOTEMP···R-squared:·······················0.996\n",254 ························"Dep.·Variable:·················TOTEMP···R-squared:·······················0.996\n",
247 ························"Model:··························GLSAR···Adj.·R-squared:··················0.992\n",255 ························"Model:··························GLSAR···Adj.·R-squared:··················0.992\n",
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270 ························"==============================================================================\n",278 ························"==============================================================================\n",
271 ························"\n",279 ························"\n",
272 ························"Notes:\n",280 ························"Notes:\n",
273 ························"[1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified.\n",281 ························"[1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified.\n",
274 ························"[2]·The·condition·number·is·large,·4.8e+09.·This·might·indicate·that·there·are\n",282 ························"[2]·The·condition·number·is·large,·4.8e+09.·This·might·indicate·that·there·are\n",
275 ························"strong·multicollinearity·or·other·numerical·problems.\n"283 ························"strong·multicollinearity·or·other·numerical·problems.\n"
276 ····················]284 ····················]
277 ················}, 
278 ················{ 
279 ····················"name":·"stderr", 
280 ····················"output_type":·"stream", 
281 ····················"text":·[ 
282 ························"/usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430:·UserWarning:·`kurtosistest`·p-value·may·be·inaccurate·with·fewer·than·20·observations;·only·n=15·observations·were·given.\n", 
283 ························"··return·hypotest_fun_in(*args,·**kwds)\n" 
284 ····················] 
285 ················}285 ················}
286 ············],286 ············],
287 ············"source":·[287 ············"source":·[
288 ················"glsar_model·=·sm.GLSAR(data.endog,·data.exog,·1)\n",288 ················"glsar_model·=·sm.GLSAR(data.endog,·data.exog,·1)\n",
289 ················"glsar_results·=·glsar_model.iterative_fit(1)\n",289 ················"glsar_results·=·glsar_model.iterative_fit(1)\n",
290 ················"print(glsar_results.summary())"290 ················"print(glsar_results.summary())"
291 ············]291 ············]
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72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span>75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span>
76 </pre></div>76 </pre></div>
77 </div>77 </div>
78 </div>78 </div>
79 <div·class="nbinput·nblast·docutils·container">79 <div·class="nbinput·docutils·container">
80 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:80 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:
81 </pre></div>81 </pre></div>
82 </div>82 </div>
83 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>83 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
84 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>84 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
  
85 <span·class="kn">import</span>·<span·class="nn">statsmodels.discrete.truncated_model</span>·<span·class="k">as</span>·<span·class="nn">smtc</span>85 <span·class="kn">import</span>·<span·class="nn">statsmodels.discrete.truncated_model</span>·<span·class="k">as</span>·<span·class="nn">smtc</span>
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98 ····<span·class="n">TruncatedLFNegativeBinomialP</span><span·class="p">,</span>98 ····<span·class="n">TruncatedLFNegativeBinomialP</span><span·class="p">,</span>
99 ····<span·class="n">_RCensoredPoisson</span><span·class="p">,</span>99 ····<span·class="n">_RCensoredPoisson</span><span·class="p">,</span>
100 ····<span·class="n">HurdleCountModel</span><span·class="p">,</span>100 ····<span·class="n">HurdleCountModel</span><span·class="p">,</span>
101 ····<span·class="p">)</span>101 ····<span·class="p">)</span>
102 </pre></div>102 </pre></div>
103 </div>103 </div>
104 </div>104 </div>
 105 <div·class="nboutput·nblast·docutils·container">
 106 <div·class="prompt·empty·docutils·container">
 107 </div>
 108 <div·class="output_area·stderr·docutils·container">
 109 <div·class="highlight"><pre>
 110 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 111 Traceback·(most·recent·call·last):
 112 ··File·&#34;/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py&#34;,·line·565,·in·_log_error
 113 ····f.result()
 114 ····~~~~~~~~^^
 115 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·302,·in·dispatch_control
 116 ····await·self.process_control(msg)
 117 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·308,·in·process_control
 118 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 119 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 120 ··File·&#34;/usr/lib/python3/dist-packages/jupyter_client/session.py&#34;,·line·994,·in·feed_identities
 121 ····raise·ValueError(msg)
 122 ValueError:·DELIM·not·in·msg_list
 123 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 124 Traceback·(most·recent·call·last):
 125 ··File·&#34;/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py&#34;,·line·565,·in·_log_error
 126 ····f.result()
 127 ····~~~~~~~~^^
 128 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·302,·in·dispatch_control
 129 ····await·self.process_control(msg)
 130 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·308,·in·process_control
 131 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 132 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 133 ··File·&#34;/usr/lib/python3/dist-packages/jupyter_client/session.py&#34;,·line·994,·in·feed_identities
 134 ····raise·ValueError(msg)
 135 ValueError:·DELIM·not·in·msg_list
 136 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 137 Traceback·(most·recent·call·last):
 138 ··File·&#34;/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py&#34;,·line·565,·in·_log_error
 139 ····f.result()
 140 ····~~~~~~~~^^
 141 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·302,·in·dispatch_control
 142 ····await·self.process_control(msg)
 143 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·308,·in·process_control
 144 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 145 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 146 ··File·&#34;/usr/lib/python3/dist-packages/jupyter_client/session.py&#34;,·line·994,·in·feed_identities
 147 ····raise·ValueError(msg)
 148 ValueError:·DELIM·not·in·msg_list
 149 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 150 Traceback·(most·recent·call·last):
 151 ··File·&#34;/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py&#34;,·line·565,·in·_log_error
 152 ····f.result()
 153 ····~~~~~~~~^^
 154 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·302,·in·dispatch_control
 155 ····await·self.process_control(msg)
 156 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·308,·in·process_control
 157 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 158 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 159 ··File·&#34;/usr/lib/python3/dist-packages/jupyter_client/session.py&#34;,·line·994,·in·feed_identities
 160 ····raise·ValueError(msg)
 161 ValueError:·DELIM·not·in·msg_list
 162 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 163 Traceback·(most·recent·call·last):
 164 ··File·&#34;/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py&#34;,·line·565,·in·_log_error
 165 ····f.result()
 166 ····~~~~~~~~^^
 167 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·302,·in·dispatch_control
 168 ····await·self.process_control(msg)
 169 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·308,·in·process_control
 170 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 171 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 172 ··File·&#34;/usr/lib/python3/dist-packages/jupyter_client/session.py&#34;,·line·994,·in·feed_identities
 173 ····raise·ValueError(msg)
 174 ValueError:·DELIM·not·in·msg_list
 175 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 176 Traceback·(most·recent·call·last):
 177 ··File·&#34;/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py&#34;,·line·565,·in·_log_error
 178 ····f.result()
 179 ····~~~~~~~~^^
 180 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·302,·in·dispatch_control
 181 ····await·self.process_control(msg)
 182 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·308,·in·process_control
 183 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 184 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 185 ··File·&#34;/usr/lib/python3/dist-packages/jupyter_client/session.py&#34;,·line·994,·in·feed_identities
 186 ····raise·ValueError(msg)
 187 ValueError:·DELIM·not·in·msg_list
 188 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 189 Traceback·(most·recent·call·last):
 190 ··File·&#34;/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py&#34;,·line·565,·in·_log_error
 191 ····f.result()
 192 ····~~~~~~~~^^
 193 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·302,·in·dispatch_control
 194 ····await·self.process_control(msg)
 195 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·308,·in·process_control
 196 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 197 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 198 ··File·&#34;/usr/lib/python3/dist-packages/jupyter_client/session.py&#34;,·line·994,·in·feed_identities
 199 ····raise·ValueError(msg)
 200 ValueError:·DELIM·not·in·msg_list
 201 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 202 Traceback·(most·recent·call·last):
 203 ··File·&#34;/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py&#34;,·line·565,·in·_log_error
 204 ····f.result()
 205 ····~~~~~~~~^^
 206 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·302,·in·dispatch_control
 207 ····await·self.process_control(msg)
 208 ··File·&#34;/usr/lib/python3/dist-packages/ipykernel/kernelbase.py&#34;,·line·308,·in·process_control
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Offset 53, 14 lines modifiedOffset 53, 558 lines modified
  
53 from·statsmodels.discrete.truncated_model·import·(53 from·statsmodels.discrete.truncated_model·import·(
54 ····TruncatedLFPoisson,54 ····TruncatedLFPoisson,
55 ····TruncatedLFNegativeBinomialP,55 ····TruncatedLFNegativeBinomialP,
56 ····_RCensoredPoisson,56 ····_RCensoredPoisson,
57 ····HurdleCountModel,57 ····HurdleCountModel,
58 ····)58 ····)
 59 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 60 Traceback·(most·recent·call·last):
 61 ··File·"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py",·line·565,
 62 in·_log_error
 63 ····f.result()
 64 ····~~~~~~~~^^
 65 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·302,·in
 66 dispatch_control
 67 ····await·self.process_control(msg)
 68 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·308,·in
 69 process_control
 70 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 71 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 72 ··File·"/usr/lib/python3/dist-packages/jupyter_client/session.py",·line·994,·in
 73 feed_identities
 74 ····raise·ValueError(msg)
 75 ValueError:·DELIM·not·in·msg_list
 76 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 77 Traceback·(most·recent·call·last):
 78 ··File·"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py",·line·565,
 79 in·_log_error
 80 ····f.result()
 81 ····~~~~~~~~^^
 82 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·302,·in
 83 dispatch_control
 84 ····await·self.process_control(msg)
 85 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·308,·in
 86 process_control
 87 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 88 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 89 ··File·"/usr/lib/python3/dist-packages/jupyter_client/session.py",·line·994,·in
 90 feed_identities
 91 ····raise·ValueError(msg)
 92 ValueError:·DELIM·not·in·msg_list
 93 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 94 Traceback·(most·recent·call·last):
 95 ··File·"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py",·line·565,
 96 in·_log_error
 97 ····f.result()
 98 ····~~~~~~~~^^
 99 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·302,·in
 100 dispatch_control
 101 ····await·self.process_control(msg)
 102 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·308,·in
 103 process_control
 104 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 105 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 106 ··File·"/usr/lib/python3/dist-packages/jupyter_client/session.py",·line·994,·in
 107 feed_identities
 108 ····raise·ValueError(msg)
 109 ValueError:·DELIM·not·in·msg_list
 110 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 111 Traceback·(most·recent·call·last):
 112 ··File·"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py",·line·565,
 113 in·_log_error
 114 ····f.result()
 115 ····~~~~~~~~^^
 116 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·302,·in
 117 dispatch_control
 118 ····await·self.process_control(msg)
 119 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·308,·in
 120 process_control
 121 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 122 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 123 ··File·"/usr/lib/python3/dist-packages/jupyter_client/session.py",·line·994,·in
 124 feed_identities
 125 ····raise·ValueError(msg)
 126 ValueError:·DELIM·not·in·msg_list
 127 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 128 Traceback·(most·recent·call·last):
 129 ··File·"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py",·line·565,
 130 in·_log_error
 131 ····f.result()
 132 ····~~~~~~~~^^
 133 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·302,·in
 134 dispatch_control
 135 ····await·self.process_control(msg)
 136 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·308,·in
 137 process_control
 138 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 139 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 140 ··File·"/usr/lib/python3/dist-packages/jupyter_client/session.py",·line·994,·in
 141 feed_identities
 142 ····raise·ValueError(msg)
 143 ValueError:·DELIM·not·in·msg_list
 144 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 145 Traceback·(most·recent·call·last):
 146 ··File·"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py",·line·565,
 147 in·_log_error
 148 ····f.result()
 149 ····~~~~~~~~^^
 150 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·302,·in
 151 dispatch_control
 152 ····await·self.process_control(msg)
 153 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·308,·in
 154 process_control
 155 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 156 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 157 ··File·"/usr/lib/python3/dist-packages/jupyter_client/session.py",·line·994,·in
 158 feed_identities
 159 ····raise·ValueError(msg)
 160 ValueError:·DELIM·not·in·msg_list
 161 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
 162 Traceback·(most·recent·call·last):
 163 ··File·"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py",·line·565,
 164 in·_log_error
 165 ····f.result()
 166 ····~~~~~~~~^^
 167 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·302,·in
 168 dispatch_control
 169 ····await·self.process_control(msg)
 170 ··File·"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py",·line·308,·in
 171 process_control
 172 ····idents,·msg·=·self.session.feed_identities(msg,·copy=False)
 173 ··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
 174 ··File·"/usr/lib/python3/dist-packages/jupyter_client/session.py",·line·994,·in
 175 feed_identities
 176 ····raise·ValueError(msg)
 177 ValueError:·DELIM·not·in·msg_list
 178 ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback
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./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/count_hurdle.ipynb.gz
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count_hurdle.ipynb
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Offset 38, 15 lines modifiedOffset 38, 564 lines modified
38 ········{38 ········{
39 ············"cell_type":·"code",39 ············"cell_type":·"code",
40 ············"execution_count":·1,40 ············"execution_count":·1,
41 ············"id":·"eed890e6",41 ············"id":·"eed890e6",
42 ············"metadata":·{42 ············"metadata":·{
43 ················"execution":·{}43 ················"execution":·{}
44 ············},44 ············},
45 ············"outputs":·[],45 ············"outputs":·[
 46 ················{
 47 ····················"name":·"stderr",
 48 ····················"output_type":·"stream",
 49 ····················"text":·[
 50 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 51 ························"Traceback·(most·recent·call·last):\n",
 52 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 53 ························"····f.result()\n",
 54 ························"····~~~~~~~~^^\n",
 55 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 56 ························"····await·self.process_control(msg)\n",
 57 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 58 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 59 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 60 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 61 ························"····raise·ValueError(msg)\n",
 62 ························"ValueError:·DELIM·not·in·msg_list\n"
 63 ····················]
 64 ················},
 65 ················{
 66 ····················"name":·"stderr",
 67 ····················"output_type":·"stream",
 68 ····················"text":·[
 69 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 70 ························"Traceback·(most·recent·call·last):\n",
 71 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 72 ························"····f.result()\n",
 73 ························"····~~~~~~~~^^\n",
 74 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 75 ························"····await·self.process_control(msg)\n",
 76 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 77 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 78 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 79 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 80 ························"····raise·ValueError(msg)\n",
 81 ························"ValueError:·DELIM·not·in·msg_list\n"
 82 ····················]
 83 ················},
 84 ················{
 85 ····················"name":·"stderr",
 86 ····················"output_type":·"stream",
 87 ····················"text":·[
 88 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 89 ························"Traceback·(most·recent·call·last):\n",
 90 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 91 ························"····f.result()\n",
 92 ························"····~~~~~~~~^^\n",
 93 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 94 ························"····await·self.process_control(msg)\n",
 95 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 96 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 97 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 98 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 99 ························"····raise·ValueError(msg)\n",
 100 ························"ValueError:·DELIM·not·in·msg_list\n"
 101 ····················]
 102 ················},
 103 ················{
 104 ····················"name":·"stderr",
 105 ····················"output_type":·"stream",
 106 ····················"text":·[
 107 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 108 ························"Traceback·(most·recent·call·last):\n",
 109 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 110 ························"····f.result()\n",
 111 ························"····~~~~~~~~^^\n",
 112 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 113 ························"····await·self.process_control(msg)\n",
 114 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 115 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 116 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 117 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 118 ························"····raise·ValueError(msg)\n",
 119 ························"ValueError:·DELIM·not·in·msg_list\n"
 120 ····················]
 121 ················},
 122 ················{
 123 ····················"name":·"stderr",
 124 ····················"output_type":·"stream",
 125 ····················"text":·[
 126 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 127 ························"Traceback·(most·recent·call·last):\n",
 128 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 129 ························"····f.result()\n",
 130 ························"····~~~~~~~~^^\n",
 131 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 132 ························"····await·self.process_control(msg)\n",
 133 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 134 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 135 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 136 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 137 ························"····raise·ValueError(msg)\n",
 138 ························"ValueError:·DELIM·not·in·msg_list\n",
 139 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 140 ························"Traceback·(most·recent·call·last):\n",
 141 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 142 ························"····f.result()\n",
 143 ························"····~~~~~~~~^^\n",
 144 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 145 ························"····await·self.process_control(msg)\n",
 146 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·308,·in·process_control\n",
 147 ························"····idents,·msg·=·self.session.feed_identities(msg,·copy=False)\n",
 148 ························"··················~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^\n",
 149 ························"··File·\"/usr/lib/python3/dist-packages/jupyter_client/session.py\",·line·994,·in·feed_identities\n",
 150 ························"····raise·ValueError(msg)\n",
 151 ························"ValueError:·DELIM·not·in·msg_list\n"
 152 ····················]
 153 ················},
 154 ················{
 155 ····················"name":·"stderr",
 156 ····················"output_type":·"stream",
 157 ····················"text":·[
 158 ························"ERROR:tornado.general:Uncaught·exception·in·ZMQStream·callback\n",
 159 ························"Traceback·(most·recent·call·last):\n",
 160 ························"··File·\"/usr/lib/python3/dist-packages/zmq/eventloop/zmqstream.py\",·line·565,·in·_log_error\n",
 161 ························"····f.result()\n",
 162 ························"····~~~~~~~~^^\n",
 163 ························"··File·\"/usr/lib/python3/dist-packages/ipykernel/kernelbase.py\",·line·302,·in·dispatch_control\n",
 164 ························"····await·self.process_control(msg)\n",
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59 ······<div·class="documentwrapper">59 ······<div·class="documentwrapper">
60 ········<div·class="bodywrapper">60 ········<div·class="bodywrapper">
61 ··········<div·class="body"·role="main">61 ··········<div·class="body"·role="main">
62 ············62 ············
63 ··<section·id="Deterministic-Terms-in-Time-Series-Models">63 ··<section·id="Deterministic-Terms-in-Time-Series-Models">
64 <h1>Deterministic·Terms·in·Time·Series·Models<a·class="headerlink"·href="#Deterministic-Terms-in-Time-Series-Models"·title="Link·to·this·heading">¶</a></h1>64 <h1>Deterministic·Terms·in·Time·Series·Models<a·class="headerlink"·href="#Deterministic-Terms-in-Time-Series-Models"·title="Link·to·this·heading">¶</a></h1>
65 <div·class="nbinput·nblast·docutils·container">65 <div·class="nbinput·nblast·docutils·container">
66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
67 </pre></div>67 </pre></div>
68 </div>68 </div>
69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
70 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>70 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
71 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>71 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
  
72 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;figure&quot;</span><span·class="p">,</span>·<span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">16</span><span·class="p">,</span>·<span·class="mi">9</span><span·class="p">))</span>72 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;figure&quot;</span><span·class="p">,</span>·<span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">16</span><span·class="p">,</span>·<span·class="mi">9</span><span·class="p">))</span>
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76 </div>76 </div>
77 </div>77 </div>
78 <section·id="Basic-Use">78 <section·id="Basic-Use">
79 <h2>Basic·Use<a·class="headerlink"·href="#Basic-Use"·title="Link·to·this·heading">¶</a></h2>79 <h2>Basic·Use<a·class="headerlink"·href="#Basic-Use"·title="Link·to·this·heading">¶</a></h2>
80 <p>Basic·configurations·can·be·directly·constructed·through·<code·class="docutils·literal·notranslate"><span·class="pre">DeterministicProcess</span></code>.·These·can·include·a·constant,·a·time·trend·of·any·order,·and·either·a·seasonal·or·a·Fourier·component.</p>80 <p>Basic·configurations·can·be·directly·constructed·through·<code·class="docutils·literal·notranslate"><span·class="pre">DeterministicProcess</span></code>.·These·can·include·a·constant,·a·time·trend·of·any·order,·and·either·a·seasonal·or·a·Fourier·component.</p>
81 <p>The·process·requires·an·index,·which·is·the·index·of·the·full-sample·(or·in-sample).</p>81 <p>The·process·requires·an·index,·which·is·the·index·of·the·full-sample·(or·in-sample).</p>
82 <p>First,·we·initialize·a·deterministic·process·with·a·constant,·a·linear·time·trend,·and·a·5-period·seasonal·term.·The·<code·class="docutils·literal·notranslate"><span·class="pre">in_sample</span></code>·method·returns·the·full·set·of·values·that·match·the·index.</p>82 <p>First,·we·initialize·a·deterministic·process·with·a·constant,·a·linear·time·trend,·and·a·5-period·seasonal·term.·The·<code·class="docutils·literal·notranslate"><span·class="pre">in_sample</span></code>·method·returns·the·full·set·of·values·that·match·the·index.</p>
83 <div·class="nbinput·docutils·container">83 <div·class="nbinput·nblast·docutils·container">
84 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:84 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
85 </pre></div>85 </pre></div>
86 </div>86 </div>
87 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.deterministic</span>·<span·class="kn">import</span>·<span·class="n">DeterministicProcess</span>87 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.deterministic</span>·<span·class="kn">import</span>·<span·class="n">DeterministicProcess</span>
  
88 <span·class="n">index</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">RangeIndex</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">100</span><span·class="p">)</span>88 <span·class="n">index</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">RangeIndex</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">100</span><span·class="p">)</span>
89 <span·class="n">det_proc</span>·<span·class="o">=</span>·<span·class="n">DeterministicProcess</span><span·class="p">(</span><span·class="n">index</span><span·class="p">,</span>·<span·class="n">constant</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="n">seasonal</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">period</span><span·class="o">=</span><span·class="mi">5</span><span·class="p">)</span>89 <span·class="n">det_proc</span>·<span·class="o">=</span>·<span·class="n">DeterministicProcess</span><span·class="p">(</span><span·class="n">index</span><span·class="p">,</span>·<span·class="n">constant</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="n">seasonal</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">period</span><span·class="o">=</span><span·class="mi">5</span><span·class="p">)</span>
90 <span·class="n">det_proc</span><span·class="o">.</span><span·class="n">in_sample</span><span·class="p">()</span>90 <span·class="n">det_proc</span><span·class="o">.</span><span·class="n">in_sample</span><span·class="p">()</span>
91 </pre></div>91 </pre></div>
92 </div>92 </div>
93 </div>93 </div>
94 <div·class="nboutput·nblast·docutils·container"> 
95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]: 
96 </pre></div> 
97 </div> 
98 <div·class="output_area·rendered_html·docutils·container"> 
99 <div> 
100 <style·scoped> 
101 ····.dataframe·tbody·tr·th:only-of-type·{ 
102 ········vertical-align:·middle; 
103 ····} 
  
104 ····.dataframe·tbody·tr·th·{ 
105 ········vertical-align:·top; 
106 ····} 
  
107 ····.dataframe·thead·th·{ 
108 ········text-align:·right; 
109 ····} 
110 </style> 
111 <table·border="1"·class="dataframe"> 
112 ··<thead> 
113 ····<tr·style="text-align:·right;"> 
114 ······<th></th> 
115 ······<th>const</th> 
116 ······<th>trend</th> 
117 ······<th>s(2,5)</th> 
118 ······<th>s(3,5)</th> 
119 ······<th>s(4,5)</th> 
120 ······<th>s(5,5)</th> 
121 ····</tr> 
122 ··</thead> 
123 ··<tbody> 
124 ····<tr> 
125 ······<th>0</th> 
126 ······<td>1.0</td> 
127 ······<td>1.0</td> 
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129 ······<td>0.0</td> 
130 ······<td>0.0</td> 
131 ······<td>0.0</td> 
132 ····</tr> 
133 ····<tr> 
134 ······<th>1</th> 
135 ······<td>1.0</td> 
136 ······<td>2.0</td> 
137 ······<td>1.0</td> 
138 ······<td>0.0</td> 
139 ······<td>0.0</td> 
140 ······<td>0.0</td> 
141 ····</tr> 
142 ····<tr> 
143 ······<th>2</th> 
144 ······<td>1.0</td> 
145 ······<td>3.0</td> 
146 ······<td>0.0</td> 
147 ······<td>1.0</td> 
148 ······<td>0.0</td> 
149 ······<td>0.0</td> 
150 ····</tr> 
151 ····<tr> 
152 ······<th>3</th> 
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154 ······<td>4.0</td> 
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157 ······<td>1.0</td> 
158 ······<td>0.0</td> 
159 ····</tr> 
160 ····<tr> 
161 ······<th>4</th> 
162 ······<td>1.0</td> 
163 ······<td>5.0</td> 
164 ······<td>0.0</td> 
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166 ······<td>0.0</td> 
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168 ····</tr> 
169 ····<tr> 
170 ······<th>...</th> 
171 ······<td>...</td> 
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173 ······<td>...</td> 
174 ······<td>...</td> 
175 ······<td>...</td> 
176 ······<td>...</td> 
177 ····</tr> 
178 ····<tr> 
179 ······<th>95</th> 
180 ······<td>1.0</td> 
181 ······<td>96.0</td> 
182 ······<td>0.0</td> 
183 ······<td>0.0</td> 
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Deterministic·Terms·in·Time·Series·Models8 ····*·Deterministic·Terms·in·Time·Series·Models
9 *\x8**\x8**\x8**\x8**\x8**\x8*·D\x8De\x8et\x8te\x8er\x8rm\x8mi\x8in\x8ni\x8is\x8st\x8ti\x8ic\x8c·T\x8Te\x8er\x8rm\x8ms\x8s·i\x8in\x8n·T\x8Ti\x8im\x8me\x8e·S\x8Se\x8er\x8ri\x8ie\x8es\x8s·M\x8Mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·D\x8De\x8et\x8te\x8er\x8rm\x8mi\x8in\x8ni\x8is\x8st\x8ti\x8ic\x8c·T\x8Te\x8er\x8rm\x8ms\x8s·i\x8in\x8n·T\x8Ti\x8im\x8me\x8e·S\x8Se\x8er\x8ri\x8ie\x8es\x8s·M\x8Mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 import·matplotlib.pyplot·as·plt11 import·matplotlib.pyplot·as·plt
12 import·numpy·as·np12 import·numpy·as·np
13 import·pandas·as·pd13 import·pandas·as·pd
  
14 plt.rc("figure",·figsize=(16,·9))14 plt.rc("figure",·figsize=(16,·9))
15 plt.rc("font",·size=16)15 plt.rc("font",·size=16)
16 *\x8**\x8**\x8**\x8**\x8*·B\x8Ba\x8as\x8si\x8ic\x8c·U\x8Us\x8se\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·B\x8Ba\x8as\x8si\x8ic\x8c·U\x8Us\x8se\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
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19 These·can·include·a·constant,·a·time·trend·of·any·order,·and·either·a·seasonal19 These·can·include·a·constant,·a·time·trend·of·any·order,·and·either·a·seasonal
20 or·a·Fourier·component.20 or·a·Fourier·component.
21 The·process·requires·an·index,·which·is·the·index·of·the·full-sample·(or·in-21 The·process·requires·an·index,·which·is·the·index·of·the·full-sample·(or·in-
22 sample).22 sample).
23 First,·we·initialize·a·deterministic·process·with·a·constant,·a·linear·time23 First,·we·initialize·a·deterministic·process·with·a·constant,·a·linear·time
24 trend,·and·a·5-period·seasonal·term.·The·in_sample·method·returns·the·full·set24 trend,·and·a·5-period·seasonal·term.·The·in_sample·method·returns·the·full·set
25 of·values·that·match·the·index.25 of·values·that·match·the·index.
26 [2]:26 [·]:
27 from·statsmodels.tsa.deterministic·import·DeterministicProcess27 from·statsmodels.tsa.deterministic·import·DeterministicProcess
  
28 index·=·pd.RangeIndex(0,·100)28 index·=·pd.RangeIndex(0,·100)
29 det_proc·=·DeterministicProcess(index,·constant=True,·order=1,·seasonal=True,29 det_proc·=·DeterministicProcess(index,·constant=True,·order=1,·seasonal=True,
30 period=5)30 period=5)
31 det_proc.in_sample()31 det_proc.in_sample()
32 [2]: 
33 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
34 |_\x8·_\x8·_\x8·_\x8|_\x8c\x8c_\x8o\x8o_\x8n\x8n_\x8s\x8s_\x8t\x8t_\x8|_\x8t\x8t_\x8r\x8r_\x8e\x8e_\x8n\x8n_\x8d\x8d_\x8|_\x8s\x8s_\x8(\x8(_\x82\x82_\x8,\x8,_\x85\x85_\x8)\x8)_\x8|_\x8s\x8s_\x8(\x8(_\x83\x83_\x8,\x8,_\x85\x85_\x8)\x8)_\x8|_\x8s\x8s_\x8(\x8(_\x84\x84_\x8,\x8,_\x85\x85_\x8)\x8)_\x8|_\x8s\x8s_\x8(\x8(_\x85\x85_\x8,\x8,_\x85\x85_\x8)\x8)| 
35 |_\x80\x80_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
36 |_\x81\x81_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
37 |_\x82\x82_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
38 |_\x83\x83_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x84_\x8._\x80_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
39 |_\x84\x84_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·| 
40 |_\x8.\x8._\x8.\x8._\x8.\x8._\x8|_\x8._\x8._\x8._\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8·_\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8·_\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8·_\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8·_\x8·_\x8·| 
41 |_\x89\x89_\x85\x85_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x89_\x86_\x8._\x80_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
42 |_\x89\x89_\x86\x86_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x89_\x87_\x8._\x80_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
43 |_\x89\x89_\x87\x87_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x89_\x88_\x8._\x80_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
44 |_\x89\x89_\x88\x88_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x89_\x89_\x8._\x80_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
45 |_\x89\x89_\x89\x89_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x80_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·| 
46 100·rows·×·6·columns 
47 The·out_of_sample·returns·the·next·steps·values·after·the·end·of·the·in-sample.32 The·out_of_sample·returns·the·next·steps·values·after·the·end·of·the·in-sample.
48 [3]:33 [·]:
49 det_proc.out_of_sample(15)34 det_proc.out_of_sample(15)
50 [3]: 
51 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
52 |_\x8·_\x8·_\x8·_\x8|_\x8c\x8c_\x8o\x8o_\x8n\x8n_\x8s\x8s_\x8t\x8t_\x8|_\x8t\x8t_\x8r\x8r_\x8e\x8e_\x8n\x8n_\x8d\x8d_\x8|_\x8s\x8s_\x8(\x8(_\x82\x82_\x8,\x8,_\x85\x85_\x8)\x8)_\x8|_\x8s\x8s_\x8(\x8(_\x83\x83_\x8,\x8,_\x85\x85_\x8)\x8)_\x8|_\x8s\x8s_\x8(\x8(_\x84\x84_\x8,\x8,_\x85\x85_\x8)\x8)_\x8|_\x8s\x8s_\x8(\x8(_\x85\x85_\x8,\x8,_\x85\x85_\x8)\x8)| 
53 |_\x81\x81_\x80\x80_\x80\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x81_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
54 |_\x81\x81_\x80\x80_\x81\x81_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x82_\x8._\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
55 |_\x81\x81_\x80\x80_\x82\x82_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x83_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
56 |_\x81\x81_\x80\x80_\x83\x83_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x84_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
57 |_\x81\x81_\x80\x80_\x84\x84_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x85_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·| 
58 |_\x81\x81_\x80\x80_\x85\x85_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x86_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
59 |_\x81\x81_\x80\x80_\x86\x86_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x87_\x8._\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
60 |_\x81\x81_\x80\x80_\x87\x87_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x88_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
61 |_\x81\x81_\x80\x80_\x88\x88_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x80_\x89_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
62 |_\x81\x81_\x80\x80_\x89\x89_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x81_\x80_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·| 
63 |_\x81\x81_\x81\x81_\x80\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x81_\x81_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
64 |_\x81\x81_\x81\x81_\x81\x81_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x81_\x82_\x8._\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
65 |_\x81\x81_\x81\x81_\x82\x82_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x81_\x83_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
66 |_\x81\x81_\x81\x81_\x83\x83_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x81_\x84_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
67 |_\x81\x81_\x81\x81_\x84\x84_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x81_\x85_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·| 
68 range(start,·stop)·can·also·be·used·to·produce·the·deterministic·terms·over·any35 range(start,·stop)·can·also·be·used·to·produce·the·deterministic·terms·over·any
69 range·including·in-·and·out-of-sample.36 range·including·in-·and·out-of-sample.
70 *\x8**\x8**\x8**\x8*·N\x8No\x8ot\x8te\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*37 *\x8**\x8**\x8**\x8*·N\x8No\x8ot\x8te\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*
71 ····*·When·the·index·is·a·pandas·DatetimeIndex·or·a·PeriodIndex,·then·start·and38 ····*·When·the·index·is·a·pandas·DatetimeIndex·or·a·PeriodIndex,·then·start·and
72 ······stop·can·be·date-like·(strings,·e.g.,·“2020-06-01”,·or·Timestamp)·or39 ······stop·can·be·date-like·(strings,·e.g.,·“2020-06-01”,·or·Timestamp)·or
73 ······integers.40 ······integers.
74 ····*·stop·is·always·included·in·the·range.·While·this·is·not·very·Pythonic,·it41 ····*·stop·is·always·included·in·the·range.·While·this·is·not·very·Pythonic,·it
75 ······is·needed·since·both·statsmodels·and·Pandas·include·stop·when·working42 ······is·needed·since·both·statsmodels·and·Pandas·include·stop·when·working
76 ······with·date-like·slices.43 ······with·date-like·slices.
77 [4]:44 [·]:
78 det_proc.range(190,·210)45 det_proc.range(190,·210)
79 [4]: 
80 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
81 |_\x8·_\x8·_\x8·_\x8|_\x8c\x8c_\x8o\x8o_\x8n\x8n_\x8s\x8s_\x8t\x8t_\x8|_\x8t\x8t_\x8r\x8r_\x8e\x8e_\x8n\x8n_\x8d\x8d_\x8|_\x8s\x8s_\x8(\x8(_\x82\x82_\x8,\x8,_\x85\x85_\x8)\x8)_\x8|_\x8s\x8s_\x8(\x8(_\x83\x83_\x8,\x8,_\x85\x85_\x8)\x8)_\x8|_\x8s\x8s_\x8(\x8(_\x84\x84_\x8,\x8,_\x85\x85_\x8)\x8)_\x8|_\x8s\x8s_\x8(\x8(_\x85\x85_\x8,\x8,_\x85\x85_\x8)\x8)| 
82 |_\x81\x81_\x89\x89_\x80\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x89_\x81_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
83 |_\x81\x81_\x89\x89_\x81\x81_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x89_\x82_\x8._\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
84 |_\x81\x81_\x89\x89_\x82\x82_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x89_\x83_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
85 |_\x81\x81_\x89\x89_\x83\x83_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x89_\x84_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
86 |_\x81\x81_\x89\x89_\x84\x84_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x89_\x85_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·| 
87 |_\x81\x81_\x89\x89_\x85\x85_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x89_\x86_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
88 |_\x81\x81_\x89\x89_\x86\x86_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x89_\x87_\x8._\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
89 |_\x81\x81_\x89\x89_\x87\x87_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x89_\x88_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
90 |_\x81\x81_\x89\x89_\x88\x88_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x89_\x89_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
91 |_\x81\x81_\x89\x89_\x89\x89_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x80_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·| 
92 |_\x82\x82_\x80\x80_\x80\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x81_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
93 |_\x82\x82_\x80\x80_\x81\x81_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x82_\x8._\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
94 |_\x82\x82_\x80\x80_\x82\x82_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x83_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
95 |_\x82\x82_\x80\x80_\x83\x83_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x84_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
96 |_\x82\x82_\x80\x80_\x84\x84_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x85_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·| 
97 |_\x82\x82_\x80\x80_\x85\x85_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x86_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
98 |_\x82\x82_\x80\x80_\x86\x86_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x87_\x8._\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
99 |_\x82\x82_\x80\x80_\x87\x87_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x88_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
100 |_\x82\x82_\x80\x80_\x88\x88_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x80_\x89_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
101 |_\x82\x82_\x80\x80_\x89\x89_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x81_\x80_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·| 
102 |_\x82\x82_\x81\x81_\x80\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x82_\x81_\x81_\x8._\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·| 
103 *\x8**\x8**\x8**\x8**\x8*·U\x8Us\x8si\x8in\x8ng\x8g·a\x8a·D\x8Da\x8at\x8te\x8e-\x8-l\x8li\x8ik\x8ke\x8e·I\x8In\x8nd\x8de\x8ex\x8x_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*46 *\x8**\x8**\x8**\x8**\x8*·U\x8Us\x8si\x8in\x8ng\x8g·a\x8a·D\x8Da\x8at\x8te\x8e-\x8-l\x8li\x8ik\x8ke\x8e·I\x8In\x8nd\x8de\x8ex\x8x_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
104 Next,·we·show·the·same·steps·using·a·PeriodIndex.47 Next,·we·show·the·same·steps·using·a·PeriodIndex.
105 [5]:48 [·]:
106 index·=·pd.period_range("2020-03-01",·freq="M",·periods=60)49 index·=·pd.period_range("2020-03-01",·freq="M",·periods=60)
107 det_proc·=·DeterministicProcess(index,·constant=True,·fourier=2)50 det_proc·=·DeterministicProcess(index,·constant=True,·fourier=2)
108 det_proc.in_sample().head(12)51 det_proc.in_sample().head(12)
109 [5]:52 [·]:
110 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
111 |_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8c\x8c_\x8o\x8o_\x8n\x8n_\x8s\x8s_\x8t\x8t_\x8|_\x8·_\x8·_\x8·_\x8·_\x8s\x8s_\x8i\x8i_\x8n\x8n_\x8(\x8(_\x81\x81_\x8,\x8,_\x81\x81_\x82\x82_\x8)\x8)_\x8|_\x8·_\x8·_\x8·_\x8·_\x8c\x8c_\x8o\x8o_\x8s\x8s_\x8(\x8(_\x81\x81_\x8,\x8,_\x81\x81_\x82\x82_\x8)\x8)_\x8|_\x8·_\x8·_\x8·_\x8·_\x8s\x8s_\x8i\x8i_\x8n\x8n_\x8(\x8(_\x82\x82_\x8,\x8,_\x81\x81_\x82\x82_\x8)\x8)_\x8|_\x8c\x8c_\x8o\x8o_\x8s\x8s_\x8(\x8(_\x82\x82_\x8,\x8,_\x81\x81_\x82\x82_\x8)\x8)| 
112 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x80\x80_\x83\x83_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8+_\x80_\x80_\x8·_\x8|_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8+_\x80_\x80_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8+_\x80_\x80_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
113 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x80\x80_\x84\x84_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x80_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
114 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x80\x80_\x85\x85_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x8-_\x80_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·| 
115 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x80\x80_\x86\x86_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8+_\x80_\x80_\x8·_\x8|_\x86_\x8._\x81_\x82_\x83_\x82_\x83_\x84_\x8e_\x8-_\x81_\x87_\x8·_\x8|_\x81_\x8._\x82_\x82_\x84_\x86_\x84_\x87_\x8e_\x8-_\x81_\x86_\x8·_\x8|_\x8-_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·| 
116 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x80\x80_\x87\x87_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x8-_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8-_\x80_\x81_\x8|_\x8-_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8|_\x8-_\x80_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·| 
117 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x80\x80_\x88\x88_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x8-_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8|_\x8-_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8|_\x80_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
118 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x80\x80_\x89\x89_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x81_\x8._\x82_\x82_\x84_\x86_\x84_\x87_\x8e_\x8-_\x81_\x86_\x8·_\x8|_\x8-_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8+_\x80_\x80_\x8|_\x8-_\x82_\x8._\x84_\x84_\x89_\x82_\x89_\x84_\x8e_\x8-_\x81_\x86_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
119 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x81\x81_\x80\x80_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x8-_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8-_\x80_\x81_\x8|_\x8-_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8|_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x80_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
120 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x81\x81_\x81\x81_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x8-_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8|_\x8-_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8-_\x80_\x81_\x8|_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x8-_\x80_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·| 
121 |_\x82\x82_\x80\x80_\x82\x82_\x80\x80_\x8-\x8-_\x81\x81_\x82\x82_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x8-_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8+_\x80_\x80_\x8|_\x8-_\x81_\x8._\x88_\x83_\x86_\x89_\x87_\x80_\x8e_\x8-_\x81_\x86_\x8|_\x83_\x8._\x86_\x87_\x83_\x89_\x84_\x80_\x8e_\x8-_\x81_\x86_\x8·_\x8|_\x8-_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·| 
122 |_\x82\x82_\x80\x80_\x82\x82_\x81\x81_\x8-\x8-_\x80\x80_\x81\x81_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x8-_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8|_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x8-_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8|_\x8-_\x80_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·| 
123 |_\x82\x82_\x80\x80_\x82\x82_\x81\x81_\x8-\x8-_\x80\x80_\x82\x82_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8|_\x8-_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8-_\x80_\x81_\x8|_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8·_\x8|_\x8-_\x88_\x8._\x86_\x86_\x80_\x82_\x85_\x84_\x8e_\x8-_\x80_\x81_\x8|_\x80_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
124 [6]: 
125 det_proc.out_of_sample(12)53 det_proc.out_of_sample(12)
126 [6]: 
127 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
128 |_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8c\x8c_\x8o\x8o_\x8n\x8n_\x8s\x8s_\x8t\x8t_\x8|_\x8·_\x8·_\x8·_\x8·_\x8s\x8s_\x8i\x8i_\x8n\x8n_\x8(\x8(_\x81\x81_\x8,\x8,_\x81\x81_\x82\x82_\x8)\x8)_\x8|_\x8·_\x8·_\x8·_\x8·_\x8c\x8c_\x8o\x8o_\x8s\x8s_\x8(\x8(_\x81\x81_\x8,\x8,_\x81\x81_\x82\x82_\x8)\x8)_\x8|_\x8·_\x8·_\x8·_\x8·_\x8s\x8s_\x8i\x8i_\x8n\x8n_\x8(\x8(_\x82\x82_\x8,\x8,_\x81\x81_\x82\x82_\x8)\x8)_\x8|_\x8c\x8c_\x8o\x8o_\x8s\x8s_\x8(\x8(_\x82\x82_\x8,\x8,_\x81\x81_\x82\x82_\x8)\x8)| 
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discrete_choice_example.ipynb
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262 ························"educ···············-0.0392······0.015·····-2.533······0.011······-0.070······-0.009\n",262 ························"educ···············-0.0392······0.015·····-2.533······0.011······-0.070······-0.009\n",
263 ························"occupation_husb·····0.0124······0.023······0.541······0.589······-0.033·······0.057\n",263 ························"occupation_husb·····0.0124······0.023······0.541······0.589······-0.033·······0.057\n",
264 ························"rate_marriage······-0.7161······0.031····-22.784······0.000······-0.778······-0.655\n",264 ························"rate_marriage······-0.7161······0.031····-22.784······0.000······-0.778······-0.655\n",
265 ························"age················-0.0605······0.010·····-5.885······0.000······-0.081······-0.040\n",265 ························"age················-0.0605······0.010·····-5.885······0.000······-0.081······-0.040\n",
266 ························"yrs_married·········0.1100······0.011·····10.054······0.000·······0.089·······0.131\n",266 ························"yrs_married·········0.1100······0.011·····10.054······0.000·······0.089·······0.131\n",
267 ························"children···········-0.0042······0.032·····-0.134······0.893······-0.066·······0.058\n",267 ························"children···········-0.0042······0.032·····-0.134······0.893······-0.066·······0.058\n",
268 ························"religious··········-0.3752······0.035····-10.792······0.000······-0.443······-0.307\n",268 ························"religious··········-0.3752······0.035····-10.792······0.000······-0.443······-0.307\n",
269 ························"==================================================================================="269 ························"===================================================================================\n"
270 ····················] 
271 ················}, 
272 ················{ 
273 ····················"name":·"stdout", 
274 ····················"output_type":·"stream", 
275 ····················"text":·[ 
276 ························"\n" 
277 ····················]270 ····················]
278 ················}271 ················}
279 ············],272 ············],
280 ············"source":·[273 ············"source":·[
281 ················"print(affair_mod.summary())"274 ················"print(affair_mod.summary())"
282 ············]275 ············]
283 ········},276 ········},
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58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Distributed-Estimation">61 ··<section·id="Distributed-Estimation">
62 <h1>Distributed·Estimation<a·class="headerlink"·href="#Distributed-Estimation"·title="Link·to·this·heading">¶</a></h1>62 <h1>Distributed·Estimation<a·class="headerlink"·href="#Distributed-Estimation"·title="Link·to·this·heading">¶</a></h1>
63 <p>This·notebook·goes·through·a·couple·of·examples·to·show·how·to·use·<code·class="docutils·literal·notranslate"><span·class="pre">distributed_estimation</span></code>.·We·import·the·<code·class="docutils·literal·notranslate"><span·class="pre">DistributedModel</span></code>·class·and·make·the·exog·and·endog·generators.</p>63 <p>This·notebook·goes·through·a·couple·of·examples·to·show·how·to·use·<code·class="docutils·literal·notranslate"><span·class="pre">distributed_estimation</span></code>.·We·import·the·<code·class="docutils·literal·notranslate"><span·class="pre">DistributedModel</span></code>·class·and·make·the·exog·and·endog·generators.</p>
64 <div·class="nbinput·nblast·docutils·container">64 <div·class="nbinput·nblast·docutils·container">
65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
66 </pre></div>66 </pre></div>
67 </div>67 </div>
68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
69 <span·class="kn">from</span>·<span·class="nn">scipy.stats.distributions</span>·<span·class="kn">import</span>·<span·class="n">norm</span>69 <span·class="kn">from</span>·<span·class="nn">scipy.stats.distributions</span>·<span·class="kn">import</span>·<span·class="n">norm</span>
70 <span·class="kn">from</span>·<span·class="nn">statsmodels.base.distributed_estimation</span>·<span·class="kn">import</span>·<span·class="n">DistributedModel</span>70 <span·class="kn">from</span>·<span·class="nn">statsmodels.base.distributed_estimation</span>·<span·class="kn">import</span>·<span·class="n">DistributedModel</span>
  
  
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95 ········<span·class="k">yield</span>·<span·class="n">endog</span><span·class="p">[</span><span·class="n">ii</span><span·class="p">:</span><span·class="n">jj</span><span·class="p">]</span>95 ········<span·class="k">yield</span>·<span·class="n">endog</span><span·class="p">[</span><span·class="n">ii</span><span·class="p">:</span><span·class="n">jj</span><span·class="p">]</span>
96 ········<span·class="n">ii</span>·<span·class="o">+=</span>·<span·class="nb">int</span><span·class="p">(</span><span·class="n">n_part</span><span·class="p">)</span>96 ········<span·class="n">ii</span>·<span·class="o">+=</span>·<span·class="nb">int</span><span·class="p">(</span><span·class="n">n_part</span><span·class="p">)</span>
97 </pre></div>97 </pre></div>
98 </div>98 </div>
99 </div>99 </div>
100 <p>Next·we·generate·some·random·data·to·serve·as·an·example.</p>100 <p>Next·we·generate·some·random·data·to·serve·as·an·example.</p>
101 <div·class="nbinput·nblast·docutils·container">101 <div·class="nbinput·nblast·docutils·container">
102 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:102 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
103 </pre></div>103 </pre></div>
104 </div>104 </div>
105 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">1000</span><span·class="p">,</span>·<span·class="mi">25</span><span·class="p">))</span>105 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">1000</span><span·class="p">,</span>·<span·class="mi">25</span><span·class="p">))</span>
106 <span·class="n">beta</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="mi">25</span><span·class="p">)</span>106 <span·class="n">beta</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="mi">25</span><span·class="p">)</span>
107 <span·class="n">beta</span>·<span·class="o">*=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">randint</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">2</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">25</span><span·class="p">)</span>107 <span·class="n">beta</span>·<span·class="o">*=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">randint</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">2</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">25</span><span·class="p">)</span>
108 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">norm</span><span·class="o">.</span><span·class="n">rvs</span><span·class="p">(</span><span·class="n">loc</span><span·class="o">=</span><span·class="n">X</span><span·class="o">.</span><span·class="n">dot</span><span·class="p">(</span><span·class="n">beta</span><span·class="p">))</span>108 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">norm</span><span·class="o">.</span><span·class="n">rvs</span><span·class="p">(</span><span·class="n">loc</span><span·class="o">=</span><span·class="n">X</span><span·class="o">.</span><span·class="n">dot</span><span·class="p">(</span><span·class="n">beta</span><span·class="p">))</span>
109 <span·class="n">m</span>·<span·class="o">=</span>·<span·class="mi">5</span>109 <span·class="n">m</span>·<span·class="o">=</span>·<span·class="mi">5</span>
110 </pre></div>110 </pre></div>
111 </div>111 </div>
112 </div>112 </div>
113 <p>This·is·the·most·basic·fit,·showing·all·of·the·defaults,·which·are·to·use·OLS·as·the·model·class,·and·the·debiasing·procedure.</p>113 <p>This·is·the·most·basic·fit,·showing·all·of·the·defaults,·which·are·to·use·OLS·as·the·model·class,·and·the·debiasing·procedure.</p>
114 <div·class="nbinput·nblast·docutils·container">114 <div·class="nbinput·nblast·docutils·container">
115 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:115 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
116 </pre></div>116 </pre></div>
117 </div>117 </div>
118 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">debiased_OLS_mod</span>·<span·class="o">=</span>·<span·class="n">DistributedModel</span><span·class="p">(</span><span·class="n">m</span><span·class="p">)</span>118 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">debiased_OLS_mod</span>·<span·class="o">=</span>·<span·class="n">DistributedModel</span><span·class="p">(</span><span·class="n">m</span><span·class="p">)</span>
119 <span·class="n">debiased_OLS_fit</span>·<span·class="o">=</span>·<span·class="n">debiased_OLS_mod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>119 <span·class="n">debiased_OLS_fit</span>·<span·class="o">=</span>·<span·class="n">debiased_OLS_mod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>
120 ····<span·class="nb">zip</span><span·class="p">(</span><span·class="n">_endog_gen</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">),</span>·<span·class="n">_exog_gen</span><span·class="p">(</span><span·class="n">X</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">)),</span>·<span·class="n">fit_kwds</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;alpha&quot;</span><span·class="p">:</span>·<span·class="mf">0.2</span><span·class="p">}</span>120 ····<span·class="nb">zip</span><span·class="p">(</span><span·class="n">_endog_gen</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">),</span>·<span·class="n">_exog_gen</span><span·class="p">(</span><span·class="n">X</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">)),</span>·<span·class="n">fit_kwds</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;alpha&quot;</span><span·class="p">:</span>·<span·class="mf">0.2</span><span·class="p">}</span>
121 <span·class="p">)</span>121 <span·class="p">)</span>
122 </pre></div>122 </pre></div>
123 </div>123 </div>
124 </div>124 </div>
125 <p>Then·we·run·through·a·slightly·more·complicated·example·which·uses·the·GLM·model·class.</p>125 <p>Then·we·run·through·a·slightly·more·complicated·example·which·uses·the·GLM·model·class.</p>
126 <div·class="nbinput·nblast·docutils·container">126 <div·class="nbinput·nblast·docutils·container">
127 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:127 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
128 </pre></div>128 </pre></div>
129 </div>129 </div>
130 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.genmod.generalized_linear_model</span>·<span·class="kn">import</span>·<span·class="n">GLM</span>130 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.genmod.generalized_linear_model</span>·<span·class="kn">import</span>·<span·class="n">GLM</span>
131 <span·class="kn">from</span>·<span·class="nn">statsmodels.genmod.families</span>·<span·class="kn">import</span>·<span·class="n">Gaussian</span>131 <span·class="kn">from</span>·<span·class="nn">statsmodels.genmod.families</span>·<span·class="kn">import</span>·<span·class="n">Gaussian</span>
  
132 <span·class="n">debiased_GLM_mod</span>·<span·class="o">=</span>·<span·class="n">DistributedModel</span><span·class="p">(</span>132 <span·class="n">debiased_GLM_mod</span>·<span·class="o">=</span>·<span·class="n">DistributedModel</span><span·class="p">(</span>
133 ····<span·class="n">m</span><span·class="p">,</span>·<span·class="n">model_class</span><span·class="o">=</span><span·class="n">GLM</span><span·class="p">,</span>·<span·class="n">init_kwds</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;family&quot;</span><span·class="p">:</span>·<span·class="n">Gaussian</span><span·class="p">()}</span>133 ····<span·class="n">m</span><span·class="p">,</span>·<span·class="n">model_class</span><span·class="o">=</span><span·class="n">GLM</span><span·class="p">,</span>·<span·class="n">init_kwds</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;family&quot;</span><span·class="p">:</span>·<span·class="n">Gaussian</span><span·class="p">()}</span>
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137 ····<span·class="nb">zip</span><span·class="p">(</span><span·class="n">_endog_gen</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">),</span>·<span·class="n">_exog_gen</span><span·class="p">(</span><span·class="n">X</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">)),</span>·<span·class="n">fit_kwds</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;alpha&quot;</span><span·class="p">:</span>·<span·class="mf">0.2</span><span·class="p">}</span>137 ····<span·class="nb">zip</span><span·class="p">(</span><span·class="n">_endog_gen</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">),</span>·<span·class="n">_exog_gen</span><span·class="p">(</span><span·class="n">X</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">)),</span>·<span·class="n">fit_kwds</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;alpha&quot;</span><span·class="p">:</span>·<span·class="mf">0.2</span><span·class="p">}</span>
138 <span·class="p">)</span>138 <span·class="p">)</span>
139 </pre></div>139 </pre></div>
140 </div>140 </div>
141 </div>141 </div>
142 <p>We·can·also·change·the·<code·class="docutils·literal·notranslate"><span·class="pre">estimation_method</span></code>·and·the·<code·class="docutils·literal·notranslate"><span·class="pre">join_method</span></code>.·The·below·example·show·how·this·works·for·the·standard·OLS·case.·Here·we·using·a·naive·averaging·approach·instead·of·the·debiasing·procedure.</p>142 <p>We·can·also·change·the·<code·class="docutils·literal·notranslate"><span·class="pre">estimation_method</span></code>·and·the·<code·class="docutils·literal·notranslate"><span·class="pre">join_method</span></code>.·The·below·example·show·how·this·works·for·the·standard·OLS·case.·Here·we·using·a·naive·averaging·approach·instead·of·the·debiasing·procedure.</p>
143 <div·class="nbinput·nblast·docutils·container">143 <div·class="nbinput·nblast·docutils·container">
144 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:144 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
145 </pre></div>145 </pre></div>
146 </div>146 </div>
147 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.base.distributed_estimation</span>·<span·class="kn">import</span>·<span·class="n">_est_regularized_naive</span><span·class="p">,</span>·<span·class="n">_join_naive</span>147 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.base.distributed_estimation</span>·<span·class="kn">import</span>·<span·class="n">_est_regularized_naive</span><span·class="p">,</span>·<span·class="n">_join_naive</span>
  
  
148 <span·class="n">naive_OLS_reg_mod</span>·<span·class="o">=</span>·<span·class="n">DistributedModel</span><span·class="p">(</span>148 <span·class="n">naive_OLS_reg_mod</span>·<span·class="o">=</span>·<span·class="n">DistributedModel</span><span·class="p">(</span>
149 ····<span·class="n">m</span><span·class="p">,</span>·<span·class="n">estimation_method</span><span·class="o">=</span><span·class="n">_est_regularized_naive</span><span·class="p">,</span>·<span·class="n">join_method</span><span·class="o">=</span><span·class="n">_join_naive</span>149 ····<span·class="n">m</span><span·class="p">,</span>·<span·class="n">estimation_method</span><span·class="o">=</span><span·class="n">_est_regularized_naive</span><span·class="p">,</span>·<span·class="n">join_method</span><span·class="o">=</span><span·class="n">_join_naive</span>
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154 ····<span·class="nb">zip</span><span·class="p">(</span><span·class="n">_endog_gen</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">),</span>·<span·class="n">_exog_gen</span><span·class="p">(</span><span·class="n">X</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">)),</span>·<span·class="n">fit_kwds</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;alpha&quot;</span><span·class="p">:</span>·<span·class="mf">0.2</span><span·class="p">}</span>154 ····<span·class="nb">zip</span><span·class="p">(</span><span·class="n">_endog_gen</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">),</span>·<span·class="n">_exog_gen</span><span·class="p">(</span><span·class="n">X</span><span·class="p">,</span>·<span·class="n">m</span><span·class="p">)),</span>·<span·class="n">fit_kwds</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;alpha&quot;</span><span·class="p">:</span>·<span·class="mf">0.2</span><span·class="p">}</span>
155 <span·class="p">)</span>155 <span·class="p">)</span>
156 </pre></div>156 </pre></div>
157 </div>157 </div>
158 </div>158 </div>
159 <p>Finally,·we·can·also·change·the·<code·class="docutils·literal·notranslate"><span·class="pre">results_class</span></code>·used.·The·following·example·shows·how·this·work·for·a·simple·case·with·an·unregularized·model·and·naive·averaging.</p>159 <p>Finally,·we·can·also·change·the·<code·class="docutils·literal·notranslate"><span·class="pre">results_class</span></code>·used.·The·following·example·shows·how·this·work·for·a·simple·case·with·an·unregularized·model·and·naive·averaging.</p>
160 <div·class="nbinput·nblast·docutils·container">160 <div·class="nbinput·nblast·docutils·container">
161 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:161 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
162 </pre></div>162 </pre></div>
163 </div>163 </div>
164 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.base.distributed_estimation</span>·<span·class="kn">import</span>·<span·class="p">(</span>164 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.base.distributed_estimation</span>·<span·class="kn">import</span>·<span·class="p">(</span>
165 ····<span·class="n">_est_unregularized_naive</span><span·class="p">,</span>165 ····<span·class="n">_est_unregularized_naive</span><span·class="p">,</span>
166 ····<span·class="n">DistributedResults</span><span·class="p">,</span>166 ····<span·class="n">DistributedResults</span><span·class="p">,</span>
167 <span·class="p">)</span>167 <span·class="p">)</span>
  
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6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Distributed·Estimation8 ····*·Distributed·Estimation
9 *\x8**\x8**\x8**\x8**\x8**\x8*·D\x8Di\x8is\x8st\x8tr\x8ri\x8ib\x8bu\x8ut\x8te\x8ed\x8d·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·D\x8Di\x8is\x8st\x8tr\x8ri\x8ib\x8bu\x8ut\x8te\x8ed\x8d·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 This·notebook·goes·through·a·couple·of·examples·to·show·how·to·use10 This·notebook·goes·through·a·couple·of·examples·to·show·how·to·use
11 distributed_estimation.·We·import·the·DistributedModel·class·and·make·the·exog11 distributed_estimation.·We·import·the·DistributedModel·class·and·make·the·exog
12 and·endog·generators.12 and·endog·generators.
13 [1]:13 [·]:
14 import·numpy·as·np14 import·numpy·as·np
15 from·scipy.stats.distributions·import·norm15 from·scipy.stats.distributions·import·norm
16 from·statsmodels.base.distributed_estimation·import·DistributedModel16 from·statsmodels.base.distributed_estimation·import·DistributedModel
  
  
17 def·_exog_gen(exog,·partitions):17 def·_exog_gen(exog,·partitions):
18 ····"""partitions·exog·data"""18 ····"""partitions·exog·data"""
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37 ····ii·=·037 ····ii·=·0
38 ····while·ii·<·n_endog:38 ····while·ii·<·n_endog:
39 ········jj·=·int(min(ii·+·n_part,·n_endog))39 ········jj·=·int(min(ii·+·n_part,·n_endog))
40 ········yield·endog[ii:jj]40 ········yield·endog[ii:jj]
41 ········ii·+=·int(n_part)41 ········ii·+=·int(n_part)
42 Next·we·generate·some·random·data·to·serve·as·an·example.42 Next·we·generate·some·random·data·to·serve·as·an·example.
43 [2]:43 [·]:
44 X·=·np.random.normal(size=(1000,·25))44 X·=·np.random.normal(size=(1000,·25))
45 beta·=·np.random.normal(size=25)45 beta·=·np.random.normal(size=25)
46 beta·*=·np.random.randint(0,·2,·size=25)46 beta·*=·np.random.randint(0,·2,·size=25)
47 y·=·norm.rvs(loc=X.dot(beta))47 y·=·norm.rvs(loc=X.dot(beta))
48 m·=·548 m·=·5
49 This·is·the·most·basic·fit,·showing·all·of·the·defaults,·which·are·to·use·OLS49 This·is·the·most·basic·fit,·showing·all·of·the·defaults,·which·are·to·use·OLS
50 as·the·model·class,·and·the·debiasing·procedure.50 as·the·model·class,·and·the·debiasing·procedure.
51 [3]:51 [·]:
52 debiased_OLS_mod·=·DistributedModel(m)52 debiased_OLS_mod·=·DistributedModel(m)
53 debiased_OLS_fit·=·debiased_OLS_mod.fit(53 debiased_OLS_fit·=·debiased_OLS_mod.fit(
54 ····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={"alpha":·0.2}54 ····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={"alpha":·0.2}
55 )55 )
56 Then·we·run·through·a·slightly·more·complicated·example·which·uses·the·GLM56 Then·we·run·through·a·slightly·more·complicated·example·which·uses·the·GLM
57 model·class.57 model·class.
58 [4]:58 [·]:
59 from·statsmodels.genmod.generalized_linear_model·import·GLM59 from·statsmodels.genmod.generalized_linear_model·import·GLM
60 from·statsmodels.genmod.families·import·Gaussian60 from·statsmodels.genmod.families·import·Gaussian
  
61 debiased_GLM_mod·=·DistributedModel(61 debiased_GLM_mod·=·DistributedModel(
62 ····m,·model_class=GLM,·init_kwds={"family":·Gaussian()}62 ····m,·model_class=GLM,·init_kwds={"family":·Gaussian()}
63 )63 )
64 debiased_GLM_fit·=·debiased_GLM_mod.fit(64 debiased_GLM_fit·=·debiased_GLM_mod.fit(
65 ····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={"alpha":·0.2}65 ····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={"alpha":·0.2}
66 )66 )
67 We·can·also·change·the·estimation_method·and·the·join_method.·The·below·example67 We·can·also·change·the·estimation_method·and·the·join_method.·The·below·example
68 show·how·this·works·for·the·standard·OLS·case.·Here·we·using·a·naive·averaging68 show·how·this·works·for·the·standard·OLS·case.·Here·we·using·a·naive·averaging
69 approach·instead·of·the·debiasing·procedure.69 approach·instead·of·the·debiasing·procedure.
70 [5]:70 [·]:
71 from·statsmodels.base.distributed_estimation·import·_est_regularized_naive,71 from·statsmodels.base.distributed_estimation·import·_est_regularized_naive,
72 _join_naive72 _join_naive
  
  
73 naive_OLS_reg_mod·=·DistributedModel(73 naive_OLS_reg_mod·=·DistributedModel(
74 ····m,·estimation_method=_est_regularized_naive,·join_method=_join_naive74 ····m,·estimation_method=_est_regularized_naive,·join_method=_join_naive
75 )75 )
76 naive_OLS_reg_params·=·naive_OLS_reg_mod.fit(76 naive_OLS_reg_params·=·naive_OLS_reg_mod.fit(
77 ····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={"alpha":·0.2}77 ····zip(_endog_gen(y,·m),·_exog_gen(X,·m)),·fit_kwds={"alpha":·0.2}
78 )78 )
79 Finally,·we·can·also·change·the·results_class·used.·The·following·example·shows79 Finally,·we·can·also·change·the·results_class·used.·The·following·example·shows
80 how·this·work·for·a·simple·case·with·an·unregularized·model·and·naive80 how·this·work·for·a·simple·case·with·an·unregularized·model·and·naive
81 averaging.81 averaging.
82 [6]:82 [·]:
83 from·statsmodels.base.distributed_estimation·import·(83 from·statsmodels.base.distributed_estimation·import·(
84 ····_est_unregularized_naive,84 ····_est_unregularized_naive,
85 ····DistributedResults,85 ····DistributedResults,
86 )86 )
  
  
87 naive_OLS_unreg_mod·=·DistributedModel(87 naive_OLS_unreg_mod·=·DistributedModel(
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774 </pre></div>774 </pre></div>
775 </div>775 </div>
776 <div·class="output_area·docutils·container">776 <div·class="output_area·docutils·container">
777 <div·class="highlight"><pre>777 <div·class="highlight"><pre>
778 &lt;matplotlib.legend.Legend·at·0xadde5de1e8ed&gt;778 &lt;matplotlib.legend.Legend·at·0xadde5de1e8ed&gt;
779 </pre></div></div>779 </pre></div></div>
780 </div>780 </div>
 781 <div·class="nboutput·docutils·container">
 782 <div·class="prompt·empty·docutils·container">
 783 </div>
 784 <div·class="output_area·stderr·docutils·container">
 785 <div·class="highlight"><pre>
 786 /usr/lib/python3/dist-packages/IPython/core/pylabtools.py:170:·UserWarning:·Creating·legend·with·loc=&#34;best&#34;·can·be·slow·with·large·amounts·of·data.
 787 ··fig.canvas.print_figure(bytes_io,·**kw)
 788 </pre></div></div>
 789 </div>
781 <div·class="nboutput·nblast·docutils·container">790 <div·class="nboutput·nblast·docutils·container">
782 <div·class="prompt·empty·docutils·container">791 <div·class="prompt·empty·docutils·container">
783 </div>792 </div>
784 <div·class="output_area·docutils·container">793 <div·class="output_area·docutils·container">
785 <img·alt="../../../_images/examples_notebooks_generated_ets_21_1.png"·src="../../../_images/examples_notebooks_generated_ets_21_1.png"·/>794 <img·alt="../../../_images/examples_notebooks_generated_ets_21_2.png"·src="../../../_images/examples_notebooks_generated_ets_21_2.png"·/>
786 </div>795 </div>
787 </div>796 </div>
788 <p>In·this·case,·we·chose·“end”·as·simulation·anchor,·which·means·that·the·first·simulated·value·will·be·the·first·out·of·sample·value.·It·is·also·possible·to·choose·other·anchor·inside·the·sample.</p>797 <p>In·this·case,·we·chose·“end”·as·simulation·anchor,·which·means·that·the·first·simulated·value·will·be·the·first·out·of·sample·value.·It·is·also·possible·to·choose·other·anchor·inside·the·sample.</p>
789 </section>798 </section>
790 </section>799 </section>
  
  
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449 df["mean"].plot(label="mean·prediction")449 df["mean"].plot(label="mean·prediction")
450 df["pi_lower"].plot(linestyle="--",·color="tab:blue",·label="95%·interval")450 df["pi_lower"].plot(linestyle="--",·color="tab:blue",·label="95%·interval")
451 df["pi_upper"].plot(linestyle="--",·color="tab:blue",·label="_")451 df["pi_upper"].plot(linestyle="--",·color="tab:blue",·label="_")
452 pred.endog.plot(label="data")452 pred.endog.plot(label="data")
453 plt.legend()453 plt.legend()
454 [14]:454 [14]:
455 <matplotlib.legend.Legend·at·0xadde5de1e8ed>455 <matplotlib.legend.Legend·at·0xadde5de1e8ed>
 456 /usr/lib/python3/dist-packages/IPython/core/pylabtools.py:170:·UserWarning:
 457 Creating·legend·with·loc="best"·can·be·slow·with·large·amounts·of·data.
 458 ··fig.canvas.print_figure(bytes_io,·**kw)
456 [../../../_images/examples_notebooks_generated_ets_21_1.png]459 [../../../_images/examples_notebooks_generated_ets_21_2.png]
457 In·this·case,·we·chose·“end”·as·simulation·anchor,·which·means·that·the·first460 In·this·case,·we·chose·“end”·as·simulation·anchor,·which·means·that·the·first
458 simulated·value·will·be·the·first·out·of·sample·value.·It·is·also·possible·to461 simulated·value·will·be·the·first·out·of·sample·value.·It·is·also·possible·to
459 choose·other·anchor·inside·the·sample.462 choose·other·anchor·inside·the·sample.
460 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]463 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
461 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*464 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*
462 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s465 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s
463 ····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d466 ····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d
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872 ····················},872 ····················},
873 ····················"execution_count":·14,873 ····················"execution_count":·14,
874 ····················"metadata":·{},874 ····················"metadata":·{},
875 ····················"output_type":·"execute_result"875 ····················"output_type":·"execute_result"
876 ················},876 ················},
877 ················{877 ················{
 878 ····················"name":·"stderr",
 879 ····················"output_type":·"stream",
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 881 ························"/usr/lib/python3/dist-packages/IPython/core/pylabtools.py:170:·UserWarning:·Creating·legend·with·loc=\"best\"·can·be·slow·with·large·amounts·of·data.\n",
 882 ························"··fig.canvas.print_figure(bytes_io,·**kw)\n"
 883 ····················]
 884 ················},
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64 <h1>Exponential·smoothing<a·class="headerlink"·href="#Exponential-smoothing"·title="Link·to·this·heading">¶</a></h1>64 <h1>Exponential·smoothing<a·class="headerlink"·href="#Exponential-smoothing"·title="Link·to·this·heading">¶</a></h1>
65 <p>Let·us·consider·chapter·7·of·the·excellent·treatise·on·the·subject·of·Exponential·Smoothing·By·Hyndman·and·Athanasopoulos·[1].·We·will·work·through·all·the·examples·in·the·chapter·as·they·unfold.</p>65 <p>Let·us·consider·chapter·7·of·the·excellent·treatise·on·the·subject·of·Exponential·Smoothing·By·Hyndman·and·Athanasopoulos·[1].·We·will·work·through·all·the·examples·in·the·chapter·as·they·unfold.</p>
66 <p>[1]·<a·class="reference·external"·href="https://www.otexts.org/fpp/7">Hyndman,·Rob·J.,·and·George·Athanasopoulos.·Forecasting:·principles·and·practice.·OTexts,·2014.</a></p>66 <p>[1]·<a·class="reference·external"·href="https://www.otexts.org/fpp/7">Hyndman,·Rob·J.,·and·George·Athanasopoulos.·Forecasting:·principles·and·practice.·OTexts,·2014.</a></p>
67 <section·id="Loading-data">67 <section·id="Loading-data">
68 <h2>Loading·data<a·class="headerlink"·href="#Loading-data"·title="Link·to·this·heading">¶</a></h2>68 <h2>Loading·data<a·class="headerlink"·href="#Loading-data"·title="Link·to·this·heading">¶</a></h2>
69 <p>First·we·load·some·data.·We·have·included·the·R·data·in·the·notebook·for·expedience.</p>69 <p>First·we·load·some·data.·We·have·included·the·R·data·in·the·notebook·for·expedience.</p>
70 <div·class="nbinput·nblast·docutils·container">70 <div·class="nbinput·nblast·docutils·container">
71 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:71 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
72 </pre></div>72 </pre></div>
73 </div>73 </div>
74 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">os</span>74 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">os</span>
  
75 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>75 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
76 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>76 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
77 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>77 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
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189 </pre></div>189 </pre></div>
190 </div>190 </div>
191 </div>191 </div>
192 </section>192 </section>
193 <section·id="Simple-Exponential-Smoothing">193 <section·id="Simple-Exponential-Smoothing">
194 <h2>Simple·Exponential·Smoothing<a·class="headerlink"·href="#Simple-Exponential-Smoothing"·title="Link·to·this·heading">¶</a></h2>194 <h2>Simple·Exponential·Smoothing<a·class="headerlink"·href="#Simple-Exponential-Smoothing"·title="Link·to·this·heading">¶</a></h2>
195 <p>Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.</p>195 <p>Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.</p>
196 <div·class="nbinput·docutils·container">196 <div·class="nbinput·nblast·docutils·container">
197 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:197 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
198 </pre></div>198 </pre></div>
199 </div>199 </div>
200 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">oildata</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">()</span>200 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">oildata</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">()</span>
201 <span·class="n">ax</span><span·class="o">.</span><span·class="n">set_xlabel</span><span·class="p">(</span><span·class="s2">&quot;Year&quot;</span><span·class="p">)</span>201 <span·class="n">ax</span><span·class="o">.</span><span·class="n">set_xlabel</span><span·class="p">(</span><span·class="s2">&quot;Year&quot;</span><span·class="p">)</span>
202 <span·class="n">ax</span><span·class="o">.</span><span·class="n">set_ylabel</span><span·class="p">(</span><span·class="s2">&quot;Oil·(millions·of·tonnes)&quot;</span><span·class="p">)</span>202 <span·class="n">ax</span><span·class="o">.</span><span·class="n">set_ylabel</span><span·class="p">(</span><span·class="s2">&quot;Oil·(millions·of·tonnes)&quot;</span><span·class="p">)</span>
203 <span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;Figure·7.1:·Oil·production·in·Saudi·Arabia·from·1996·to·2007.&quot;</span><span·class="p">)</span>203 <span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;Figure·7.1:·Oil·production·in·Saudi·Arabia·from·1996·to·2007.&quot;</span><span·class="p">)</span>
204 </pre></div>204 </pre></div>
205 </div>205 </div>
206 </div>206 </div>
207 <div·class="nboutput·docutils·container"> 
208 <div·class="prompt·empty·docutils·container"> 
209 </div> 
210 <div·class="output_area·docutils·container"> 
211 <div·class="highlight"><pre> 
212 Figure·7.1:·Oil·production·in·Saudi·Arabia·from·1996·to·2007. 
213 </pre></div></div> 
214 </div> 
215 <div·class="nboutput·nblast·docutils·container"> 
216 <div·class="prompt·empty·docutils·container"> 
217 </div> 
218 <div·class="output_area·docutils·container"> 
219 <img·alt="../../../_images/examples_notebooks_generated_exponential_smoothing_4_1.png"·src="../../../_images/examples_notebooks_generated_exponential_smoothing_4_1.png"·/> 
220 </div> 
221 </div> 
222 <p>Here·we·run·three·variants·of·simple·exponential·smoothing:·1.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit1</span></code>·we·do·not·use·the·auto·optimization·but·instead·choose·to·explicitly·provide·the·model·with·the·<span·class="math·notranslate·nohighlight">\(\alpha=0.2\)</span>·parameter·2.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit2</span></code>·as·above·we·choose·an·<span·class="math·notranslate·nohighlight">\(\alpha=0.6\)</span>·3.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit3</span></code>·we·allow·statsmodels·to·automatically·find·an·optimized·<span·class="math·notranslate·nohighlight">\(\alpha\)</span>·value·for·us.·This·is·the·recommended·approach.</p>207 <p>Here·we·run·three·variants·of·simple·exponential·smoothing:·1.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit1</span></code>·we·do·not·use·the·auto·optimization·but·instead·choose·to·explicitly·provide·the·model·with·the·<span·class="math·notranslate·nohighlight">\(\alpha=0.2\)</span>·parameter·2.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit2</span></code>·as·above·we·choose·an·<span·class="math·notranslate·nohighlight">\(\alpha=0.6\)</span>·3.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit3</span></code>·we·allow·statsmodels·to·automatically·find·an·optimized·<span·class="math·notranslate·nohighlight">\(\alpha\)</span>·value·for·us.·This·is·the·recommended·approach.</p>
223 <div·class="nbinput·docutils·container">208 <div·class="nbinput·nblast·docutils·container">
224 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:209 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
225 </pre></div>210 </pre></div>
226 </div>211 </div>
227 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fit1</span>·<span·class="o">=</span>·<span·class="n">SimpleExpSmoothing</span><span·class="p">(</span><span·class="n">oildata</span><span·class="p">,</span>·<span·class="n">initialization_method</span><span·class="o">=</span><span·class="s2">&quot;heuristic&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>212 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fit1</span>·<span·class="o">=</span>·<span·class="n">SimpleExpSmoothing</span><span·class="p">(</span><span·class="n">oildata</span><span·class="p">,</span>·<span·class="n">initialization_method</span><span·class="o">=</span><span·class="s2">&quot;heuristic&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>
228 ····<span·class="n">smoothing_level</span><span·class="o">=</span><span·class="mf">0.2</span><span·class="p">,</span>·<span·class="n">optimized</span><span·class="o">=</span><span·class="kc">False</span>213 ····<span·class="n">smoothing_level</span><span·class="o">=</span><span·class="mf">0.2</span><span·class="p">,</span>·<span·class="n">optimized</span><span·class="o">=</span><span·class="kc">False</span>
229 <span·class="p">)</span>214 <span·class="p">)</span>
230 <span·class="n">fcast1</span>·<span·class="o">=</span>·<span·class="n">fit1</span><span·class="o">.</span><span·class="n">forecast</span><span·class="p">(</span><span·class="mi">3</span><span·class="p">)</span><span·class="o">.</span><span·class="n">rename</span><span·class="p">(</span><span·class="sa">r</span><span·class="s2">&quot;$\alpha=0.2$&quot;</span><span·class="p">)</span>215 <span·class="n">fcast1</span>·<span·class="o">=</span>·<span·class="n">fit1</span><span·class="o">.</span><span·class="n">forecast</span><span·class="p">(</span><span·class="mi">3</span><span·class="p">)</span><span·class="o">.</span><span·class="n">rename</span><span·class="p">(</span><span·class="sa">r</span><span·class="s2">&quot;$\alpha=0.2$&quot;</span><span·class="p">)</span>
231 <span·class="n">fit2</span>·<span·class="o">=</span>·<span·class="n">SimpleExpSmoothing</span><span·class="p">(</span><span·class="n">oildata</span><span·class="p">,</span>·<span·class="n">initialization_method</span><span·class="o">=</span><span·class="s2">&quot;heuristic&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>216 <span·class="n">fit2</span>·<span·class="o">=</span>·<span·class="n">SimpleExpSmoothing</span><span·class="p">(</span><span·class="n">oildata</span><span·class="p">,</span>·<span·class="n">initialization_method</span><span·class="o">=</span><span·class="s2">&quot;heuristic&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>
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243 <span·class="p">(</span><span·class="n">line2</span><span·class="p">,)</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fcast2</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;red&quot;</span><span·class="p">)</span>228 <span·class="p">(</span><span·class="n">line2</span><span·class="p">,)</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fcast2</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;red&quot;</span><span·class="p">)</span>
244 <span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fit3</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;green&quot;</span><span·class="p">)</span>229 <span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fit3</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;green&quot;</span><span·class="p">)</span>
245 <span·class="p">(</span><span·class="n">line3</span><span·class="p">,)</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fcast3</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;green&quot;</span><span·class="p">)</span>230 <span·class="p">(</span><span·class="n">line3</span><span·class="p">,)</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fcast3</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;green&quot;</span><span·class="p">)</span>
246 <span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">([</span><span·class="n">line1</span><span·class="p">,</span>·<span·class="n">line2</span><span·class="p">,</span>·<span·class="n">line3</span><span·class="p">],</span>·<span·class="p">[</span><span·class="n">fcast1</span><span·class="o">.</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">fcast2</span><span·class="o">.</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">fcast3</span><span·class="o">.</span><span·class="n">name</span><span·class="p">])</span>231 <span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">([</span><span·class="n">line1</span><span·class="p">,</span>·<span·class="n">line2</span><span·class="p">,</span>·<span·class="n">line3</span><span·class="p">],</span>·<span·class="p">[</span><span·class="n">fcast1</span><span·class="o">.</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">fcast2</span><span·class="o">.</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">fcast3</span><span·class="o">.</span><span·class="n">name</span><span·class="p">])</span>
247 </pre></div>232 </pre></div>
248 </div>233 </div>
249 </div>234 </div>
250 <div·class="nboutput·docutils·container"> 
251 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]: 
252 </pre></div> 
253 </div> 
254 <div·class="output_area·docutils·container"> 
255 <div·class="highlight"><pre> 
256 &lt;matplotlib.legend.Legend·at·0xadde5de1e8ed&gt; 
257 </pre></div></div> 
258 </div> 
259 <div·class="nboutput·nblast·docutils·container"> 
260 <div·class="prompt·empty·docutils·container"> 
261 </div> 
262 <div·class="output_area·docutils·container"> 
263 <img·alt="../../../_images/examples_notebooks_generated_exponential_smoothing_6_1.png"·src="../../../_images/examples_notebooks_generated_exponential_smoothing_6_1.png"·/> 
264 </div> 
265 </div> 
266 </section>235 </section>
267 <section·id="Holt's-Method">236 <section·id="Holt's-Method">
268 <h2>Holt’s·Method<a·class="headerlink"·href="#Holt's-Method"·title="Link·to·this·heading">¶</a></h2>237 <h2>Holt’s·Method<a·class="headerlink"·href="#Holt's-Method"·title="Link·to·this·heading">¶</a></h2>
269 <p>Lets·take·a·look·at·another·example.·This·time·we·use·air·pollution·data·and·the·Holt’s·Method.·We·will·fit·three·examples·again.·1.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit1</span></code>·we·again·choose·not·to·use·the·optimizer·and·provide·explicit·values·for·<span·class="math·notranslate·nohighlight">\(\alpha=0.8\)</span>·and·<span·class="math·notranslate·nohighlight">\(\beta=0.2\)</span>·2.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit2</span></code>·we·do·the·same·as·in·<code·class="docutils·literal·notranslate"><span·class="pre">fit1</span></code>·but·choose·to·use·an·exponential·model·rather·than·a·Holt’s·additive·model.·3.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit3</span></code>·we·used·a·damped·versions·of·the·Holt’s·additive·model·but·allow·the·dampening·parameter·<span·class="math·notranslate·nohighlight">\(\phi\)</span>·to238 <p>Lets·take·a·look·at·another·example.·This·time·we·use·air·pollution·data·and·the·Holt’s·Method.·We·will·fit·three·examples·again.·1.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit1</span></code>·we·again·choose·not·to·use·the·optimizer·and·provide·explicit·values·for·<span·class="math·notranslate·nohighlight">\(\alpha=0.8\)</span>·and·<span·class="math·notranslate·nohighlight">\(\beta=0.2\)</span>·2.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit2</span></code>·we·do·the·same·as·in·<code·class="docutils·literal·notranslate"><span·class="pre">fit1</span></code>·but·choose·to·use·an·exponential·model·rather·than·a·Holt’s·additive·model.·3.·In·<code·class="docutils·literal·notranslate"><span·class="pre">fit3</span></code>·we·used·a·damped·versions·of·the·Holt’s·additive·model·but·allow·the·dampening·parameter·<span·class="math·notranslate·nohighlight">\(\phi\)</span>·to
270 be·optimized·while·fixing·the·values·for·<span·class="math·notranslate·nohighlight">\(\alpha=0.8\)</span>·and·<span·class="math·notranslate·nohighlight">\(\beta=0.2\)</span></p>239 be·optimized·while·fixing·the·values·for·<span·class="math·notranslate·nohighlight">\(\alpha=0.8\)</span>·and·<span·class="math·notranslate·nohighlight">\(\beta=0.2\)</span></p>
271 <div·class="nbinput·docutils·container">240 <div·class="nbinput·nblast·docutils·container">
272 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:241 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
273 </pre></div>242 </pre></div>
274 </div>243 </div>
275 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fit1</span>·<span·class="o">=</span>·<span·class="n">Holt</span><span·class="p">(</span><span·class="n">air</span><span·class="p">,</span>·<span·class="n">initialization_method</span><span·class="o">=</span><span·class="s2">&quot;estimated&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>244 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fit1</span>·<span·class="o">=</span>·<span·class="n">Holt</span><span·class="p">(</span><span·class="n">air</span><span·class="p">,</span>·<span·class="n">initialization_method</span><span·class="o">=</span><span·class="s2">&quot;estimated&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>
276 ····<span·class="n">smoothing_level</span><span·class="o">=</span><span·class="mf">0.8</span><span·class="p">,</span>·<span·class="n">smoothing_trend</span><span·class="o">=</span><span·class="mf">0.2</span><span·class="p">,</span>·<span·class="n">optimized</span><span·class="o">=</span><span·class="kc">False</span>245 ····<span·class="n">smoothing_level</span><span·class="o">=</span><span·class="mf">0.8</span><span·class="p">,</span>·<span·class="n">smoothing_trend</span><span·class="o">=</span><span·class="mf">0.2</span><span·class="p">,</span>·<span·class="n">optimized</span><span·class="o">=</span><span·class="kc">False</span>
277 <span·class="p">)</span>246 <span·class="p">)</span>
278 <span·class="n">fcast1</span>·<span·class="o">=</span>·<span·class="n">fit1</span><span·class="o">.</span><span·class="n">forecast</span><span·class="p">(</span><span·class="mi">5</span><span·class="p">)</span><span·class="o">.</span><span·class="n">rename</span><span·class="p">(</span><span·class="s2">&quot;Holt&#39;s·linear·trend&quot;</span><span·class="p">)</span>247 <span·class="n">fcast1</span>·<span·class="o">=</span>·<span·class="n">fit1</span><span·class="o">.</span><span·class="n">forecast</span><span·class="p">(</span><span·class="mi">5</span><span·class="p">)</span><span·class="o">.</span><span·class="n">rename</span><span·class="p">(</span><span·class="s2">&quot;Holt&#39;s·linear·trend&quot;</span><span·class="p">)</span>
279 <span·class="n">fit2</span>·<span·class="o">=</span>·<span·class="n">Holt</span><span·class="p">(</span><span·class="n">air</span><span·class="p">,</span>·<span·class="n">exponential</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">initialization_method</span><span·class="o">=</span><span·class="s2">&quot;estimated&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>248 <span·class="n">fit2</span>·<span·class="o">=</span>·<span·class="n">Holt</span><span·class="p">(</span><span·class="n">air</span><span·class="p">,</span>·<span·class="n">exponential</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">initialization_method</span><span·class="o">=</span><span·class="s2">&quot;estimated&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span>
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293 <span·class="p">(</span><span·class="n">line2</span><span·class="p">,)</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fcast2</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;red&quot;</span><span·class="p">)</span>262 <span·class="p">(</span><span·class="n">line2</span><span·class="p">,)</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fcast2</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;red&quot;</span><span·class="p">)</span>
294 <span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fit3</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;green&quot;</span><span·class="p">)</span>263 <span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fit3</span><span·class="o">.</span><span·class="n">fittedvalues</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;green&quot;</span><span·class="p">)</span>
295 <span·class="p">(</span><span·class="n">line3</span><span·class="p">,)</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fcast3</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;green&quot;</span><span·class="p">)</span>264 <span·class="p">(</span><span·class="n">line3</span><span·class="p">,)</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">fcast3</span><span·class="p">,</span>·<span·class="n">marker</span><span·class="o">=</span><span·class="s2">&quot;o&quot;</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;green&quot;</span><span·class="p">)</span>
296 <span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">([</span><span·class="n">line1</span><span·class="p">,</span>·<span·class="n">line2</span><span·class="p">,</span>·<span·class="n">line3</span><span·class="p">],</span>·<span·class="p">[</span><span·class="n">fcast1</span><span·class="o">.</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">fcast2</span><span·class="o">.</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">fcast3</span><span·class="o">.</span><span·class="n">name</span><span·class="p">])</span>265 <span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">([</span><span·class="n">line1</span><span·class="p">,</span>·<span·class="n">line2</span><span·class="p">,</span>·<span·class="n">line3</span><span·class="p">],</span>·<span·class="p">[</span><span·class="n">fcast1</span><span·class="o">.</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">fcast2</span><span·class="o">.</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">fcast3</span><span·class="o">.</span><span·class="n">name</span><span·class="p">])</span>
297 </pre></div>266 </pre></div>
298 </div>267 </div>
299 </div>268 </div>
300 <div·class="nboutput·docutils·container"> 
301 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]: 
302 </pre></div> 
303 </div> 
304 <div·class="output_area·docutils·container"> 
305 <div·class="highlight"><pre> 
306 &lt;matplotlib.legend.Legend·at·0xadde5de1e8ed&gt; 
307 </pre></div></div> 
308 </div> 
309 <div·class="nboutput·nblast·docutils·container"> 
310 <div·class="prompt·empty·docutils·container"> 
311 </div> 
312 <div·class="output_area·docutils·container"> 
313 <img·alt="../../../_images/examples_notebooks_generated_exponential_smoothing_8_1.png"·src="../../../_images/examples_notebooks_generated_exponential_smoothing_8_1.png"·/> 
314 </div> 
315 </div> 
316 <section·id="Seasonally-adjusted-data">269 <section·id="Seasonally-adjusted-data">
317 <h3>Seasonally·adjusted·data<a·class="headerlink"·href="#Seasonally-adjusted-data"·title="Link·to·this·heading">¶</a></h3>270 <h3>Seasonally·adjusted·data<a·class="headerlink"·href="#Seasonally-adjusted-data"·title="Link·to·this·heading">¶</a></h3>
318 <p>Lets·look·at·some·seasonally·adjusted·livestock·data.·We·fit·five·Holt’s·models.·The·below·table·allows·us·to·compare·results·when·we·use·exponential·versus·additive·and·damped·versus·non-damped.</p>271 <p>Lets·look·at·some·seasonally·adjusted·livestock·data.·We·fit·five·Holt’s·models.·The·below·table·allows·us·to·compare·results·when·we·use·exponential·versus·additive·and·damped·versus·non-damped.</p>
319 <p>Note:·<code·class="docutils·literal·notranslate"><span·class="pre">fit4</span></code>·does·not·allow·the·parameter·<span·class="math·notranslate·nohighlight">\(\phi\)</span>·to·be·optimized·by·providing·a·fixed·value·of·<span·class="math·notranslate·nohighlight">\(\phi=0.98\)</span></p>272 <p>Note:·<code·class="docutils·literal·notranslate"><span·class="pre">fit4</span></code>·does·not·allow·the·parameter·<span·class="math·notranslate·nohighlight">\(\phi\)</span>·to·be·optimized·by·providing·a·fixed·value·of·<span·class="math·notranslate·nohighlight">\(\phi=0.98\)</span></p>
320 <div·class="nbinput·docutils·container">273 <div·class="nbinput·nblast·docutils·container">
321 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:274 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
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11 Exponential·Smoothing·By·Hyndman·and·Athanasopoulos·[1].·We·will·work·through11 Exponential·Smoothing·By·Hyndman·and·Athanasopoulos·[1].·We·will·work·through
12 all·the·examples·in·the·chapter·as·they·unfold.12 all·the·examples·in·the·chapter·as·they·unfold.
13 [1]·_\x8H_\x8y_\x8n_\x8d_\x8m_\x8a_\x8n_\x8,_\x8·_\x8R_\x8o_\x8b_\x8·_\x8J_\x8._\x8,_\x8·_\x8a_\x8n_\x8d_\x8·_\x8G_\x8e_\x8o_\x8r_\x8g_\x8e_\x8·_\x8A_\x8t_\x8h_\x8a_\x8n_\x8a_\x8s_\x8o_\x8p_\x8o_\x8u_\x8l_\x8o_\x8s_\x8._\x8·_\x8F_\x8o_\x8r_\x8e_\x8c_\x8a_\x8s_\x8t_\x8i_\x8n_\x8g_\x8:_\x8·_\x8p_\x8r_\x8i_\x8n_\x8c_\x8i_\x8p_\x8l_\x8e_\x8s_\x8·_\x8a_\x8n_\x8d13 [1]·_\x8H_\x8y_\x8n_\x8d_\x8m_\x8a_\x8n_\x8,_\x8·_\x8R_\x8o_\x8b_\x8·_\x8J_\x8._\x8,_\x8·_\x8a_\x8n_\x8d_\x8·_\x8G_\x8e_\x8o_\x8r_\x8g_\x8e_\x8·_\x8A_\x8t_\x8h_\x8a_\x8n_\x8a_\x8s_\x8o_\x8p_\x8o_\x8u_\x8l_\x8o_\x8s_\x8._\x8·_\x8F_\x8o_\x8r_\x8e_\x8c_\x8a_\x8s_\x8t_\x8i_\x8n_\x8g_\x8:_\x8·_\x8p_\x8r_\x8i_\x8n_\x8c_\x8i_\x8p_\x8l_\x8e_\x8s_\x8·_\x8a_\x8n_\x8d
14 _\x8p_\x8r_\x8a_\x8c_\x8t_\x8i_\x8c_\x8e_\x8._\x8·_\x8O_\x8T_\x8e_\x8x_\x8t_\x8s_\x8,_\x8·_\x82_\x80_\x81_\x84_\x8.14 _\x8p_\x8r_\x8a_\x8c_\x8t_\x8i_\x8c_\x8e_\x8._\x8·_\x8O_\x8T_\x8e_\x8x_\x8t_\x8s_\x8,_\x8·_\x82_\x80_\x81_\x84_\x8.
15 *\x8**\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8di\x8in\x8ng\x8g·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8di\x8in\x8ng\x8g·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
16 First·we·load·some·data.·We·have·included·the·R·data·in·the·notebook·for16 First·we·load·some·data.·We·have·included·the·R·data·in·the·notebook·for
17 expedience.17 expedience.
18 [1]:18 [·]:
19 import·os19 import·os
  
20 import·matplotlib.pyplot·as·plt20 import·matplotlib.pyplot·as·plt
21 import·numpy·as·np21 import·numpy·as·np
22 import·pandas·as·pd22 import·pandas·as·pd
23 from·statsmodels.tsa.api·import·ExponentialSmoothing,·Holt,·SimpleExpSmoothing23 from·statsmodels.tsa.api·import·ExponentialSmoothing,·Holt,·SimpleExpSmoothing
24 np.random.seed(1234)·#·for·reproducibility24 np.random.seed(1234)·#·for·reproducibility
Offset 129, 27 lines modifiedOffset 129, 25 lines modified
129 ····44.3197,129 ····44.3197,
130 ····47.9137,130 ····47.9137,
131 ]131 ]
132 index·=·pd.date_range(start="2005",·end="2010-Q4",·freq="QS-OCT")132 index·=·pd.date_range(start="2005",·end="2010-Q4",·freq="QS-OCT")
133 aust·=·pd.Series(data,·index)133 aust·=·pd.Series(data,·index)
134 *\x8**\x8**\x8**\x8**\x8*·S\x8Si\x8im\x8mp\x8pl\x8le\x8e·E\x8Ex\x8xp\x8po\x8on\x8ne\x8en\x8nt\x8ti\x8ia\x8al\x8l·S\x8Sm\x8mo\x8oo\x8ot\x8th\x8hi\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*134 *\x8**\x8**\x8**\x8**\x8*·S\x8Si\x8im\x8mp\x8pl\x8le\x8e·E\x8Ex\x8xp\x8po\x8on\x8ne\x8en\x8nt\x8ti\x8ia\x8al\x8l·S\x8Sm\x8mo\x8oo\x8ot\x8th\x8hi\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
135 Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.135 Lets·use·Simple·Exponential·Smoothing·to·forecast·the·below·oil·data.
136 [2]:136 [·]:
137 ax·=·oildata.plot()137 ax·=·oildata.plot()
138 ax.set_xlabel("Year")138 ax.set_xlabel("Year")
139 ax.set_ylabel("Oil·(millions·of·tonnes)")139 ax.set_ylabel("Oil·(millions·of·tonnes)")
140 print("Figure·7.1:·Oil·production·in·Saudi·Arabia·from·1996·to·2007.")140 print("Figure·7.1:·Oil·production·in·Saudi·Arabia·from·1996·to·2007.")
141 Figure·7.1:·Oil·production·in·Saudi·Arabia·from·1996·to·2007. 
142 [../../../_images/examples_notebooks_generated_exponential_smoothing_4_1.png] 
143 Here·we·run·three·variants·of·simple·exponential·smoothing:·1.·In·fit1·we·do141 Here·we·run·three·variants·of·simple·exponential·smoothing:·1.·In·fit1·we·do
144 not·use·the·auto·optimization·but·instead·choose·to·explicitly·provide·the142 not·use·the·auto·optimization·but·instead·choose·to·explicitly·provide·the
145 model·with·the·\(\alpha=0.2\)·parameter·2.·In·fit2·as·above·we·choose·an·\143 model·with·the·\(\alpha=0.2\)·parameter·2.·In·fit2·as·above·we·choose·an·\
146 (\alpha=0.6\)·3.·In·fit3·we·allow·statsmodels·to·automatically·find·an144 (\alpha=0.6\)·3.·In·fit3·we·allow·statsmodels·to·automatically·find·an
147 optimized·\(\alpha\)·value·for·us.·This·is·the·recommended·approach.145 optimized·\(\alpha\)·value·for·us.·This·is·the·recommended·approach.
148 [3]:146 [·]:
149 fit1·=·SimpleExpSmoothing(oildata,·initialization_method="heuristic").fit(147 fit1·=·SimpleExpSmoothing(oildata,·initialization_method="heuristic").fit(
150 ····smoothing_level=0.2,·optimized=False148 ····smoothing_level=0.2,·optimized=False
151 )149 )
152 fcast1·=·fit1.forecast(3).rename(r"$\alpha=0.2$")150 fcast1·=·fit1.forecast(3).rename(r"$\alpha=0.2$")
153 fit2·=·SimpleExpSmoothing(oildata,·initialization_method="heuristic").fit(151 fit2·=·SimpleExpSmoothing(oildata,·initialization_method="heuristic").fit(
154 ····smoothing_level=0.6,·optimized=False152 ····smoothing_level=0.6,·optimized=False
155 )153 )
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163 plt.plot(fit1.fittedvalues,·marker="o",·color="blue")161 plt.plot(fit1.fittedvalues,·marker="o",·color="blue")
164 (line1,)·=·plt.plot(fcast1,·marker="o",·color="blue")162 (line1,)·=·plt.plot(fcast1,·marker="o",·color="blue")
165 plt.plot(fit2.fittedvalues,·marker="o",·color="red")163 plt.plot(fit2.fittedvalues,·marker="o",·color="red")
166 (line2,)·=·plt.plot(fcast2,·marker="o",·color="red")164 (line2,)·=·plt.plot(fcast2,·marker="o",·color="red")
167 plt.plot(fit3.fittedvalues,·marker="o",·color="green")165 plt.plot(fit3.fittedvalues,·marker="o",·color="green")
168 (line3,)·=·plt.plot(fcast3,·marker="o",·color="green")166 (line3,)·=·plt.plot(fcast3,·marker="o",·color="green")
169 plt.legend([line1,·line2,·line3],·[fcast1.name,·fcast2.name,·fcast3.name])167 plt.legend([line1,·line2,·line3],·[fcast1.name,·fcast2.name,·fcast3.name])
170 [3]: 
171 <matplotlib.legend.Legend·at·0xadde5de1e8ed> 
172 [../../../_images/examples_notebooks_generated_exponential_smoothing_6_1.png] 
173 *\x8**\x8**\x8**\x8**\x8*·H\x8Ho\x8ol\x8lt\x8t?\x8’s\x8s·M\x8Me\x8et\x8th\x8ho\x8od\x8d_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*168 *\x8**\x8**\x8**\x8**\x8*·H\x8Ho\x8ol\x8lt\x8t?\x8’s\x8s·M\x8Me\x8et\x8th\x8ho\x8od\x8d_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
174 Lets·take·a·look·at·another·example.·This·time·we·use·air·pollution·data·and169 Lets·take·a·look·at·another·example.·This·time·we·use·air·pollution·data·and
175 the·Holt’s·Method.·We·will·fit·three·examples·again.·1.·In·fit1·we·again·choose170 the·Holt’s·Method.·We·will·fit·three·examples·again.·1.·In·fit1·we·again·choose
176 not·to·use·the·optimizer·and·provide·explicit·values·for·\(\alpha=0.8\)·and·\171 not·to·use·the·optimizer·and·provide·explicit·values·for·\(\alpha=0.8\)·and·\
177 (\beta=0.2\)·2.·In·fit2·we·do·the·same·as·in·fit1·but·choose·to·use·an172 (\beta=0.2\)·2.·In·fit2·we·do·the·same·as·in·fit1·but·choose·to·use·an
178 exponential·model·rather·than·a·Holt’s·additive·model.·3.·In·fit3·we·used·a173 exponential·model·rather·than·a·Holt’s·additive·model.·3.·In·fit3·we·used·a
179 damped·versions·of·the·Holt’s·additive·model·but·allow·the·dampening·parameter174 damped·versions·of·the·Holt’s·additive·model·but·allow·the·dampening·parameter
180 \(\phi\)·to·be·optimized·while·fixing·the·values·for·\(\alpha=0.8\)·and·\175 \(\phi\)·to·be·optimized·while·fixing·the·values·for·\(\alpha=0.8\)·and·\
181 (\beta=0.2\)176 (\beta=0.2\)
182 [4]:177 [·]:
183 fit1·=·Holt(air,·initialization_method="estimated").fit(178 fit1·=·Holt(air,·initialization_method="estimated").fit(
184 ····smoothing_level=0.8,·smoothing_trend=0.2,·optimized=False179 ····smoothing_level=0.8,·smoothing_trend=0.2,·optimized=False
185 )180 )
186 fcast1·=·fit1.forecast(5).rename("Holt's·linear·trend")181 fcast1·=·fit1.forecast(5).rename("Holt's·linear·trend")
187 fit2·=·Holt(air,·exponential=True,·initialization_method="estimated").fit(182 fit2·=·Holt(air,·exponential=True,·initialization_method="estimated").fit(
188 ····smoothing_level=0.8,·smoothing_trend=0.2,·optimized=False183 ····smoothing_level=0.8,·smoothing_trend=0.2,·optimized=False
189 )184 )
Offset 198, 24 lines modifiedOffset 193, 21 lines modified
198 plt.plot(fit1.fittedvalues,·color="blue")193 plt.plot(fit1.fittedvalues,·color="blue")
199 (line1,)·=·plt.plot(fcast1,·marker="o",·color="blue")194 (line1,)·=·plt.plot(fcast1,·marker="o",·color="blue")
200 plt.plot(fit2.fittedvalues,·color="red")195 plt.plot(fit2.fittedvalues,·color="red")
201 (line2,)·=·plt.plot(fcast2,·marker="o",·color="red")196 (line2,)·=·plt.plot(fcast2,·marker="o",·color="red")
202 plt.plot(fit3.fittedvalues,·color="green")197 plt.plot(fit3.fittedvalues,·color="green")
203 (line3,)·=·plt.plot(fcast3,·marker="o",·color="green")198 (line3,)·=·plt.plot(fcast3,·marker="o",·color="green")
204 plt.legend([line1,·line2,·line3],·[fcast1.name,·fcast2.name,·fcast3.name])199 plt.legend([line1,·line2,·line3],·[fcast1.name,·fcast2.name,·fcast3.name])
205 [4]: 
206 <matplotlib.legend.Legend·at·0xadde5de1e8ed> 
207 [../../../_images/examples_notebooks_generated_exponential_smoothing_8_1.png] 
208 *\x8**\x8**\x8**\x8*·S\x8Se\x8ea\x8as\x8so\x8on\x8na\x8al\x8ll\x8ly\x8y·a\x8ad\x8dj\x8ju\x8us\x8st\x8te\x8ed\x8d·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*200 *\x8**\x8**\x8**\x8*·S\x8Se\x8ea\x8as\x8so\x8on\x8na\x8al\x8ll\x8ly\x8y·a\x8ad\x8dj\x8ju\x8us\x8st\x8te\x8ed\x8d·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*
209 Lets·look·at·some·seasonally·adjusted·livestock·data.·We·fit·five·Holt’s201 Lets·look·at·some·seasonally·adjusted·livestock·data.·We·fit·five·Holt’s
210 models.·The·below·table·allows·us·to·compare·results·when·we·use·exponential202 models.·The·below·table·allows·us·to·compare·results·when·we·use·exponential
211 versus·additive·and·damped·versus·non-damped.203 versus·additive·and·damped·versus·non-damped.
212 Note:·fit4·does·not·allow·the·parameter·\(\phi\)·to·be·optimized·by·providing·a204 Note:·fit4·does·not·allow·the·parameter·\(\phi\)·to·be·optimized·by·providing·a
213 fixed·value·of·\(\phi=0.98\)205 fixed·value·of·\(\phi=0.98\)
214 [5]:206 [·]:
215 fit1·=·SimpleExpSmoothing(livestock2,·initialization_method="estimated").fit()207 fit1·=·SimpleExpSmoothing(livestock2,·initialization_method="estimated").fit()
216 fit2·=·Holt(livestock2,·initialization_method="estimated").fit()208 fit2·=·Holt(livestock2,·initialization_method="estimated").fit()
217 fit3·=·Holt(livestock2,·exponential=True,209 fit3·=·Holt(livestock2,·exponential=True,
218 initialization_method="estimated").fit()210 initialization_method="estimated").fit()
219 fit4·=·Holt(livestock2,·damped_trend=True,211 fit4·=·Holt(livestock2,·damped_trend=True,
220 initialization_method="estimated").fit(212 initialization_method="estimated").fit(
221 ····damping_trend=0.98213 ····damping_trend=0.98
Offset 237, 45 lines modifiedOffset 229, 32 lines modified
237 )229 )
238 results["SES"]·=·[fit1.params[p]·for·p·in·params]·+·[fit1.sse]230 results["SES"]·=·[fit1.params[p]·for·p·in·params]·+·[fit1.sse]
239 results["Holt's"]·=·[fit2.params[p]·for·p·in·params]·+·[fit2.sse]231 results["Holt's"]·=·[fit2.params[p]·for·p·in·params]·+·[fit2.sse]
240 results["Exponential"]·=·[fit3.params[p]·for·p·in·params]·+·[fit3.sse]232 results["Exponential"]·=·[fit3.params[p]·for·p·in·params]·+·[fit3.sse]
241 results["Additive"]·=·[fit4.params[p]·for·p·in·params]·+·[fit4.sse]233 results["Additive"]·=·[fit4.params[p]·for·p·in·params]·+·[fit4.sse]
242 results["Multiplicative"]·=·[fit5.params[p]·for·p·in·params]·+·[fit5.sse]234 results["Multiplicative"]·=·[fit5.params[p]·for·p·in·params]·+·[fit5.sse]
243 results235 results
244 [5]: 
245 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
246 |_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8S\x8S_\x8E\x8E_\x8S\x8S_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8H\x8H_\x8o\x8o_\x8l\x8l_\x8t\x8t_\x8'\x8'_\x8s\x8s_\x8|_\x8E\x8E_\x8x\x8x_\x8p\x8p_\x8o\x8o_\x8n\x8n_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8i\x8i_\x8a\x8a_\x8l\x8l_\x8|_\x8·_\x8·_\x8·_\x8A\x8A_\x8d\x8d_\x8d\x8d_\x8i\x8i_\x8t\x8t_\x8i\x8i_\x8v\x8v_\x8e\x8e_\x8|_\x8M\x8M_\x8u\x8u_\x8l\x8l_\x8t\x8t_\x8i\x8i_\x8p\x8p_\x8l\x8l_\x8i\x8i_\x8c\x8c_\x8a\x8a_\x8t\x8t_\x8i\x8i_\x8v\x8v_\x8e\x8e| 
247 |_\x8$\x8$_\x8\\x8\_\x8a\x8a_\x8l\x8l_\x8p\x8p_\x8h\x8h_\x8a\x8a_\x8$\x8$_\x8|_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x89_\x87_\x84_\x83_\x80_\x86_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x89_\x87_\x87_\x86_\x83_\x83_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x89_\x87_\x88_\x88_\x84_\x88_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x89_\x87_\x84_\x89_\x81_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
248 |_\x8$\x8$_\x8\\x8\_\x8b\x8b_\x8e\x8e_\x8t\x8t_\x8a\x8a_\x8$\x8$_\x8·_\x8|_\x8N_\x8a_\x8N_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
249 |_\x8$\x8$_\x8\\x8\_\x8p\x8p_\x8h\x8h_\x8i\x8i_\x8$\x8$_\x8·_\x8·_\x8|_\x8N_\x8a_\x8N_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8N_\x8a_\x8N_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8N_\x8a_\x8N_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x89_\x88_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x89_\x88_\x81_\x86_\x84_\x86_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
250 |_\x8$\x8$_\x8l\x8l_\x8_\x8__\x80\x80_\x8$\x8$_\x8·_\x8·_\x8·_\x8|_\x82_\x86_\x83_\x8._\x89_\x81_\x87_\x86_\x88_\x89_\x8·_\x8|_\x82_\x85_\x88_\x8._\x88_\x88_\x82_\x85_\x82_\x89_\x8·_\x8|_\x82_\x86_\x80_\x8._\x83_\x84_\x81_\x84_\x87_\x88_\x8·_\x8|_\x82_\x85_\x87_\x8._\x83_\x85_\x87_\x86_\x84_\x80_\x8·_\x8|_\x82_\x85_\x88_\x8._\x89_\x85_\x81_\x88_\x82_\x84_\x8·_\x8·_\x8·_\x8·| 
251 |_\x8$\x8$_\x8b\x8b_\x8_\x8__\x80\x80_\x8$\x8$_\x8·_\x8·_\x8·_\x8|_\x8N_\x8a_\x8N_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x81_\x80_\x87_\x89_\x85_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x81_\x83_\x87_\x88_\x80_\x8·_\x8·_\x8·_\x8|_\x86_\x8._\x86_\x84_\x84_\x85_\x83_\x87_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x83_\x88_\x81_\x84_\x84_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
252 |_\x8S\x8S_\x8S\x8S_\x8E\x8E_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x86_\x87_\x86_\x81_\x8._\x83_\x85_\x80_\x82_\x83_\x85_\x8|_\x86_\x80_\x80_\x84_\x8._\x81_\x83_\x88_\x82_\x80_\x80_\x8|_\x86_\x81_\x80_\x84_\x8._\x81_\x89_\x84_\x87_\x84_\x86_\x8|_\x86_\x80_\x83_\x86_\x8._\x85_\x85_\x85_\x80_\x80_\x84_\x8|_\x86_\x80_\x88_\x81_\x8._\x89_\x89_\x85_\x80_\x84_\x85_\x8·_\x8·_\x8·| 
253 *\x8**\x8**\x8**\x8*·P\x8Pl\x8lo\x8ot\x8ts\x8s·o\x8of\x8f·S\x8Se\x8ea\x8as\x8so\x8on\x8na\x8al\x8ll\x8ly\x8y·A\x8Ad\x8dj\x8ju\x8us\x8st\x8te\x8ed\x8d·D\x8Da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*236 *\x8**\x8**\x8**\x8*·P\x8Pl\x8lo\x8ot\x8ts\x8s·o\x8of\x8f·S\x8Se\x8ea\x8as\x8so\x8on\x8na\x8al\x8ll\x8ly\x8y·A\x8Ad\x8dj\x8ju\x8us\x8st\x8te\x8ed\x8d·D\x8Da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*
254 The·following·plots·allow·us·to·evaluate·the·level·and·slope/trend·components237 The·following·plots·allow·us·to·evaluate·the·level·and·slope/trend·components
255 of·the·above·table’s·fits.238 of·the·above·table’s·fits.
256 [6]:239 [·]:
257 for·fit·in·[fit2,·fit4]:240 for·fit·in·[fit2,·fit4]:
258 ····pd.DataFrame(np.c_[fit.level,·fit.trend]).rename(241 ····pd.DataFrame(np.c_[fit.level,·fit.trend]).rename(
259 ········columns={0:·"level",·1:·"slope"}242 ········columns={0:·"level",·1:·"slope"}
260 ····).plot(subplots=True)243 ····).plot(subplots=True)
261 plt.show()244 plt.show()
262 print(245 print(
263 ····"Figure·7.4:·Level·and·slope·components·for·Holt’s·linear·trend·method·and246 ····"Figure·7.4:·Level·and·slope·components·for·Holt’s·linear·trend·method·and
264 the·additive·damped·trend·method."247 the·additive·damped·trend·method."
265 )248 )
266 [../../../_images/examples_notebooks_generated_exponential_smoothing_12_0.png] 
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63 <p>Since·version·0.5.0,·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>·allows·users·to·fit·statistical·models·using·R-style·formulas.·Internally,·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>·uses·the·<a·class="reference·external"·href="http://patsy.readthedocs.org/">patsy</a>·package·to·convert·formulas·and·data·to·the·matrices·that·are·used·in·model·fitting.·The·formula·framework·is·quite·powerful;·this·tutorial·only·scratches·the·surface.·A·full·description·of·the·formula·language·can·be·found·in·the·<code·class="docutils·literal·notranslate"><span·class="pre">patsy</span></code>·docs:</p>63 <p>Since·version·0.5.0,·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>·allows·users·to·fit·statistical·models·using·R-style·formulas.·Internally,·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>·uses·the·<a·class="reference·external"·href="http://patsy.readthedocs.org/">patsy</a>·package·to·convert·formulas·and·data·to·the·matrices·that·are·used·in·model·fitting.·The·formula·framework·is·quite·powerful;·this·tutorial·only·scratches·the·surface.·A·full·description·of·the·formula·language·can·be·found·in·the·<code·class="docutils·literal·notranslate"><span·class="pre">patsy</span></code>·docs:</p>
64 <ul·class="simple">64 <ul·class="simple">
65 <li><p><a·class="reference·external"·href="http://patsy.readthedocs.org/">Patsy·formula·language·description</a></p></li>65 <li><p><a·class="reference·external"·href="http://patsy.readthedocs.org/">Patsy·formula·language·description</a></p></li>
66 </ul>66 </ul>
67 <section·id="Loading-modules-and-functions">67 <section·id="Loading-modules-and-functions">
68 <h2>Loading·modules·and·functions<a·class="headerlink"·href="#Loading-modules-and-functions"·title="Link·to·this·heading">¶</a></h2>68 <h2>Loading·modules·and·functions<a·class="headerlink"·href="#Loading-modules-and-functions"·title="Link·to·this·heading">¶</a></h2>
69 <div·class="nbinput·nblast·docutils·container">69 <div·class="nbinput·nblast·docutils·container">
70 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:70 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
71 </pre></div>71 </pre></div>
72 </div>72 </div>
73 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>··<span·class="c1">#·noqa:F401··needed·in·namespace·for·patsy</span>73 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>··<span·class="c1">#·noqa:F401··needed·in·namespace·for·patsy</span>
74 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>74 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
75 </pre></div>75 </pre></div>
76 </div>76 </div>
77 </div>77 </div>
78 <section·id="Import-convention">78 <section·id="Import-convention">
79 <h3>Import·convention<a·class="headerlink"·href="#Import-convention"·title="Link·to·this·heading">¶</a></h3>79 <h3>Import·convention<a·class="headerlink"·href="#Import-convention"·title="Link·to·this·heading">¶</a></h3>
80 <p>You·can·import·explicitly·from·statsmodels.formula.api</p>80 <p>You·can·import·explicitly·from·statsmodels.formula.api</p>
81 <div·class="nbinput·nblast·docutils·container">81 <div·class="nbinput·nblast·docutils·container">
82 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:82 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
83 </pre></div>83 </pre></div>
84 </div>84 </div>
85 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="kn">import</span>·<span·class="n">ols</span>85 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="kn">import</span>·<span·class="n">ols</span>
86 </pre></div>86 </pre></div>
87 </div>87 </div>
88 </div>88 </div>
89 <p>Alternatively,·you·can·just·use·the·<code·class="docutils·literal·notranslate"><span·class="pre">formula</span></code>·namespace·of·the·main·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.api</span></code>.</p>89 <p>Alternatively,·you·can·just·use·the·<code·class="docutils·literal·notranslate"><span·class="pre">formula</span></code>·namespace·of·the·main·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.api</span></code>.</p>
90 <div·class="nbinput·docutils·container">90 <div·class="nbinput·nblast·docutils·container">
91 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:91 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
92 </pre></div>92 </pre></div>
93 </div>93 </div>
94 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">sm</span><span·class="o">.</span><span·class="n">formula</span><span·class="o">.</span><span·class="n">ols</span>94 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">sm</span><span·class="o">.</span><span·class="n">formula</span><span·class="o">.</span><span·class="n">ols</span>
95 </pre></div>95 </pre></div>
96 </div>96 </div>
97 </div>97 </div>
98 <div·class="nboutput·nblast·docutils·container"> 
99 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]: 
100 </pre></div> 
101 </div> 
102 <div·class="output_area·docutils·container"> 
103 <div·class="highlight"><pre> 
104 &lt;bound·method·Model.from_formula·of·&lt;class·&#39;statsmodels.regression.linear_model.OLS&#39;&gt;&gt; 
105 </pre></div></div> 
106 </div> 
107 <p>Or·you·can·use·the·following·convention</p>98 <p>Or·you·can·use·the·following·convention</p>
108 <div·class="nbinput·nblast·docutils·container">99 <div·class="nbinput·nblast·docutils·container">
109 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:100 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
110 </pre></div>101 </pre></div>
111 </div>102 </div>
112 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="k">as</span>·<span·class="nn">smf</span>103 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="k">as</span>·<span·class="nn">smf</span>
113 </pre></div>104 </pre></div>
114 </div>105 </div>
115 </div>106 </div>
116 <p>These·names·are·just·a·convenient·way·to·get·access·to·each·model’s·<code·class="docutils·literal·notranslate"><span·class="pre">from_formula</span></code>·classmethod.·See,·for·instance</p>107 <p>These·names·are·just·a·convenient·way·to·get·access·to·each·model’s·<code·class="docutils·literal·notranslate"><span·class="pre">from_formula</span></code>·classmethod.·See,·for·instance</p>
117 <div·class="nbinput·docutils·container">108 <div·class="nbinput·nblast·docutils·container">
118 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:109 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
119 </pre></div>110 </pre></div>
120 </div>111 </div>
121 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">sm</span><span·class="o">.</span><span·class="n">OLS</span><span·class="o">.</span><span·class="n">from_formula</span>112 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">sm</span><span·class="o">.</span><span·class="n">OLS</span><span·class="o">.</span><span·class="n">from_formula</span>
122 </pre></div>113 </pre></div>
123 </div>114 </div>
124 </div>115 </div>
125 <div·class="nboutput·nblast·docutils·container"> 
126 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]: 
127 </pre></div> 
128 </div> 
129 <div·class="output_area·docutils·container"> 
130 <div·class="highlight"><pre> 
131 &lt;bound·method·Model.from_formula·of·&lt;class·&#39;statsmodels.regression.linear_model.OLS&#39;&gt;&gt; 
132 </pre></div></div> 
133 </div> 
134 <p>All·of·the·lower·case·models·accept·<code·class="docutils·literal·notranslate"><span·class="pre">formula</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">data</span></code>·arguments,·whereas·upper·case·ones·take·<code·class="docutils·literal·notranslate"><span·class="pre">endog</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">exog</span></code>·design·matrices.·<code·class="docutils·literal·notranslate"><span·class="pre">formula</span></code>·accepts·a·string·which·describes·the·model·in·terms·of·a·<code·class="docutils·literal·notranslate"><span·class="pre">patsy</span></code>·formula.·<code·class="docutils·literal·notranslate"><span·class="pre">data</span></code>·takes·a·<a·class="reference·external"·href="https://pandas.pydata.org/">pandas</a>·data·frame·or·any·other·data·structure·that·defines·a·<code·class="docutils·literal·notranslate"><span·class="pre">__getitem__</span></code>·for·variable·names·like·a·structured·array·or·a·dictionary·of·variables.</p>116 <p>All·of·the·lower·case·models·accept·<code·class="docutils·literal·notranslate"><span·class="pre">formula</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">data</span></code>·arguments,·whereas·upper·case·ones·take·<code·class="docutils·literal·notranslate"><span·class="pre">endog</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">exog</span></code>·design·matrices.·<code·class="docutils·literal·notranslate"><span·class="pre">formula</span></code>·accepts·a·string·which·describes·the·model·in·terms·of·a·<code·class="docutils·literal·notranslate"><span·class="pre">patsy</span></code>·formula.·<code·class="docutils·literal·notranslate"><span·class="pre">data</span></code>·takes·a·<a·class="reference·external"·href="https://pandas.pydata.org/">pandas</a>·data·frame·or·any·other·data·structure·that·defines·a·<code·class="docutils·literal·notranslate"><span·class="pre">__getitem__</span></code>·for·variable·names·like·a·structured·array·or·a·dictionary·of·variables.</p>
135 <p><code·class="docutils·literal·notranslate"><span·class="pre">dir(sm.formula)</span></code>·will·print·a·list·of·available·models.</p>117 <p><code·class="docutils·literal·notranslate"><span·class="pre">dir(sm.formula)</span></code>·will·print·a·list·of·available·models.</p>
136 <p>Formula-compatible·models·have·the·following·generic·call·signature:·<code·class="docutils·literal·notranslate"><span·class="pre">(formula,</span>·<span·class="pre">data,</span>·<span·class="pre">subset=None,</span>·<span·class="pre">*args,</span>·<span·class="pre">**kwargs)</span></code></p>118 <p>Formula-compatible·models·have·the·following·generic·call·signature:·<code·class="docutils·literal·notranslate"><span·class="pre">(formula,</span>·<span·class="pre">data,</span>·<span·class="pre">subset=None,</span>·<span·class="pre">*args,</span>·<span·class="pre">**kwargs)</span></code></p>
137 </section>119 </section>
138 </section>120 </section>
139 <section·id="OLS-regression-using-formulas">121 <section·id="OLS-regression-using-formulas">
140 <h2>OLS·regression·using·formulas<a·class="headerlink"·href="#OLS-regression-using-formulas"·title="Link·to·this·heading">¶</a></h2>122 <h2>OLS·regression·using·formulas<a·class="headerlink"·href="#OLS-regression-using-formulas"·title="Link·to·this·heading">¶</a></h2>
141 <p>To·begin,·we·fit·the·linear·model·described·on·the·<a·class="reference·external"·href="./regression_diagnostics.html">Getting·Started</a>·page.·Download·the·data,·subset·columns,·and·list-wise·delete·to·remove·missing·observations:</p>123 <p>To·begin,·we·fit·the·linear·model·described·on·the·<a·class="reference·external"·href="./regression_diagnostics.html">Getting·Started</a>·page.·Download·the·data,·subset·columns,·and·list-wise·delete·to·remove·missing·observations:</p>
142 <div·class="nbinput·nblast·docutils·container">124 <div·class="nbinput·nblast·docutils·container">
143 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:125 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
144 </pre></div>126 </pre></div>
145 </div>127 </div>
146 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">get_rdataset</span><span·class="p">(</span><span·class="s2">&quot;Guerry&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;HistData&quot;</span><span·class="p">,</span>·<span·class="n">cache</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>128 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">get_rdataset</span><span·class="p">(</span><span·class="s2">&quot;Guerry&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;HistData&quot;</span><span·class="p">,</span>·<span·class="n">cache</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>
147 </pre></div>129 </pre></div>
148 </div>130 </div>
149 </div>131 </div>
150 <div·class="nbinput·docutils·container">132 <div·class="nbinput·nblast·docutils·container">
151 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:133 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
152 </pre></div>134 </pre></div>
153 </div>135 </div>
154 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">dta</span><span·class="o">.</span><span·class="n">data</span><span·class="p">[[</span><span·class="s2">&quot;Lottery&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Literacy&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Wealth&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Region&quot;</span><span·class="p">]]</span><span·class="o">.</span><span·class="n">dropna</span><span·class="p">()</span>136 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">dta</span><span·class="o">.</span><span·class="n">data</span><span·class="p">[[</span><span·class="s2">&quot;Lottery&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Literacy&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Wealth&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Region&quot;</span><span·class="p">]]</span><span·class="o">.</span><span·class="n">dropna</span><span·class="p">()</span>
155 <span·class="n">df</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>137 <span·class="n">df</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>
156 </pre></div>138 </pre></div>
157 </div>139 </div>
158 </div>140 </div>
159 <div·class="nboutput·nblast·docutils·container"> 
160 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]: 
161 </pre></div> 
162 </div> 
163 <div·class="output_area·rendered_html·docutils·container"> 
164 <div> 
165 <style·scoped> 
166 ····.dataframe·tbody·tr·th:only-of-type·{ 
167 ········vertical-align:·middle; 
168 ····} 
  
169 ····.dataframe·tbody·tr·th·{ 
170 ········vertical-align:·top; 
171 ····} 
  
172 ····.dataframe·thead·th·{ 
173 ········text-align:·right; 
174 ····} 
175 </style> 
176 <table·border="1"·class="dataframe"> 
177 ··<thead> 
178 ····<tr·style="text-align:·right;"> 
179 ······<th></th> 
180 ······<th>Lottery</th> 
181 ······<th>Literacy</th> 
182 ······<th>Wealth</th> 
183 ······<th>Region</th> 
184 ····</tr> 
185 ··</thead> 
186 ··<tbody> 
187 ····<tr> 
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10 Since·version·0.5.0,·statsmodels·allows·users·to·fit·statistical·models·using10 Since·version·0.5.0,·statsmodels·allows·users·to·fit·statistical·models·using
11 R-style·formulas.·Internally,·statsmodels·uses·the·_\x8p_\x8a_\x8t_\x8s_\x8y·package·to·convert11 R-style·formulas.·Internally,·statsmodels·uses·the·_\x8p_\x8a_\x8t_\x8s_\x8y·package·to·convert
12 formulas·and·data·to·the·matrices·that·are·used·in·model·fitting.·The·formula12 formulas·and·data·to·the·matrices·that·are·used·in·model·fitting.·The·formula
13 framework·is·quite·powerful;·this·tutorial·only·scratches·the·surface.·A·full13 framework·is·quite·powerful;·this·tutorial·only·scratches·the·surface.·A·full
14 description·of·the·formula·language·can·be·found·in·the·patsy·docs:14 description·of·the·formula·language·can·be·found·in·the·patsy·docs:
15 ····*·_\x8P_\x8a_\x8t_\x8s_\x8y_\x8·_\x8f_\x8o_\x8r_\x8m_\x8u_\x8l_\x8a_\x8·_\x8l_\x8a_\x8n_\x8g_\x8u_\x8a_\x8g_\x8e_\x8·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8p_\x8t_\x8i_\x8o_\x8n15 ····*·_\x8P_\x8a_\x8t_\x8s_\x8y_\x8·_\x8f_\x8o_\x8r_\x8m_\x8u_\x8l_\x8a_\x8·_\x8l_\x8a_\x8n_\x8g_\x8u_\x8a_\x8g_\x8e_\x8·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8p_\x8t_\x8i_\x8o_\x8n
16 *\x8**\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8di\x8in\x8ng\x8g·m\x8mo\x8od\x8du\x8ul\x8le\x8es\x8s·a\x8an\x8nd\x8d·f\x8fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8di\x8in\x8ng\x8g·m\x8mo\x8od\x8du\x8ul\x8le\x8es\x8s·a\x8an\x8nd\x8d·f\x8fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
17 [1]:17 [·]:
18 import·numpy·as·np··#·noqa:F401··needed·in·namespace·for·patsy18 import·numpy·as·np··#·noqa:F401··needed·in·namespace·for·patsy
19 import·statsmodels.api·as·sm19 import·statsmodels.api·as·sm
20 *\x8**\x8**\x8**\x8*·I\x8Im\x8mp\x8po\x8or\x8rt\x8t·c\x8co\x8on\x8nv\x8ve\x8en\x8nt\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8*·I\x8Im\x8mp\x8po\x8or\x8rt\x8t·c\x8co\x8on\x8nv\x8ve\x8en\x8nt\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8*
21 You·can·import·explicitly·from·statsmodels.formula.api21 You·can·import·explicitly·from·statsmodels.formula.api
22 [2]:22 [·]:
23 from·statsmodels.formula.api·import·ols23 from·statsmodels.formula.api·import·ols
24 Alternatively,·you·can·just·use·the·formula·namespace·of·the·main24 Alternatively,·you·can·just·use·the·formula·namespace·of·the·main
25 statsmodels.api.25 statsmodels.api.
26 [3]:26 [·]:
27 sm.formula.ols27 sm.formula.ols
28 [3]: 
29 <bound·method·Model.from_formula·of·<class 
30 'statsmodels.regression.linear_model.OLS'>> 
31 Or·you·can·use·the·following·convention28 Or·you·can·use·the·following·convention
32 [4]:29 [·]:
33 import·statsmodels.formula.api·as·smf30 import·statsmodels.formula.api·as·smf
34 These·names·are·just·a·convenient·way·to·get·access·to·each·model’s31 These·names·are·just·a·convenient·way·to·get·access·to·each·model’s
35 from_formula·classmethod.·See,·for·instance32 from_formula·classmethod.·See,·for·instance
36 [5]:33 [·]:
37 sm.OLS.from_formula34 sm.OLS.from_formula
38 [5]: 
39 <bound·method·Model.from_formula·of·<class 
40 'statsmodels.regression.linear_model.OLS'>> 
41 All·of·the·lower·case·models·accept·formula·and·data·arguments,·whereas·upper35 All·of·the·lower·case·models·accept·formula·and·data·arguments,·whereas·upper
42 case·ones·take·endog·and·exog·design·matrices.·formula·accepts·a·string·which36 case·ones·take·endog·and·exog·design·matrices.·formula·accepts·a·string·which
43 describes·the·model·in·terms·of·a·patsy·formula.·data·takes·a·_\x8p_\x8a_\x8n_\x8d_\x8a_\x8s·data·frame37 describes·the·model·in·terms·of·a·patsy·formula.·data·takes·a·_\x8p_\x8a_\x8n_\x8d_\x8a_\x8s·data·frame
44 or·any·other·data·structure·that·defines·a·__getitem__·for·variable·names·like38 or·any·other·data·structure·that·defines·a·__getitem__·for·variable·names·like
45 a·structured·array·or·a·dictionary·of·variables.39 a·structured·array·or·a·dictionary·of·variables.
46 dir(sm.formula)·will·print·a·list·of·available·models.40 dir(sm.formula)·will·print·a·list·of·available·models.
47 Formula-compatible·models·have·the·following·generic·call·signature:·(formula,41 Formula-compatible·models·have·the·following·generic·call·signature:·(formula,
48 data,·subset=None,·*args,·**kwargs)42 data,·subset=None,·*args,·**kwargs)
49 *\x8**\x8**\x8**\x8**\x8*·O\x8OL\x8LS\x8S·r\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·u\x8us\x8si\x8in\x8ng\x8g·f\x8fo\x8or\x8rm\x8mu\x8ul\x8la\x8as\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*43 *\x8**\x8**\x8**\x8**\x8*·O\x8OL\x8LS\x8S·r\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·u\x8us\x8si\x8in\x8ng\x8g·f\x8fo\x8or\x8rm\x8mu\x8ul\x8la\x8as\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
50 To·begin,·we·fit·the·linear·model·described·on·the·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8S_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d·page.44 To·begin,·we·fit·the·linear·model·described·on·the·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8S_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d·page.
51 Download·the·data,·subset·columns,·and·list-wise·delete·to·remove·missing45 Download·the·data,·subset·columns,·and·list-wise·delete·to·remove·missing
52 observations:46 observations:
53 [6]:47 [·]:
54 dta·=·sm.datasets.get_rdataset("Guerry",·"HistData",·cache=True)48 dta·=·sm.datasets.get_rdataset("Guerry",·"HistData",·cache=True)
55 [7]:49 [·]:
56 df·=·dta.data[["Lottery",·"Literacy",·"Wealth",·"Region"]].dropna()50 df·=·dta.data[["Lottery",·"Literacy",·"Wealth",·"Region"]].dropna()
57 df.head()51 df.head()
58 [7]: 
59 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
60 |_\x8·_\x8|_\x8L\x8L_\x8o\x8o_\x8t\x8t_\x8t\x8t_\x8e\x8e_\x8r\x8r_\x8y\x8y_\x8|_\x8L\x8L_\x8i\x8i_\x8t\x8t_\x8e\x8e_\x8r\x8r_\x8a\x8a_\x8c\x8c_\x8y\x8y_\x8|_\x8W\x8W_\x8e\x8e_\x8a\x8a_\x8l\x8l_\x8t\x8t_\x8h\x8h_\x8|_\x8R\x8R_\x8e\x8e_\x8g\x8g_\x8i\x8i_\x8o\x8o_\x8n\x8n| 
61 |_\x80\x80_\x8|_\x84_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x87_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x87_\x83_\x8·_\x8·_\x8·_\x8·_\x8|_\x8E_\x8·_\x8·_\x8·_\x8·_\x8·| 
62 |_\x81\x81_\x8|_\x83_\x88_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x85_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x82_\x8·_\x8·_\x8·_\x8·_\x8|_\x8N_\x8·_\x8·_\x8·_\x8·_\x8·| 
63 |_\x82\x82_\x8|_\x86_\x86_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x83_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x86_\x81_\x8·_\x8·_\x8·_\x8·_\x8|_\x8C_\x8·_\x8·_\x8·_\x8·_\x8·| 
64 |_\x83\x83_\x8|_\x88_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x84_\x86_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x87_\x86_\x8·_\x8·_\x8·_\x8·_\x8|_\x8E_\x8·_\x8·_\x8·_\x8·_\x8·| 
65 |_\x84\x84_\x8|_\x87_\x89_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x86_\x89_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x88_\x83_\x8·_\x8·_\x8·_\x8·_\x8|_\x8E_\x8·_\x8·_\x8·_\x8·_\x8·| 
66 Fit·the·model:52 Fit·the·model:
67 [8]:53 [·]:
68 mod·=·ols(formula="Lottery·~·Literacy·+·Wealth·+·Region",·data=df)54 mod·=·ols(formula="Lottery·~·Literacy·+·Wealth·+·Region",·data=df)
69 res·=·mod.fit()55 res·=·mod.fit()
70 print(res.summary())56 print(res.summary())
71 ····························OLS·Regression·Results 
72 ============================================================================== 
73 Dep.·Variable:················Lottery···R-squared:·······················0.338 
74 Model:····························OLS···Adj.·R-squared:··················0.287 
75 Method:·················Least·Squares···F-statistic:·····················6.636 
76 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········1.07e-05 
77 Time:························13:13:47···Log-Likelihood:················-375.30 
78 No.·Observations:··················85···AIC:·····························764.6 
79 Df·Residuals:······················78···BIC:·····························781.7 
80 Df·Model:···························6 
81 Covariance·Type:············nonrobust 
82 =============================================================================== 
83 ··················coef····std·err··········t······P>|t|······[0.025······0.975] 
84 ------------------------------------------------------------------------------- 
85 Intercept······38.6517······9.456······4.087······0.000······19.826······57.478 
86 Region[T.E]···-15.4278······9.727·····-1.586······0.117·····-34.793·······3.938 
87 Region[T.N]···-10.0170······9.260·····-1.082······0.283·····-28.453·······8.419 
88 Region[T.S]····-4.5483······7.279·····-0.625······0.534·····-19.039·······9.943 
89 Region[T.W]···-10.0913······7.196·····-1.402······0.165·····-24.418·······4.235 
90 Literacy·······-0.1858······0.210·····-0.886······0.378······-0.603·······0.232 
91 Wealth··········0.4515······0.103······4.390······0.000·······0.247·······0.656 
92 ============================================================================== 
93 Omnibus:························3.049···Durbin-Watson:···················1.785 
94 Prob(Omnibus):··················0.218···Jarque-Bera·(JB):················2.694 
95 Skew:··························-0.340···Prob(JB):························0.260 
96 Kurtosis:·······················2.454···Cond.·No.·························371. 
97 ============================================================================== 
  
98 Notes: 
99 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is 
100 correctly·specified. 
101 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8at\x8te\x8eg\x8go\x8or\x8ri\x8ic\x8ca\x8al\x8l·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*57 *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8at\x8te\x8eg\x8go\x8or\x8ri\x8ic\x8ca\x8al\x8l·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
102 Looking·at·the·summary·printed·above,·notice·that·patsy·determined·that58 Looking·at·the·summary·printed·above,·notice·that·patsy·determined·that
103 elements·of·R\x8Re\x8eg\x8gi\x8io\x8on\x8n·were·text·strings,·so·it·treated·R\x8Re\x8eg\x8gi\x8io\x8on\x8n·as·a·categorical59 elements·of·R\x8Re\x8eg\x8gi\x8io\x8on\x8n·were·text·strings,·so·it·treated·R\x8Re\x8eg\x8gi\x8io\x8on\x8n·as·a·categorical
104 variable.·patsy’s·default·is·also·to·include·an·intercept,·so·we·automatically60 variable.·patsy’s·default·is·also·to·include·an·intercept,·so·we·automatically
105 dropped·one·of·the·R\x8Re\x8eg\x8gi\x8io\x8on\x8n·categories.61 dropped·one·of·the·R\x8Re\x8eg\x8gi\x8io\x8on\x8n·categories.
106 If·R\x8Re\x8eg\x8gi\x8io\x8on\x8n·had·been·an·integer·variable·that·we·wanted·to·treat·explicitly·as62 If·R\x8Re\x8eg\x8gi\x8io\x8on\x8n·had·been·an·integer·variable·that·we·wanted·to·treat·explicitly·as
107 categorical,·we·could·have·done·so·by·using·the·C()·operator:63 categorical,·we·could·have·done·so·by·using·the·C()·operator:
108 [9]:64 [·]:
109 res·=·ols(formula="Lottery·~·Literacy·+·Wealth·+·C(Region)",·data=df).fit()65 res·=·ols(formula="Lottery·~·Literacy·+·Wealth·+·C(Region)",·data=df).fit()
110 print(res.params)66 print(res.params)
111 Intercept·········38.651655 
112 C(Region)[T.E]···-15.427785 
113 C(Region)[T.N]···-10.016961 
114 C(Region)[T.S]····-4.548257 
115 C(Region)[T.W]···-10.091276 
116 Literacy··········-0.185819 
117 Wealth·············0.451475 
118 dtype:·float64 
119 Patsy’s·mode·advanced·features·for·categorical·variables·are·discussed·in:67 Patsy’s·mode·advanced·features·for·categorical·variables·are·discussed·in:
120 _\x8P_\x8a_\x8t_\x8s_\x8y_\x8:_\x8·_\x8C_\x8o_\x8n_\x8t_\x8r_\x8a_\x8s_\x8t_\x8·_\x8C_\x8o_\x8d_\x8i_\x8n_\x8g_\x8·_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8s_\x8·_\x8f_\x8o_\x8r_\x8·_\x8c_\x8a_\x8t_\x8e_\x8g_\x8o_\x8r_\x8i_\x8c_\x8a_\x8l_\x8·_\x8v_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8s68 _\x8P_\x8a_\x8t_\x8s_\x8y_\x8:_\x8·_\x8C_\x8o_\x8n_\x8t_\x8r_\x8a_\x8s_\x8t_\x8·_\x8C_\x8o_\x8d_\x8i_\x8n_\x8g_\x8·_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8s_\x8·_\x8f_\x8o_\x8r_\x8·_\x8c_\x8a_\x8t_\x8e_\x8g_\x8o_\x8r_\x8i_\x8c_\x8a_\x8l_\x8·_\x8v_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8s
121 *\x8**\x8**\x8**\x8**\x8*·O\x8Op\x8pe\x8er\x8ra\x8at\x8to\x8or\x8rs\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*69 *\x8**\x8**\x8**\x8**\x8*·O\x8Op\x8pe\x8er\x8ra\x8at\x8to\x8or\x8rs\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
122 We·have·already·seen·that·“~”·separates·the·left-hand·side·of·the·model·from70 We·have·already·seen·that·“~”·separates·the·left-hand·side·of·the·model·from
123 the·right-hand·side,·and·that·“+”·adds·new·columns·to·the·design·matrix.71 the·right-hand·side,·and·that·“+”·adds·new·columns·to·the·design·matrix.
124 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8em\x8mo\x8ov\x8vi\x8in\x8ng\x8g·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*72 *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8em\x8mo\x8ov\x8vi\x8in\x8ng\x8g·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
125 The·“-”·sign·can·be·used·to·remove·columns/variables.·For·instance,·we·can73 The·“-”·sign·can·be·used·to·remove·columns/variables.·For·instance,·we·can
126 remove·the·intercept·from·a·model·by:74 remove·the·intercept·from·a·model·by:
127 [10]:75 [·]:
128 res·=·ols(formula="Lottery·~·Literacy·+·Wealth·+·C(Region)·-1·",·data=df).fit()76 res·=·ols(formula="Lottery·~·Literacy·+·Wealth·+·C(Region)·-1·",·data=df).fit()
129 print(res.params)77 print(res.params)
130 C(Region)[C]····38.651655 
131 C(Region)[E]····23.223870 
132 C(Region)[N]····28.634694 
133 C(Region)[S]····34.103399 
134 C(Region)[W]····28.560379 
135 Literacy········-0.185819 
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59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="GEE-nested-covariance-structure-simulation-study">61 ··<section·id="GEE-nested-covariance-structure-simulation-study">
62 <h1>GEE·nested·covariance·structure·simulation·study<a·class="headerlink"·href="#GEE-nested-covariance-structure-simulation-study"·title="Link·to·this·heading">¶</a></h1>62 <h1>GEE·nested·covariance·structure·simulation·study<a·class="headerlink"·href="#GEE-nested-covariance-structure-simulation-study"·title="Link·to·this·heading">¶</a></h1>
63 <p>This·notebook·is·a·simulation·study·that·illustrates·and·evaluates·the·performance·of·the·GEE·nested·covariance·structure.</p>63 <p>This·notebook·is·a·simulation·study·that·illustrates·and·evaluates·the·performance·of·the·GEE·nested·covariance·structure.</p>
64 <p>A·nested·covariance·structure·is·based·on·a·nested·sequence·of·groups,·or·“levels”.·The·top·level·in·the·hierarchy·is·defined·by·the·<code·class="docutils·literal·notranslate"><span·class="pre">groups</span></code>·argument·to·GEE.·Subsequent·levels·are·defined·by·the·<code·class="docutils·literal·notranslate"><span·class="pre">dep_data</span></code>·argument·to·GEE.</p>64 <p>A·nested·covariance·structure·is·based·on·a·nested·sequence·of·groups,·or·“levels”.·The·top·level·in·the·hierarchy·is·defined·by·the·<code·class="docutils·literal·notranslate"><span·class="pre">groups</span></code>·argument·to·GEE.·Subsequent·levels·are·defined·by·the·<code·class="docutils·literal·notranslate"><span·class="pre">dep_data</span></code>·argument·to·GEE.</p>
65 <div·class="nbinput·nblast·docutils·container">65 <div·class="nbinput·nblast·docutils·container">
66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
67 </pre></div>67 </pre></div>
68 </div>68 </div>
69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
70 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>70 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
71 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>71 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
72 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1234</span><span·class="p">)</span>·<span·class="c1">#·for·reproducibility</span>72 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1234</span><span·class="p">)</span>·<span·class="c1">#·for·reproducibility</span>
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 </div>75 </div>
76 <p>Set·the·number·of·covariates.</p>76 <p>Set·the·number·of·covariates.</p>
77 <div·class="nbinput·nblast·docutils·container">77 <div·class="nbinput·nblast·docutils·container">
78 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:78 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
79 </pre></div>79 </pre></div>
80 </div>80 </div>
81 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">p</span>·<span·class="o">=</span>·<span·class="mi">5</span>81 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">p</span>·<span·class="o">=</span>·<span·class="mi">5</span>
82 </pre></div>82 </pre></div>
83 </div>83 </div>
84 </div>84 </div>
85 <p>These·parameters·define·the·population·variance·for·each·level·of·grouping.</p>85 <p>These·parameters·define·the·population·variance·for·each·level·of·grouping.</p>
86 <div·class="nbinput·nblast·docutils·container">86 <div·class="nbinput·nblast·docutils·container">
87 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:87 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
88 </pre></div>88 </pre></div>
89 </div>89 </div>
90 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">groups_var</span>·<span·class="o">=</span>·<span·class="mi">1</span>90 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">groups_var</span>·<span·class="o">=</span>·<span·class="mi">1</span>
91 <span·class="n">level1_var</span>·<span·class="o">=</span>·<span·class="mi">2</span>91 <span·class="n">level1_var</span>·<span·class="o">=</span>·<span·class="mi">2</span>
92 <span·class="n">level2_var</span>·<span·class="o">=</span>·<span·class="mi">3</span>92 <span·class="n">level2_var</span>·<span·class="o">=</span>·<span·class="mi">3</span>
93 <span·class="n">resid_var</span>·<span·class="o">=</span>·<span·class="mi">4</span>93 <span·class="n">resid_var</span>·<span·class="o">=</span>·<span·class="mi">4</span>
94 </pre></div>94 </pre></div>
95 </div>95 </div>
96 </div>96 </div>
97 <p>Set·the·number·of·groups</p>97 <p>Set·the·number·of·groups</p>
98 <div·class="nbinput·nblast·docutils·container">98 <div·class="nbinput·nblast·docutils·container">
99 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:99 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
100 </pre></div>100 </pre></div>
101 </div>101 </div>
102 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">n_groups</span>·<span·class="o">=</span>·<span·class="mi">100</span>102 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">n_groups</span>·<span·class="o">=</span>·<span·class="mi">100</span>
103 </pre></div>103 </pre></div>
104 </div>104 </div>
105 </div>105 </div>
106 <p>Set·the·number·of·observations·at·each·level·of·grouping.·Here,·everything·is·balanced,·i.e.·within·a·level·every·group·has·the·same·size.</p>106 <p>Set·the·number·of·observations·at·each·level·of·grouping.·Here,·everything·is·balanced,·i.e.·within·a·level·every·group·has·the·same·size.</p>
107 <div·class="nbinput·nblast·docutils·container">107 <div·class="nbinput·nblast·docutils·container">
108 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:108 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
109 </pre></div>109 </pre></div>
110 </div>110 </div>
111 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">group_size</span>·<span·class="o">=</span>·<span·class="mi">20</span>111 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">group_size</span>·<span·class="o">=</span>·<span·class="mi">20</span>
112 <span·class="n">level1_size</span>·<span·class="o">=</span>·<span·class="mi">10</span>112 <span·class="n">level1_size</span>·<span·class="o">=</span>·<span·class="mi">10</span>
113 <span·class="n">level2_size</span>·<span·class="o">=</span>·<span·class="mi">5</span>113 <span·class="n">level2_size</span>·<span·class="o">=</span>·<span·class="mi">5</span>
114 </pre></div>114 </pre></div>
115 </div>115 </div>
116 </div>116 </div>
117 <p>Calculate·the·total·sample·size.</p>117 <p>Calculate·the·total·sample·size.</p>
118 <div·class="nbinput·nblast·docutils·container">118 <div·class="nbinput·nblast·docutils·container">
119 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:119 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
120 </pre></div>120 </pre></div>
121 </div>121 </div>
122 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">n</span>·<span·class="o">=</span>·<span·class="n">n_groups</span>·<span·class="o">*</span>·<span·class="n">group_size</span>·<span·class="o">*</span>·<span·class="n">level1_size</span>·<span·class="o">*</span>·<span·class="n">level2_size</span>122 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">n</span>·<span·class="o">=</span>·<span·class="n">n_groups</span>·<span·class="o">*</span>·<span·class="n">group_size</span>·<span·class="o">*</span>·<span·class="n">level1_size</span>·<span·class="o">*</span>·<span·class="n">level2_size</span>
123 </pre></div>123 </pre></div>
124 </div>124 </div>
125 </div>125 </div>
126 <p>Construct·the·design·matrix.</p>126 <p>Construct·the·design·matrix.</p>
127 <div·class="nbinput·nblast·docutils·container">127 <div·class="nbinput·nblast·docutils·container">
128 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:128 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
129 </pre></div>129 </pre></div>
130 </div>130 </div>
131 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">xmat</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="p">(</span><span·class="n">n</span><span·class="p">,</span>·<span·class="n">p</span><span·class="p">))</span>131 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">xmat</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="p">(</span><span·class="n">n</span><span·class="p">,</span>·<span·class="n">p</span><span·class="p">))</span>
132 </pre></div>132 </pre></div>
133 </div>133 </div>
134 </div>134 </div>
135 <p>Construct·labels·showing·which·group·each·observation·belongs·to·at·each·level.</p>135 <p>Construct·labels·showing·which·group·each·observation·belongs·to·at·each·level.</p>
136 <div·class="nbinput·nblast·docutils·container">136 <div·class="nbinput·nblast·docutils·container">
137 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[8]:137 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
138 </pre></div>138 </pre></div>
139 </div>139 </div>
140 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">groups_ix</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">kron</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">group_size</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">group_size</span><span·class="p">))</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>140 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">groups_ix</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">kron</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">group_size</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">group_size</span><span·class="p">))</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>
141 <span·class="n">level1_ix</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">kron</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">level1_size</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">level1_size</span><span·class="p">))</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>141 <span·class="n">level1_ix</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">kron</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">level1_size</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">level1_size</span><span·class="p">))</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>
142 <span·class="n">level2_ix</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">kron</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">level2_size</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">level2_size</span><span·class="p">))</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>142 <span·class="n">level2_ix</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">kron</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">level2_size</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">level2_size</span><span·class="p">))</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>
143 </pre></div>143 </pre></div>
144 </div>144 </div>
145 </div>145 </div>
146 <p>Simulate·the·random·effects.</p>146 <p>Simulate·the·random·effects.</p>
147 <div·class="nbinput·nblast·docutils·container">147 <div·class="nbinput·nblast·docutils·container">
148 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[9]:148 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
149 </pre></div>149 </pre></div>
150 </div>150 </div>
151 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">groups_re</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sqrt</span><span·class="p">(</span><span·class="n">groups_var</span><span·class="p">)</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">group_size</span><span·class="p">)</span>151 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">groups_re</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sqrt</span><span·class="p">(</span><span·class="n">groups_var</span><span·class="p">)</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">group_size</span><span·class="p">)</span>
152 <span·class="n">level1_re</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sqrt</span><span·class="p">(</span><span·class="n">level1_var</span><span·class="p">)</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">level1_size</span><span·class="p">)</span>152 <span·class="n">level1_re</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sqrt</span><span·class="p">(</span><span·class="n">level1_var</span><span·class="p">)</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">level1_size</span><span·class="p">)</span>
153 <span·class="n">level2_re</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sqrt</span><span·class="p">(</span><span·class="n">level2_var</span><span·class="p">)</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">level2_size</span><span·class="p">)</span>153 <span·class="n">level2_re</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sqrt</span><span·class="p">(</span><span·class="n">level2_var</span><span·class="p">)</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span>·<span·class="o">//</span>·<span·class="n">level2_size</span><span·class="p">)</span>
154 </pre></div>154 </pre></div>
155 </div>155 </div>
156 </div>156 </div>
157 <p>Simulate·the·response·variable.</p>157 <p>Simulate·the·response·variable.</p>
158 <div·class="nbinput·nblast·docutils·container">158 <div·class="nbinput·nblast·docutils·container">
159 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[10]:159 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
160 </pre></div>160 </pre></div>
161 </div>161 </div>
162 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">groups_re</span><span·class="p">[</span><span·class="n">groups_ix</span><span·class="p">]</span>·<span·class="o">+</span>·<span·class="n">level1_re</span><span·class="p">[</span><span·class="n">level1_ix</span><span·class="p">]</span>·<span·class="o">+</span>·<span·class="n">level2_re</span><span·class="p">[</span><span·class="n">level2_ix</span><span·class="p">]</span>162 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">groups_re</span><span·class="p">[</span><span·class="n">groups_ix</span><span·class="p">]</span>·<span·class="o">+</span>·<span·class="n">level1_re</span><span·class="p">[</span><span·class="n">level1_ix</span><span·class="p">]</span>·<span·class="o">+</span>·<span·class="n">level2_re</span><span·class="p">[</span><span·class="n">level2_ix</span><span·class="p">]</span>
163 <span·class="n">y</span>·<span·class="o">+=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sqrt</span><span·class="p">(</span><span·class="n">resid_var</span><span·class="p">)</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">)</span>163 <span·class="n">y</span>·<span·class="o">+=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sqrt</span><span·class="p">(</span><span·class="n">resid_var</span><span·class="p">)</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">)</span>
164 </pre></div>164 </pre></div>
165 </div>165 </div>
166 </div>166 </div>
167 <p>Put·everything·into·a·dataframe.</p>167 <p>Put·everything·into·a·dataframe.</p>
168 <div·class="nbinput·nblast·docutils·container">168 <div·class="nbinput·nblast·docutils·container">
169 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[11]:169 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
170 </pre></div>170 </pre></div>
171 </div>171 </div>
172 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">DataFrame</span><span·class="p">(</span><span·class="n">xmat</span><span·class="p">,</span>·<span·class="n">columns</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;x</span><span·class="si">%d</span><span·class="s2">&quot;</span>·<span·class="o">%</span>·<span·class="n">j</span>·<span·class="k">for</span>·<span·class="n">j</span>·<span·class="ow">in</span>·<span·class="nb">range</span><span·class="p">(</span><span·class="n">p</span><span·class="p">)])</span>172 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">DataFrame</span><span·class="p">(</span><span·class="n">xmat</span><span·class="p">,</span>·<span·class="n">columns</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;x</span><span·class="si">%d</span><span·class="s2">&quot;</span>·<span·class="o">%</span>·<span·class="n">j</span>·<span·class="k">for</span>·<span·class="n">j</span>·<span·class="ow">in</span>·<span·class="nb">range</span><span·class="p">(</span><span·class="n">p</span><span·class="p">)])</span>
173 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;y&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">y</span>·<span·class="o">+</span>·<span·class="n">xmat</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">]</span>·<span·class="o">-</span>·<span·class="n">xmat</span><span·class="p">[:,</span>·<span·class="mi">3</span><span·class="p">]</span>173 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;y&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">y</span>·<span·class="o">+</span>·<span·class="n">xmat</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">]</span>·<span·class="o">-</span>·<span·class="n">xmat</span><span·class="p">[:,</span>·<span·class="mi">3</span><span·class="p">]</span>
174 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;groups_ix&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">groups_ix</span>174 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;groups_ix&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">groups_ix</span>
175 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;level1_ix&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">level1_ix</span>175 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;level1_ix&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">level1_ix</span>
176 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;level2_ix&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">level2_ix</span>176 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;level2_ix&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">level2_ix</span>
177 </pre></div>177 </pre></div>
178 </div>178 </div>
179 </div>179 </div>
180 <p>Fit·the·model.</p>180 <p>Fit·the·model.</p>
181 <div·class="nbinput·nblast·docutils·container">181 <div·class="nbinput·nblast·docutils·container">
182 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[12]:182 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
183 </pre></div>183 </pre></div>
184 </div>184 </div>
185 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">cs</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">cov_struct</span><span·class="o">.</span><span·class="n">Nested</span><span·class="p">()</span>185 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">cs</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">cov_struct</span><span·class="o">.</span><span·class="n">Nested</span><span·class="p">()</span>
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8 ····*·GEE·nested·covariance·structure·simulation·study8 ····*·GEE·nested·covariance·structure·simulation·study
9 *\x8**\x8**\x8**\x8**\x8**\x8*·G\x8GE\x8EE\x8E·n\x8ne\x8es\x8st\x8te\x8ed\x8d·c\x8co\x8ov\x8va\x8ar\x8ri\x8ia\x8an\x8nc\x8ce\x8e·s\x8st\x8tr\x8ru\x8uc\x8ct\x8tu\x8ur\x8re\x8e·s\x8si\x8im\x8mu\x8ul\x8la\x8at\x8ti\x8io\x8on\x8n·s\x8st\x8tu\x8ud\x8dy\x8y_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·G\x8GE\x8EE\x8E·n\x8ne\x8es\x8st\x8te\x8ed\x8d·c\x8co\x8ov\x8va\x8ar\x8ri\x8ia\x8an\x8nc\x8ce\x8e·s\x8st\x8tr\x8ru\x8uc\x8ct\x8tu\x8ur\x8re\x8e·s\x8si\x8im\x8mu\x8ul\x8la\x8at\x8ti\x8io\x8on\x8n·s\x8st\x8tu\x8ud\x8dy\x8y_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 This·notebook·is·a·simulation·study·that·illustrates·and·evaluates·the10 This·notebook·is·a·simulation·study·that·illustrates·and·evaluates·the
11 performance·of·the·GEE·nested·covariance·structure.11 performance·of·the·GEE·nested·covariance·structure.
12 A·nested·covariance·structure·is·based·on·a·nested·sequence·of·groups,·or12 A·nested·covariance·structure·is·based·on·a·nested·sequence·of·groups,·or
13 “levels”.·The·top·level·in·the·hierarchy·is·defined·by·the·groups·argument·to13 “levels”.·The·top·level·in·the·hierarchy·is·defined·by·the·groups·argument·to
14 GEE.·Subsequent·levels·are·defined·by·the·dep_data·argument·to·GEE.14 GEE.·Subsequent·levels·are·defined·by·the·dep_data·argument·to·GEE.
15 [1]:15 [·]:
16 import·numpy·as·np16 import·numpy·as·np
17 import·pandas·as·pd17 import·pandas·as·pd
18 import·statsmodels.api·as·sm18 import·statsmodels.api·as·sm
19 np.random.seed(1234)·#·for·reproducibility19 np.random.seed(1234)·#·for·reproducibility
20 Set·the·number·of·covariates.20 Set·the·number·of·covariates.
21 [2]:21 [·]:
22 p·=·522 p·=·5
23 These·parameters·define·the·population·variance·for·each·level·of·grouping.23 These·parameters·define·the·population·variance·for·each·level·of·grouping.
24 [3]:24 [·]:
25 groups_var·=·125 groups_var·=·1
26 level1_var·=·226 level1_var·=·2
27 level2_var·=·327 level2_var·=·3
28 resid_var·=·428 resid_var·=·4
29 Set·the·number·of·groups29 Set·the·number·of·groups
30 [4]:30 [·]:
31 n_groups·=·10031 n_groups·=·100
32 Set·the·number·of·observations·at·each·level·of·grouping.·Here,·everything·is32 Set·the·number·of·observations·at·each·level·of·grouping.·Here,·everything·is
33 balanced,·i.e.·within·a·level·every·group·has·the·same·size.33 balanced,·i.e.·within·a·level·every·group·has·the·same·size.
34 [5]:34 [·]:
35 group_size·=·2035 group_size·=·20
36 level1_size·=·1036 level1_size·=·10
37 level2_size·=·537 level2_size·=·5
38 Calculate·the·total·sample·size.38 Calculate·the·total·sample·size.
39 [6]:39 [·]:
40 n·=·n_groups·*·group_size·*·level1_size·*·level2_size40 n·=·n_groups·*·group_size·*·level1_size·*·level2_size
41 Construct·the·design·matrix.41 Construct·the·design·matrix.
42 [7]:42 [·]:
43 xmat·=·np.random.normal(size=(n,·p))43 xmat·=·np.random.normal(size=(n,·p))
44 Construct·labels·showing·which·group·each·observation·belongs·to·at·each·level.44 Construct·labels·showing·which·group·each·observation·belongs·to·at·each·level.
45 [8]:45 [·]:
46 groups_ix·=·np.kron(np.arange(n·//·group_size),·np.ones(group_size)).astype46 groups_ix·=·np.kron(np.arange(n·//·group_size),·np.ones(group_size)).astype
47 (int)47 (int)
48 level1_ix·=·np.kron(np.arange(n·//·level1_size),·np.ones(level1_size)).astype48 level1_ix·=·np.kron(np.arange(n·//·level1_size),·np.ones(level1_size)).astype
49 (int)49 (int)
50 level2_ix·=·np.kron(np.arange(n·//·level2_size),·np.ones(level2_size)).astype50 level2_ix·=·np.kron(np.arange(n·//·level2_size),·np.ones(level2_size)).astype
51 (int)51 (int)
52 Simulate·the·random·effects.52 Simulate·the·random·effects.
53 [9]:53 [·]:
54 groups_re·=·np.sqrt(groups_var)·*·np.random.normal(size=n·//·group_size)54 groups_re·=·np.sqrt(groups_var)·*·np.random.normal(size=n·//·group_size)
55 level1_re·=·np.sqrt(level1_var)·*·np.random.normal(size=n·//·level1_size)55 level1_re·=·np.sqrt(level1_var)·*·np.random.normal(size=n·//·level1_size)
56 level2_re·=·np.sqrt(level2_var)·*·np.random.normal(size=n·//·level2_size)56 level2_re·=·np.sqrt(level2_var)·*·np.random.normal(size=n·//·level2_size)
57 Simulate·the·response·variable.57 Simulate·the·response·variable.
58 [10]:58 [·]:
59 y·=·groups_re[groups_ix]·+·level1_re[level1_ix]·+·level2_re[level2_ix]59 y·=·groups_re[groups_ix]·+·level1_re[level1_ix]·+·level2_re[level2_ix]
60 y·+=·np.sqrt(resid_var)·*·np.random.normal(size=n)60 y·+=·np.sqrt(resid_var)·*·np.random.normal(size=n)
61 Put·everything·into·a·dataframe.61 Put·everything·into·a·dataframe.
62 [11]:62 [·]:
63 df·=·pd.DataFrame(xmat,·columns=["x%d"·%·j·for·j·in·range(p)])63 df·=·pd.DataFrame(xmat,·columns=["x%d"·%·j·for·j·in·range(p)])
64 df["y"]·=·y·+·xmat[:,·0]·-·xmat[:,·3]64 df["y"]·=·y·+·xmat[:,·0]·-·xmat[:,·3]
65 df["groups_ix"]·=·groups_ix65 df["groups_ix"]·=·groups_ix
66 df["level1_ix"]·=·level1_ix66 df["level1_ix"]·=·level1_ix
67 df["level2_ix"]·=·level2_ix67 df["level2_ix"]·=·level2_ix
68 Fit·the·model.68 Fit·the·model.
69 [12]:69 [·]:
70 cs·=·sm.cov_struct.Nested()70 cs·=·sm.cov_struct.Nested()
71 dep_fml·=·"0·+·level1_ix·+·level2_ix"71 dep_fml·=·"0·+·level1_ix·+·level2_ix"
72 m·=·sm.GEE.from_formula(72 m·=·sm.GEE.from_formula(
73 ····"y·~·x0·+·x1·+·x2·+·x3·+·x4",73 ····"y·~·x0·+·x1·+·x2·+·x3·+·x4",
74 ····cov_struct=cs,74 ····cov_struct=cs,
75 ····dep_data=dep_fml,75 ····dep_data=dep_fml,
76 ····groups="groups_ix",76 ····groups="groups_ix",
77 ····data=df,77 ····data=df,
78 )78 )
79 r·=·m.fit()79 r·=·m.fit()
80 The·estimated·covariance·parameters·should·be·similar·to·groups_var,80 The·estimated·covariance·parameters·should·be·similar·to·groups_var,
81 level1_var,·etc.·as·defined·above.81 level1_var,·etc.·as·defined·above.
82 [13]:82 [·]:
83 r.cov_struct.summary()83 r.cov_struct.summary()
84 [13]: 
85 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
86 |_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8V\x8V_\x8a\x8a_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8n\x8n_\x8c\x8c_\x8e\x8e| 
87 |_\x8g\x8g_\x8r\x8r_\x8o\x8o_\x8u\x8u_\x8p\x8p_\x8s\x8s_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8|_\x81_\x8._\x81_\x83_\x88_\x86_\x87_\x85| 
88 |_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x81\x81_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8|_\x81_\x8._\x89_\x82_\x86_\x85_\x80_\x85| 
89 |_\x8l\x8l_\x8e\x8e_\x8v\x8v_\x8e\x8e_\x8l\x8l_\x82\x82_\x8_\x8__\x8i\x8i_\x8x\x8x_\x8|_\x83_\x8._\x80_\x85_\x84_\x87_\x88_\x88| 
90 |_\x8R\x8R_\x8e\x8e_\x8s\x8s_\x8i\x8i_\x8d\x8d_\x8u\x8u_\x8a\x8a_\x8l\x8l_\x8·_\x8|_\x84_\x8._\x80_\x80_\x86_\x89_\x89_\x84| 
91 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]84 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
92 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*85 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*
93 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s86 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s
94 ····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d87 ····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d
95 ····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e88 ····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e
96 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s89 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s
97 ····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e90 ····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e
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./usr/share/doc/python-statsmodels-doc/html/examples/notebooks/generated/gee_score_test_simulation.html
    
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60 ············60 ············
61 ··<section·id="GEE-score-tests">61 ··<section·id="GEE-score-tests">
62 <h1>GEE·score·tests<a·class="headerlink"·href="#GEE-score-tests"·title="Link·to·this·heading">¶</a></h1>62 <h1>GEE·score·tests<a·class="headerlink"·href="#GEE-score-tests"·title="Link·to·this·heading">¶</a></h1>
63 <p>This·notebook·uses·simulation·to·demonstrate·robust·GEE·score·tests.·These·tests·can·be·used·in·a·GEE·analysis·to·compare·nested·hypotheses·about·the·mean·structure.·The·tests·are·robust·to·miss-specification·of·the·working·correlation·model,·and·to·certain·forms·of·misspecification·of·the·variance·structure·(e.g.·as·captured·by·the·scale·parameter·in·a·quasi-Poisson·analysis).</p>63 <p>This·notebook·uses·simulation·to·demonstrate·robust·GEE·score·tests.·These·tests·can·be·used·in·a·GEE·analysis·to·compare·nested·hypotheses·about·the·mean·structure.·The·tests·are·robust·to·miss-specification·of·the·working·correlation·model,·and·to·certain·forms·of·misspecification·of·the·variance·structure·(e.g.·as·captured·by·the·scale·parameter·in·a·quasi-Poisson·analysis).</p>
64 <p>The·data·are·simulated·as·clusters,·where·there·is·dependence·within·but·not·between·clusters.·The·cluster-wise·dependence·is·induced·using·a·copula·approach.·The·data·marginally·follow·a·negative·binomial·(gamma/Poisson)·mixture.</p>64 <p>The·data·are·simulated·as·clusters,·where·there·is·dependence·within·but·not·between·clusters.·The·cluster-wise·dependence·is·induced·using·a·copula·approach.·The·data·marginally·follow·a·negative·binomial·(gamma/Poisson)·mixture.</p>
65 <p>The·level·and·power·of·the·tests·are·considered·below·to·assess·the·performance·of·the·tests.</p>65 <p>The·level·and·power·of·the·tests·are·considered·below·to·assess·the·performance·of·the·tests.</p>
66 <div·class="nbinput·nblast·docutils·container">66 <div·class="nbinput·nblast·docutils·container">
67 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:67 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>70 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
71 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>71 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
72 <span·class="kn">from</span>·<span·class="nn">scipy.stats.distributions</span>·<span·class="kn">import</span>·<span·class="n">norm</span><span·class="p">,</span>·<span·class="n">poisson</span>72 <span·class="kn">from</span>·<span·class="nn">scipy.stats.distributions</span>·<span·class="kn">import</span>·<span·class="n">norm</span><span·class="p">,</span>·<span·class="n">poisson</span>
73 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>73 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
74 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>74 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
75 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1234</span><span·class="p">)</span>·<span·class="c1">#·for·reproducibility</span>75 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1234</span><span·class="p">)</span>·<span·class="c1">#·for·reproducibility</span>
76 </pre></div>76 </pre></div>
77 </div>77 </div>
78 </div>78 </div>
79 <p>The·function·defined·in·the·following·cell·uses·a·copula·approach·to·simulate·correlated·random·values·that·marginally·follow·a·negative·binomial·distribution.·The·input·parameter·<code·class="docutils·literal·notranslate"><span·class="pre">u</span></code>·is·an·array·of·values·in·(0,·1).·The·elements·of·<code·class="docutils·literal·notranslate"><span·class="pre">u</span></code>·must·be·marginally·uniformly·distributed·on·(0,·1).·Correlation·in·<code·class="docutils·literal·notranslate"><span·class="pre">u</span></code>·will·induce·correlations·in·the·returned·negative·binomial·values.·The·array·parameter·<code·class="docutils·literal·notranslate"><span·class="pre">mu</span></code>·gives·the·marginal·means,·and·the·scalar·parameter·<code·class="docutils·literal·notranslate"><span·class="pre">scale</span></code>·defines·the·mean/variance79 <p>The·function·defined·in·the·following·cell·uses·a·copula·approach·to·simulate·correlated·random·values·that·marginally·follow·a·negative·binomial·distribution.·The·input·parameter·<code·class="docutils·literal·notranslate"><span·class="pre">u</span></code>·is·an·array·of·values·in·(0,·1).·The·elements·of·<code·class="docutils·literal·notranslate"><span·class="pre">u</span></code>·must·be·marginally·uniformly·distributed·on·(0,·1).·Correlation·in·<code·class="docutils·literal·notranslate"><span·class="pre">u</span></code>·will·induce·correlations·in·the·returned·negative·binomial·values.·The·array·parameter·<code·class="docutils·literal·notranslate"><span·class="pre">mu</span></code>·gives·the·marginal·means,·and·the·scalar·parameter·<code·class="docutils·literal·notranslate"><span·class="pre">scale</span></code>·defines·the·mean/variance
80 relationship·(the·variance·is·<code·class="docutils·literal·notranslate"><span·class="pre">scale</span></code>·times·the·mean).·The·lengths·of·<code·class="docutils·literal·notranslate"><span·class="pre">u</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">mu</span></code>·must·be·the·same.</p>80 relationship·(the·variance·is·<code·class="docutils·literal·notranslate"><span·class="pre">scale</span></code>·times·the·mean).·The·lengths·of·<code·class="docutils·literal·notranslate"><span·class="pre">u</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">mu</span></code>·must·be·the·same.</p>
81 <div·class="nbinput·nblast·docutils·container">81 <div·class="nbinput·nblast·docutils·container">
82 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:82 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
83 </pre></div>83 </pre></div>
84 </div>84 </div>
85 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">negbinom</span><span·class="p">(</span><span·class="n">u</span><span·class="p">,</span>·<span·class="n">mu</span><span·class="p">,</span>·<span·class="n">scale</span><span·class="p">):</span>85 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">negbinom</span><span·class="p">(</span><span·class="n">u</span><span·class="p">,</span>·<span·class="n">mu</span><span·class="p">,</span>·<span·class="n">scale</span><span·class="p">):</span>
86 ····<span·class="n">p</span>·<span·class="o">=</span>·<span·class="p">(</span><span·class="n">scale</span>·<span·class="o">-</span>·<span·class="mi">1</span><span·class="p">)</span>·<span·class="o">/</span>·<span·class="n">scale</span>86 ····<span·class="n">p</span>·<span·class="o">=</span>·<span·class="p">(</span><span·class="n">scale</span>·<span·class="o">-</span>·<span·class="mi">1</span><span·class="p">)</span>·<span·class="o">/</span>·<span·class="n">scale</span>
87 ····<span·class="n">r</span>·<span·class="o">=</span>·<span·class="n">mu</span>·<span·class="o">*</span>·<span·class="p">(</span><span·class="mi">1</span>·<span·class="o">-</span>·<span·class="n">p</span><span·class="p">)</span>·<span·class="o">/</span>·<span·class="n">p</span>87 ····<span·class="n">r</span>·<span·class="o">=</span>·<span·class="n">mu</span>·<span·class="o">*</span>·<span·class="p">(</span><span·class="mi">1</span>·<span·class="o">-</span>·<span·class="n">p</span><span·class="p">)</span>·<span·class="o">/</span>·<span·class="n">p</span>
88 ····<span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">gamma</span><span·class="p">(</span><span·class="n">r</span><span·class="p">,</span>·<span·class="n">p</span>·<span·class="o">/</span>·<span·class="p">(</span><span·class="mi">1</span>·<span·class="o">-</span>·<span·class="n">p</span><span·class="p">),</span>·<span·class="nb">len</span><span·class="p">(</span><span·class="n">u</span><span·class="p">))</span>88 ····<span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">gamma</span><span·class="p">(</span><span·class="n">r</span><span·class="p">,</span>·<span·class="n">p</span>·<span·class="o">/</span>·<span·class="p">(</span><span·class="mi">1</span>·<span·class="o">-</span>·<span·class="n">p</span><span·class="p">),</span>·<span·class="nb">len</span><span·class="p">(</span><span·class="n">u</span><span·class="p">))</span>
89 ····<span·class="k">return</span>·<span·class="n">poisson</span><span·class="o">.</span><span·class="n">ppf</span><span·class="p">(</span><span·class="n">u</span><span·class="p">,</span>·<span·class="n">mu</span><span·class="o">=</span><span·class="n">x</span><span·class="p">)</span>89 ····<span·class="k">return</span>·<span·class="n">poisson</span><span·class="o">.</span><span·class="n">ppf</span><span·class="p">(</span><span·class="n">u</span><span·class="p">,</span>·<span·class="n">mu</span><span·class="o">=</span><span·class="n">x</span><span·class="p">)</span>
90 </pre></div>90 </pre></div>
91 </div>91 </div>
92 </div>92 </div>
93 <p>Below·are·some·parameters·that·govern·the·data·used·in·the·simulation.</p>93 <p>Below·are·some·parameters·that·govern·the·data·used·in·the·simulation.</p>
94 <div·class="nbinput·nblast·docutils·container">94 <div·class="nbinput·nblast·docutils·container">
95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
96 </pre></div>96 </pre></div>
97 </div>97 </div>
98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Sample·size</span>98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Sample·size</span>
99 <span·class="n">n</span>·<span·class="o">=</span>·<span·class="mi">1000</span>99 <span·class="n">n</span>·<span·class="o">=</span>·<span·class="mi">1000</span>
  
100 <span·class="c1">#·Number·of·covariates·(including·intercept)·in·the·alternative·hypothesis·model</span>100 <span·class="c1">#·Number·of·covariates·(including·intercept)·in·the·alternative·hypothesis·model</span>
101 <span·class="n">p</span>·<span·class="o">=</span>·<span·class="mi">5</span>101 <span·class="n">p</span>·<span·class="o">=</span>·<span·class="mi">5</span>
Offset 110, 45 lines modifiedOffset 110, 45 lines modified
110 <span·class="c1">#·Group·indicators</span>110 <span·class="c1">#·Group·indicators</span>
111 <span·class="n">grp</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">kron</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n</span><span·class="o">/</span><span·class="n">m</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">m</span><span·class="p">))</span>111 <span·class="n">grp</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">kron</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n</span><span·class="o">/</span><span·class="n">m</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">m</span><span·class="p">))</span>
112 </pre></div>112 </pre></div>
113 </div>113 </div>
114 </div>114 </div>
115 <p>The·simulation·uses·a·fixed·design·matrix.</p>115 <p>The·simulation·uses·a·fixed·design·matrix.</p>
116 <div·class="nbinput·nblast·docutils·container">116 <div·class="nbinput·nblast·docutils·container">
117 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:117 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
118 </pre></div>118 </pre></div>
119 </div>119 </div>
120 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Build·a·design·matrix·for·the·alternative·(more·complex)·model</span>120 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Build·a·design·matrix·for·the·alternative·(more·complex)·model</span>
121 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="p">(</span><span·class="n">n</span><span·class="p">,</span>·<span·class="n">p</span><span·class="p">))</span>121 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="p">(</span><span·class="n">n</span><span·class="p">,</span>·<span·class="n">p</span><span·class="p">))</span>
122 <span·class="n">x</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="mi">1</span>122 <span·class="n">x</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="mi">1</span>
123 </pre></div>123 </pre></div>
124 </div>124 </div>
125 </div>125 </div>
126 <p>The·null·design·matrix·is·nested·in·the·alternative·design·matrix.·It·has·rank·two·less·than·the·alternative·design·matrix.</p>126 <p>The·null·design·matrix·is·nested·in·the·alternative·design·matrix.·It·has·rank·two·less·than·the·alternative·design·matrix.</p>
127 <div·class="nbinput·nblast·docutils·container">127 <div·class="nbinput·nblast·docutils·container">
128 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:128 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
129 </pre></div>129 </pre></div>
130 </div>130 </div>
131 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">x0</span>·<span·class="o">=</span>·<span·class="n">x</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">:</span><span·class="mi">3</span><span·class="p">]</span>131 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">x0</span>·<span·class="o">=</span>·<span·class="n">x</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">:</span><span·class="mi">3</span><span·class="p">]</span>
132 </pre></div>132 </pre></div>
133 </div>133 </div>
134 </div>134 </div>
135 <p>The·GEE·score·test·is·robust·to·dependence·and·overdispersion.·Here·we·set·the·overdispersion·parameter.·The·variance·of·the·negative·binomial·distribution·for·each·observation·is·equal·to·<code·class="docutils·literal·notranslate"><span·class="pre">scale</span></code>·times·its·mean·value.</p>135 <p>The·GEE·score·test·is·robust·to·dependence·and·overdispersion.·Here·we·set·the·overdispersion·parameter.·The·variance·of·the·negative·binomial·distribution·for·each·observation·is·equal·to·<code·class="docutils·literal·notranslate"><span·class="pre">scale</span></code>·times·its·mean·value.</p>
136 <div·class="nbinput·nblast·docutils·container">136 <div·class="nbinput·nblast·docutils·container">
137 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:137 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
138 </pre></div>138 </pre></div>
139 </div>139 </div>
140 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Scale·parameter·for·negative·binomial·distribution</span>140 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Scale·parameter·for·negative·binomial·distribution</span>
141 <span·class="n">scale</span>·<span·class="o">=</span>·<span·class="mi">10</span>141 <span·class="n">scale</span>·<span·class="o">=</span>·<span·class="mi">10</span>
142 </pre></div>142 </pre></div>
143 </div>143 </div>
144 </div>144 </div>
145 <p>In·the·next·cell,·we·set·up·the·mean·structures·for·the·null·and·alternative·models</p>145 <p>In·the·next·cell,·we·set·up·the·mean·structures·for·the·null·and·alternative·models</p>
146 <div·class="nbinput·nblast·docutils·container">146 <div·class="nbinput·nblast·docutils·container">
147 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:147 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
148 </pre></div>148 </pre></div>
149 </div>149 </div>
150 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·The·coefficients·used·to·define·the·linear·predictors</span>150 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·The·coefficients·used·to·define·the·linear·predictors</span>
151 <span·class="n">coeff</span>·<span·class="o">=</span>·<span·class="p">[[</span><span·class="mi">4</span><span·class="p">,</span>·<span·class="mf">0.4</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mf">0.2</span><span·class="p">],</span>·<span·class="p">[</span><span·class="mi">4</span><span·class="p">,</span>·<span·class="mf">0.4</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mf">0.2</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mf">0.04</span><span·class="p">]]</span>151 <span·class="n">coeff</span>·<span·class="o">=</span>·<span·class="p">[[</span><span·class="mi">4</span><span·class="p">,</span>·<span·class="mf">0.4</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mf">0.2</span><span·class="p">],</span>·<span·class="p">[</span><span·class="mi">4</span><span·class="p">,</span>·<span·class="mf">0.4</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mf">0.2</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mf">0.04</span><span·class="p">]]</span>
  
152 <span·class="c1">#·The·linear·predictors</span>152 <span·class="c1">#·The·linear·predictors</span>
153 <span·class="n">lp</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">np</span><span·class="o">.</span><span·class="n">dot</span><span·class="p">(</span><span·class="n">x0</span><span·class="p">,</span>·<span·class="n">coeff</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">]),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">dot</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">coeff</span><span·class="p">[</span><span·class="mi">1</span><span·class="p">])]</span>153 <span·class="n">lp</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">np</span><span·class="o">.</span><span·class="n">dot</span><span·class="p">(</span><span·class="n">x0</span><span·class="p">,</span>·<span·class="n">coeff</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">]),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">dot</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">coeff</span><span·class="p">[</span><span·class="mi">1</span><span·class="p">])]</span>
Offset 156, 15 lines modifiedOffset 156, 15 lines modified
156 <span·class="c1">#·The·mean·values</span>156 <span·class="c1">#·The·mean·values</span>
157 <span·class="n">mu</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">np</span><span·class="o">.</span><span·class="n">exp</span><span·class="p">(</span><span·class="n">lp</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">]),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">exp</span><span·class="p">(</span><span·class="n">lp</span><span·class="p">[</span><span·class="mi">1</span><span·class="p">])]</span>157 <span·class="n">mu</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">np</span><span·class="o">.</span><span·class="n">exp</span><span·class="p">(</span><span·class="n">lp</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">]),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">exp</span><span·class="p">(</span><span·class="n">lp</span><span·class="p">[</span><span·class="mi">1</span><span·class="p">])]</span>
158 </pre></div>158 </pre></div>
159 </div>159 </div>
160 </div>160 </div>
161 <p>Below·is·a·function·that·carries·out·the·simulation.</p>161 <p>Below·is·a·function·that·carries·out·the·simulation.</p>
162 <div·class="nbinput·nblast·docutils·container">162 <div·class="nbinput·nblast·docutils·container">
163 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[8]:163 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
164 </pre></div>164 </pre></div>
165 </div>165 </div>
166 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·hyp·=·0·is·the·null·hypothesis,·hyp·=·1·is·the·alternative·hypothesis.</span>166 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·hyp·=·0·is·the·null·hypothesis,·hyp·=·1·is·the·alternative·hypothesis.</span>
167 <span·class="c1">#·cov_struct·is·a·statsmodels·covariance·structure</span>167 <span·class="c1">#·cov_struct·is·a·statsmodels·covariance·structure</span>
168 <span·class="k">def</span>·<span·class="nf">dosim</span><span·class="p">(</span><span·class="n">hyp</span><span·class="p">,</span>·<span·class="n">cov_struct</span><span·class="o">=</span><span·class="kc">None</span><span·class="p">,</span>·<span·class="n">mcrep</span><span·class="o">=</span><span·class="mi">500</span><span·class="p">):</span>168 <span·class="k">def</span>·<span·class="nf">dosim</span><span·class="p">(</span><span·class="n">hyp</span><span·class="p">,</span>·<span·class="n">cov_struct</span><span·class="o">=</span><span·class="kc">None</span><span·class="p">,</span>·<span·class="n">mcrep</span><span·class="o">=</span><span·class="mi">500</span><span·class="p">):</span>
  
169 ····<span·class="c1">#·Storage·for·the·simulation·results</span>169 ····<span·class="c1">#·Storage·for·the·simulation·results</span>
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205 ····<span·class="n">rslt</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">np</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(</span><span·class="n">pv</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(</span><span·class="n">pv</span>·<span·class="o">&lt;</span>·<span·class="mf">0.1</span><span·class="p">)]</span>205 ····<span·class="n">rslt</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">np</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(</span><span·class="n">pv</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(</span><span·class="n">pv</span>·<span·class="o">&lt;</span>·<span·class="mf">0.1</span><span·class="p">)]</span>
  
206 ····<span·class="k">return</span>·<span·class="n">rslt</span><span·class="p">,</span>·<span·class="n">scales</span>206 ····<span·class="k">return</span>·<span·class="n">rslt</span><span·class="p">,</span>·<span·class="n">scales</span>
207 </pre></div>207 </pre></div>
208 </div>208 </div>
209 </div>209 </div>
210 <p>Run·the·simulation·using·the·independence·working·covariance·structure.·We·expect·the·mean·to·be·around·0·under·the·null·hypothesis,·and·much·lower·under·the·alternative·hypothesis.·Similarly,·we·expect·that·under·the·null·hypothesis,·around·10%·of·the·p-values·are·less·than·0.1,·and·a·much·greater·fraction·of·the·p-values·are·less·than·0.1·under·the·alternative·hypothesis.</p>210 <p>Run·the·simulation·using·the·independence·working·covariance·structure.·We·expect·the·mean·to·be·around·0·under·the·null·hypothesis,·and·much·lower·under·the·alternative·hypothesis.·Similarly,·we·expect·that·under·the·null·hypothesis,·around·10%·of·the·p-values·are·less·than·0.1,·and·a·much·greater·fraction·of·the·p-values·are·less·than·0.1·under·the·alternative·hypothesis.</p>
211 <div·class="nbinput·docutils·container">211 <div·class="nbinput·nblast·docutils·container">
212 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[9]:212 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
213 </pre></div>213 </pre></div>
214 </div>214 </div>
215 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">rslt</span><span·class="p">,</span>·<span·class="n">scales</span>·<span·class="o">=</span>·<span·class="p">[],</span>·<span·class="p">[]</span>215 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">rslt</span><span·class="p">,</span>·<span·class="n">scales</span>·<span·class="o">=</span>·<span·class="p">[],</span>·<span·class="p">[]</span>
  
216 <span·class="k">for</span>·<span·class="n">hyp</span>·<span·class="ow">in</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">1</span><span·class="p">:</span>216 <span·class="k">for</span>·<span·class="n">hyp</span>·<span·class="ow">in</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">1</span><span·class="p">:</span>
217 ····<span·class="n">s</span><span·class="p">,</span>·<span·class="n">t</span>·<span·class="o">=</span>·<span·class="n">dosim</span><span·class="p">(</span><span·class="n">hyp</span><span·class="p">,</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">cov_struct</span><span·class="o">.</span><span·class="n">Independence</span><span·class="p">())</span>217 ····<span·class="n">s</span><span·class="p">,</span>·<span·class="n">t</span>·<span·class="o">=</span>·<span·class="n">dosim</span><span·class="p">(</span><span·class="n">hyp</span><span·class="p">,</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">cov_struct</span><span·class="o">.</span><span·class="n">Independence</span><span·class="p">())</span>
218 ····<span·class="n">rslt</span><span·class="o">.</span><span·class="n">append</span><span·class="p">(</span><span·class="n">s</span><span·class="p">)</span>218 ····<span·class="n">rslt</span><span·class="o">.</span><span·class="n">append</span><span·class="p">(</span><span·class="n">s</span><span·class="p">)</span>
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222 <span·class="n">rslt</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">DataFrame</span><span·class="p">(</span><span·class="n">rslt</span><span·class="p">,</span>·<span·class="n">index</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;H0&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;H1&quot;</span><span·class="p">],</span>·<span·class="n">columns</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;Mean&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Prop(p&lt;0.1)&quot;</span><span·class="p">])</span>222 <span·class="n">rslt</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">DataFrame</span><span·class="p">(</span><span·class="n">rslt</span><span·class="p">,</span>·<span·class="n">index</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;H0&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;H1&quot;</span><span·class="p">],</span>·<span·class="n">columns</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;Mean&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Prop(p&lt;0.1)&quot;</span><span·class="p">])</span>
  
223 <span·class="nb">print</span><span·class="p">(</span><span·class="n">rslt</span><span·class="p">)</span>223 <span·class="nb">print</span><span·class="p">(</span><span·class="n">rslt</span><span·class="p">)</span>
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15 analysis).15 analysis).
16 The·data·are·simulated·as·clusters,·where·there·is·dependence·within·but·not16 The·data·are·simulated·as·clusters,·where·there·is·dependence·within·but·not
17 between·clusters.·The·cluster-wise·dependence·is·induced·using·a·copula17 between·clusters.·The·cluster-wise·dependence·is·induced·using·a·copula
18 approach.·The·data·marginally·follow·a·negative·binomial·(gamma/Poisson)18 approach.·The·data·marginally·follow·a·negative·binomial·(gamma/Poisson)
19 mixture.19 mixture.
20 The·level·and·power·of·the·tests·are·considered·below·to·assess·the·performance20 The·level·and·power·of·the·tests·are·considered·below·to·assess·the·performance
21 of·the·tests.21 of·the·tests.
22 [1]:22 [·]:
23 import·pandas·as·pd23 import·pandas·as·pd
24 import·numpy·as·np24 import·numpy·as·np
25 from·scipy.stats.distributions·import·norm,·poisson25 from·scipy.stats.distributions·import·norm,·poisson
26 import·statsmodels.api·as·sm26 import·statsmodels.api·as·sm
27 import·matplotlib.pyplot·as·plt27 import·matplotlib.pyplot·as·plt
28 np.random.seed(1234)·#·for·reproducibility28 np.random.seed(1234)·#·for·reproducibility
29 The·function·defined·in·the·following·cell·uses·a·copula·approach·to·simulate29 The·function·defined·in·the·following·cell·uses·a·copula·approach·to·simulate
30 correlated·random·values·that·marginally·follow·a·negative·binomial30 correlated·random·values·that·marginally·follow·a·negative·binomial
31 distribution.·The·input·parameter·u·is·an·array·of·values·in·(0,·1).·The31 distribution.·The·input·parameter·u·is·an·array·of·values·in·(0,·1).·The
32 elements·of·u·must·be·marginally·uniformly·distributed·on·(0,·1).·Correlation32 elements·of·u·must·be·marginally·uniformly·distributed·on·(0,·1).·Correlation
33 in·u·will·induce·correlations·in·the·returned·negative·binomial·values.·The33 in·u·will·induce·correlations·in·the·returned·negative·binomial·values.·The
34 array·parameter·mu·gives·the·marginal·means,·and·the·scalar·parameter·scale34 array·parameter·mu·gives·the·marginal·means,·and·the·scalar·parameter·scale
35 defines·the·mean/variance·relationship·(the·variance·is·scale·times·the·mean).35 defines·the·mean/variance·relationship·(the·variance·is·scale·times·the·mean).
36 The·lengths·of·u·and·mu·must·be·the·same.36 The·lengths·of·u·and·mu·must·be·the·same.
37 [2]:37 [·]:
38 def·negbinom(u,·mu,·scale):38 def·negbinom(u,·mu,·scale):
39 ····p·=·(scale·-·1)·/·scale39 ····p·=·(scale·-·1)·/·scale
40 ····r·=·mu·*·(1·-·p)·/·p40 ····r·=·mu·*·(1·-·p)·/·p
41 ····x·=·np.random.gamma(r,·p·/·(1·-·p),·len(u))41 ····x·=·np.random.gamma(r,·p·/·(1·-·p),·len(u))
42 ····return·poisson.ppf(u,·mu=x)42 ····return·poisson.ppf(u,·mu=x)
43 Below·are·some·parameters·that·govern·the·data·used·in·the·simulation.43 Below·are·some·parameters·that·govern·the·data·used·in·the·simulation.
44 [3]:44 [·]:
45 #·Sample·size45 #·Sample·size
46 n·=·100046 n·=·1000
  
47 #·Number·of·covariates·(including·intercept)·in·the·alternative·hypothesis47 #·Number·of·covariates·(including·intercept)·in·the·alternative·hypothesis
48 model48 model
49 p·=·549 p·=·5
  
Offset 54, 41 lines modifiedOffset 54, 41 lines modified
  
54 #·Intraclass·correlation·(controls·strength·of·clustering)54 #·Intraclass·correlation·(controls·strength·of·clustering)
55 r·=·0.555 r·=·0.5
  
56 #·Group·indicators56 #·Group·indicators
57 grp·=·np.kron(np.arange(n/m),·np.ones(m))57 grp·=·np.kron(np.arange(n/m),·np.ones(m))
58 The·simulation·uses·a·fixed·design·matrix.58 The·simulation·uses·a·fixed·design·matrix.
59 [4]:59 [·]:
60 #·Build·a·design·matrix·for·the·alternative·(more·complex)·model60 #·Build·a·design·matrix·for·the·alternative·(more·complex)·model
61 x·=·np.random.normal(size=(n,·p))61 x·=·np.random.normal(size=(n,·p))
62 x[:,·0]·=·162 x[:,·0]·=·1
63 The·null·design·matrix·is·nested·in·the·alternative·design·matrix.·It·has·rank63 The·null·design·matrix·is·nested·in·the·alternative·design·matrix.·It·has·rank
64 two·less·than·the·alternative·design·matrix.64 two·less·than·the·alternative·design·matrix.
65 [5]:65 [·]:
66 x0·=·x[:,·0:3]66 x0·=·x[:,·0:3]
67 The·GEE·score·test·is·robust·to·dependence·and·overdispersion.·Here·we·set·the67 The·GEE·score·test·is·robust·to·dependence·and·overdispersion.·Here·we·set·the
68 overdispersion·parameter.·The·variance·of·the·negative·binomial·distribution68 overdispersion·parameter.·The·variance·of·the·negative·binomial·distribution
69 for·each·observation·is·equal·to·scale·times·its·mean·value.69 for·each·observation·is·equal·to·scale·times·its·mean·value.
70 [6]:70 [·]:
71 #·Scale·parameter·for·negative·binomial·distribution71 #·Scale·parameter·for·negative·binomial·distribution
72 scale·=·1072 scale·=·10
73 In·the·next·cell,·we·set·up·the·mean·structures·for·the·null·and·alternative73 In·the·next·cell,·we·set·up·the·mean·structures·for·the·null·and·alternative
74 models74 models
75 [7]:75 [·]:
76 #·The·coefficients·used·to·define·the·linear·predictors76 #·The·coefficients·used·to·define·the·linear·predictors
77 coeff·=·[[4,·0.4,·-0.2],·[4,·0.4,·-0.2,·0,·-0.04]]77 coeff·=·[[4,·0.4,·-0.2],·[4,·0.4,·-0.2,·0,·-0.04]]
  
78 #·The·linear·predictors78 #·The·linear·predictors
79 lp·=·[np.dot(x0,·coeff[0]),·np.dot(x,·coeff[1])]79 lp·=·[np.dot(x0,·coeff[0]),·np.dot(x,·coeff[1])]
  
80 #·The·mean·values80 #·The·mean·values
81 mu·=·[np.exp(lp[0]),·np.exp(lp[1])]81 mu·=·[np.exp(lp[0]),·np.exp(lp[1])]
82 Below·is·a·function·that·carries·out·the·simulation.82 Below·is·a·function·that·carries·out·the·simulation.
83 [8]:83 [·]:
84 #·hyp·=·0·is·the·null·hypothesis,·hyp·=·1·is·the·alternative·hypothesis.84 #·hyp·=·0·is·the·null·hypothesis,·hyp·=·1·is·the·alternative·hypothesis.
85 #·cov_struct·is·a·statsmodels·covariance·structure85 #·cov_struct·is·a·statsmodels·covariance·structure
86 def·dosim(hyp,·cov_struct=None,·mcrep=500):86 def·dosim(hyp,·cov_struct=None,·mcrep=500):
  
87 ····#·Storage·for·the·simulation·results87 ····#·Storage·for·the·simulation·results
88 ····scales·=·[[],·[]]88 ····scales·=·[[],·[]]
  
Offset 130, 56 lines modifiedOffset 130, 46 lines modified
  
130 ····return·rslt,·scales130 ····return·rslt,·scales
131 Run·the·simulation·using·the·independence·working·covariance·structure.·We131 Run·the·simulation·using·the·independence·working·covariance·structure.·We
132 expect·the·mean·to·be·around·0·under·the·null·hypothesis,·and·much·lower·under132 expect·the·mean·to·be·around·0·under·the·null·hypothesis,·and·much·lower·under
133 the·alternative·hypothesis.·Similarly,·we·expect·that·under·the·null133 the·alternative·hypothesis.·Similarly,·we·expect·that·under·the·null
134 hypothesis,·around·10%·of·the·p-values·are·less·than·0.1,·and·a·much·greater134 hypothesis,·around·10%·of·the·p-values·are·less·than·0.1,·and·a·much·greater
135 fraction·of·the·p-values·are·less·than·0.1·under·the·alternative·hypothesis.135 fraction·of·the·p-values·are·less·than·0.1·under·the·alternative·hypothesis.
136 [9]:136 [·]:
137 rslt,·scales·=·[],·[]137 rslt,·scales·=·[],·[]
  
138 for·hyp·in·0,·1:138 for·hyp·in·0,·1:
139 ····s,·t·=·dosim(hyp,·sm.cov_struct.Independence())139 ····s,·t·=·dosim(hyp,·sm.cov_struct.Independence())
140 ····rslt.append(s)140 ····rslt.append(s)
141 ····scales.append(t)141 ····scales.append(t)
  
142 rslt·=·pd.DataFrame(rslt,·index=["H0",·"H1"],·columns=["Mean",·"Prop(p<0.1)"])142 rslt·=·pd.DataFrame(rslt,·index=["H0",·"H1"],·columns=["Mean",·"Prop(p<0.1)"])
  
143 print(rslt)143 print(rslt)
144 ········Mean··Prop(p<0.1) 
145 H0··0.481567········0.112 
146 H1··0.073157········0.792 
147 Next·we·check·to·make·sure·that·the·scale·parameter·estimates·are·reasonable.144 Next·we·check·to·make·sure·that·the·scale·parameter·estimates·are·reasonable.
148 We·are·assessing·the·robustness·of·the·GEE·score·test·to·dependence·and145 We·are·assessing·the·robustness·of·the·GEE·score·test·to·dependence·and
149 overdispersion,·so·here·we·are·confirming·that·the·overdispersion·is·present·as146 overdispersion,·so·here·we·are·confirming·that·the·overdispersion·is·present·as
150 expected.147 expected.
151 [10]:148 [·]:
152 _·=·plt.boxplot([scales[0][0],·scales[0][1],·scales[1][0],·scales[1][1]])149 _·=·plt.boxplot([scales[0][0],·scales[0][1],·scales[1][0],·scales[1][1]])
153 plt.ylabel("Estimated·scale")150 plt.ylabel("Estimated·scale")
154 [10]: 
155 Text(0,·0.5,·'Estimated·scale') 
156 [../../../_images/ 
157 examples_notebooks_generated_gee_score_test_simulation_19_1.png] 
158 Next·we·conduct·the·same·analysis·using·an·exchangeable·working·correlation151 Next·we·conduct·the·same·analysis·using·an·exchangeable·working·correlation
159 model.·Note·that·this·will·be·slower·than·the·example·above·using·independent152 model.·Note·that·this·will·be·slower·than·the·example·above·using·independent
160 working·correlation,·so·we·use·fewer·Monte·Carlo·repetitions.153 working·correlation,·so·we·use·fewer·Monte·Carlo·repetitions.
161 [11]:154 [·]:
162 rslt,·scales·=·[],·[]155 rslt,·scales·=·[],·[]
  
163 for·hyp·in·0,·1:156 for·hyp·in·0,·1:
164 ····s,·t·=·dosim(hyp,·sm.cov_struct.Exchangeable(),·mcrep=100)157 ····s,·t·=·dosim(hyp,·sm.cov_struct.Exchangeable(),·mcrep=100)
165 ····rslt.append(s)158 ····rslt.append(s)
166 ····scales.append(t)159 ····scales.append(t)
  
167 rslt·=·pd.DataFrame(rslt,·index=["H0",·"H1"],·columns=["Mean",·"Prop(p<0.1)"])160 rslt·=·pd.DataFrame(rslt,·index=["H0",·"H1"],·columns=["Mean",·"Prop(p<0.1)"])
  
168 print(rslt)161 print(rslt)
169 ········Mean··Prop(p<0.1) 
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Similarity: 0.9998502466525723% Differences: {"'cells'": "{11: {'outputs': {1: {'text': {delete: [3, 2, 1, 0]}}, insert: [(0, " "OrderedDict({'name': 'stdout', 'output_type': 'stream', 'text': ['Optimization " "terminated successfully.\\n', ' Current function value: 0.400588\\n', " "' Iterations: 292\\n', ' Function evaluations: 494\\n']}))]}}}"}
    
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162 ················{162 ················{
163 ····················"name":·"stdout",163 ····················"name":·"stdout",
164 ····················"output_type":·"stream",164 ····················"output_type":·"stream",
165 ····················"text":·[165 ····················"text":·[
166 ························"Optimization·terminated·successfully.\n",166 ························"Optimization·terminated·successfully.\n",
167 ························"·········Current·function·value:·0.400588\n",167 ························"·········Current·function·value:·0.400588\n",
168 ························"·········Iterations:·292\n",168 ························"·········Iterations:·292\n",
169 ························"·········Function·evaluations:·494\n",169 ························"·········Function·evaluations:·494\n"
 170 ····················]
 171 ················},
 172 ················{
 173 ····················"name":·"stdout",
 174 ····················"output_type":·"stream",
 175 ····················"text":·[
170 ························"·······························MyProbit·Results·······························\n",176 ························"·······························MyProbit·Results·······························\n",
171 ························"==============================================================================\n",177 ························"==============================================================================\n",
172 ························"Dep.·Variable:··················GRADE···Log-Likelihood:················-12.819\n",178 ························"Dep.·Variable:··················GRADE···Log-Likelihood:················-12.819\n",
173 ························"Model:·······················MyProbit···AIC:·····························33.64\n",179 ························"Model:·······················MyProbit···AIC:·····························33.64\n",
174 ························"Method:············Maximum·Likelihood···BIC:·····························39.50\n",180 ························"Method:············Maximum·Likelihood···BIC:·····························39.50\n",
175 ························"Date:················Sun,·10·Aug·2025·········································\n",181 ························"Date:················Sun,·10·Aug·2025·········································\n",
176 ························"Time:························13:13:47·········································\n",182 ························"Time:························13:13:47·········································\n",
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57 ······<div·class="documentwrapper">57 ······<div·class="documentwrapper">
58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Generalized-Linear-Models">61 ··<section·id="Generalized-Linear-Models">
62 <h1>Generalized·Linear·Models<a·class="headerlink"·href="#Generalized-Linear-Models"·title="Link·to·this·heading">¶</a></h1>62 <h1>Generalized·Linear·Models<a·class="headerlink"·href="#Generalized-Linear-Models"·title="Link·to·this·heading">¶</a></h1>
63 <div·class="nbinput·nblast·docutils·container">63 <div·class="nbinput·nblast·docutils·container">
64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
65 </pre></div>65 </pre></div>
66 </div>66 </div>
67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 </div>70 </div>
71 <div·class="nbinput·nblast·docutils·container">71 <div·class="nbinput·nblast·docutils·container">
72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
76 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>76 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
77 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>77 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>
78 <span·class="kn">from</span>·<span·class="nn">matplotlib</span>·<span·class="kn">import</span>·<span·class="n">pyplot</span>·<span·class="k">as</span>·<span·class="n">plt</span>78 <span·class="kn">from</span>·<span·class="nn">matplotlib</span>·<span·class="kn">import</span>·<span·class="n">pyplot</span>·<span·class="k">as</span>·<span·class="n">plt</span>
  
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83 </div>83 </div>
84 </div>84 </div>
85 <section·id="GLM:-Binomial-response-data">85 <section·id="GLM:-Binomial-response-data">
86 <h2>GLM:·Binomial·response·data<a·class="headerlink"·href="#GLM:-Binomial-response-data"·title="Link·to·this·heading">¶</a></h2>86 <h2>GLM:·Binomial·response·data<a·class="headerlink"·href="#GLM:-Binomial-response-data"·title="Link·to·this·heading">¶</a></h2>
87 <section·id="Load-Star98-data">87 <section·id="Load-Star98-data">
88 <h3>Load·Star98·data<a·class="headerlink"·href="#Load-Star98-data"·title="Link·to·this·heading">¶</a></h3>88 <h3>Load·Star98·data<a·class="headerlink"·href="#Load-Star98-data"·title="Link·to·this·heading">¶</a></h3>
89 <p>In·this·example,·we·use·the·Star98·dataset·which·was·taken·with·permission·from·Jeff·Gill·(2000)·Generalized·linear·models:·A·unified·approach.·Codebook·information·can·be·obtained·by·typing:</p>89 <p>In·this·example,·we·use·the·Star98·dataset·which·was·taken·with·permission·from·Jeff·Gill·(2000)·Generalized·linear·models:·A·unified·approach.·Codebook·information·can·be·obtained·by·typing:</p>
90 <div·class="nbinput·docutils·container">90 <div·class="nbinput·nblast·docutils·container">
91 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:91 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
92 </pre></div>92 </pre></div>
93 </div>93 </div>
94 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">star98</span><span·class="o">.</span><span·class="n">NOTE</span><span·class="p">)</span>94 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">star98</span><span·class="o">.</span><span·class="n">NOTE</span><span·class="p">)</span>
95 </pre></div>95 </pre></div>
96 </div>96 </div>
97 </div>97 </div>
98 <div·class="nboutput·nblast·docutils·container"> 
99 <div·class="prompt·empty·docutils·container"> 
100 </div> 
101 <div·class="output_area·docutils·container"> 
102 <div·class="highlight"><pre> 
103 :: 
  
104 ····Number·of·Observations·-·303·(counties·in·California). 
  
105 ····Number·of·Variables·-·13·and·8·interaction·terms. 
  
106 ····Definition·of·variables·names:: 
  
107 ········NABOVE···-·Total·number·of·students·above·the·national·median·for·the 
108 ···················math·section. 
109 ········NBELOW···-·Total·number·of·students·below·the·national·median·for·the 
110 ···················math·section. 
111 ········LOWINC···-·Percentage·of·low·income·students 
112 ········PERASIAN·-·Percentage·of·Asian·student 
113 ········PERBLACK·-·Percentage·of·black·students 
114 ········PERHISP··-·Percentage·of·Hispanic·students 
115 ········PERMINTE·-·Percentage·of·minority·teachers 
116 ········AVYRSEXP·-·Sum·of·teachers&#39;·years·in·educational·service·divided·by·the 
117 ················number·of·teachers. 
118 ········AVSALK···-·Total·salary·budget·including·benefits·divided·by·the·number 
119 ···················of·full-time·teachers·(in·thousands) 
120 ········PERSPENK·-·Per-pupil·spending·(in·thousands) 
121 ········PTRATIO··-·Pupil-teacher·ratio. 
122 ········PCTAF····-·Percentage·of·students·taking·UC/CSU·prep·courses 
123 ········PCTCHRT··-·Percentage·of·charter·schools 
124 ········PCTYRRND·-·Percentage·of·year-round·schools 
  
125 ········The·below·variables·are·interaction·terms·of·the·variables·defined 
126 ········above. 
  
127 ········PERMINTE_AVYRSEXP 
128 ········PEMINTE_AVSAL 
129 ········AVYRSEXP_AVSAL 
130 ········PERSPEN_PTRATIO 
131 ········PERSPEN_PCTAF 
132 ········PTRATIO_PCTAF 
133 ········PERMINTE_AVTRSEXP_AVSAL 
134 ········PERSPEN_PTRATIO_PCTAF 
  
135 </pre></div></div> 
136 </div> 
137 <p>Load·the·data·and·add·a·constant·to·the·exogenous·(independent)·variables:</p>98 <p>Load·the·data·and·add·a·constant·to·the·exogenous·(independent)·variables:</p>
138 <div·class="nbinput·nblast·docutils·container">99 <div·class="nbinput·nblast·docutils·container">
139 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:100 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
140 </pre></div>101 </pre></div>
141 </div>102 </div>
142 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">star98</span><span·class="o">.</span><span·class="n">load</span><span·class="p">()</span>103 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">star98</span><span·class="o">.</span><span·class="n">load</span><span·class="p">()</span>
143 <span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">,</span>·<span·class="n">prepend</span><span·class="o">=</span><span·class="kc">False</span><span·class="p">)</span>104 <span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">,</span>·<span·class="n">prepend</span><span·class="o">=</span><span·class="kc">False</span><span·class="p">)</span>
144 </pre></div>105 </pre></div>
145 </div>106 </div>
146 </div>107 </div>
147 <p>The·dependent·variable·is·N·by·2·(Success:·NABOVE,·Failure:·NBELOW):</p>108 <p>The·dependent·variable·is·N·by·2·(Success:·NABOVE,·Failure:·NBELOW):</p>
148 <div·class="nbinput·docutils·container">109 <div·class="nbinput·nblast·docutils·container">
149 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:110 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
150 </pre></div>111 </pre></div>
151 </div>112 </div>
152 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">endog</span><span·class="o">.</span><span·class="n">head</span><span·class="p">())</span>113 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">endog</span><span·class="o">.</span><span·class="n">head</span><span·class="p">())</span>
153 </pre></div>114 </pre></div>
154 </div>115 </div>
155 </div>116 </div>
156 <div·class="nboutput·nblast·docutils·container"> 
157 <div·class="prompt·empty·docutils·container"> 
158 </div> 
159 <div·class="output_area·docutils·container"> 
160 <div·class="highlight"><pre> 
161 ···NABOVE··NBELOW 
162 0···452.0···355.0 
163 1···144.0····40.0 
164 2···337.0···234.0 
165 3···395.0···178.0 
166 4·····8.0····57.0 
167 </pre></div></div> 
168 </div> 
169 <p>The·independent·variables·include·all·the·other·variables·described·above,·as·well·as·the·interaction·terms:</p>117 <p>The·independent·variables·include·all·the·other·variables·described·above,·as·well·as·the·interaction·terms:</p>
170 <div·class="nbinput·docutils·container">118 <div·class="nbinput·nblast·docutils·container">
171 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:119 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
172 </pre></div>120 </pre></div>
173 </div>121 </div>
174 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="o">.</span><span·class="n">head</span><span·class="p">())</span>122 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="o">.</span><span·class="n">head</span><span·class="p">())</span>
175 </pre></div>123 </pre></div>
176 </div>124 </div>
177 </div>125 </div>
178 <div·class="nboutput·nblast·docutils·container"> 
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Generalized·Linear·Models8 ····*·Generalized·Linear·Models
9 *\x8**\x8**\x8**\x8**\x8**\x8*·G\x8Ge\x8en\x8ne\x8er\x8ra\x8al\x8li\x8iz\x8ze\x8ed\x8d·L\x8Li\x8in\x8ne\x8ea\x8ar\x8r·M\x8Mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·G\x8Ge\x8en\x8ne\x8er\x8ra\x8al\x8li\x8iz\x8ze\x8ed\x8d·L\x8Li\x8in\x8ne\x8ea\x8ar\x8r·M\x8Mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 %matplotlib·inline11 %matplotlib·inline
12 [2]:12 [·]:
13 import·numpy·as·np13 import·numpy·as·np
14 import·statsmodels.api·as·sm14 import·statsmodels.api·as·sm
15 from·scipy·import·stats15 from·scipy·import·stats
16 from·matplotlib·import·pyplot·as·plt16 from·matplotlib·import·pyplot·as·plt
  
17 plt.rc("figure",·figsize=(16,8))17 plt.rc("figure",·figsize=(16,8))
18 plt.rc("font",·size=14)18 plt.rc("font",·size=14)
19 *\x8**\x8**\x8**\x8**\x8*·G\x8GL\x8LM\x8M:\x8:·B\x8Bi\x8in\x8no\x8om\x8mi\x8ia\x8al\x8l·r\x8re\x8es\x8sp\x8po\x8on\x8ns\x8se\x8e·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·G\x8GL\x8LM\x8M:\x8:·B\x8Bi\x8in\x8no\x8om\x8mi\x8ia\x8al\x8l·r\x8re\x8es\x8sp\x8po\x8on\x8ns\x8se\x8e·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
20 *\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8d·S\x8St\x8ta\x8ar\x8r9\x898\x88·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8d·S\x8St\x8ta\x8ar\x8r9\x898\x88·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*
21 In·this·example,·we·use·the·Star98·dataset·which·was·taken·with·permission·from21 In·this·example,·we·use·the·Star98·dataset·which·was·taken·with·permission·from
22 Jeff·Gill·(2000)·Generalized·linear·models:·A·unified·approach.·Codebook22 Jeff·Gill·(2000)·Generalized·linear·models:·A·unified·approach.·Codebook
23 information·can·be·obtained·by·typing:23 information·can·be·obtained·by·typing:
24 [3]:24 [·]:
25 print(sm.datasets.star98.NOTE)25 print(sm.datasets.star98.NOTE)
26 :: 
  
27 ····Number·of·Observations·-·303·(counties·in·California). 
  
28 ····Number·of·Variables·-·13·and·8·interaction·terms. 
  
29 ····Definition·of·variables·names:: 
  
30 ········NABOVE···-·Total·number·of·students·above·the·national·median·for·the 
31 ···················math·section. 
32 ········NBELOW···-·Total·number·of·students·below·the·national·median·for·the 
33 ···················math·section. 
34 ········LOWINC···-·Percentage·of·low·income·students 
35 ········PERASIAN·-·Percentage·of·Asian·student 
36 ········PERBLACK·-·Percentage·of·black·students 
37 ········PERHISP··-·Percentage·of·Hispanic·students 
38 ········PERMINTE·-·Percentage·of·minority·teachers 
39 ········AVYRSEXP·-·Sum·of·teachers'·years·in·educational·service·divided·by·the 
40 ················number·of·teachers. 
41 ········AVSALK···-·Total·salary·budget·including·benefits·divided·by·the·number 
42 ···················of·full-time·teachers·(in·thousands) 
43 ········PERSPENK·-·Per-pupil·spending·(in·thousands) 
44 ········PTRATIO··-·Pupil-teacher·ratio. 
45 ········PCTAF····-·Percentage·of·students·taking·UC/CSU·prep·courses 
46 ········PCTCHRT··-·Percentage·of·charter·schools 
47 ········PCTYRRND·-·Percentage·of·year-round·schools 
  
48 ········The·below·variables·are·interaction·terms·of·the·variables·defined 
49 ········above. 
  
50 ········PERMINTE_AVYRSEXP 
51 ········PEMINTE_AVSAL 
52 ········AVYRSEXP_AVSAL 
53 ········PERSPEN_PTRATIO 
54 ········PERSPEN_PCTAF 
55 ········PTRATIO_PCTAF 
56 ········PERMINTE_AVTRSEXP_AVSAL 
57 ········PERSPEN_PTRATIO_PCTAF 
58 Load·the·data·and·add·a·constant·to·the·exogenous·(independent)·variables:26 Load·the·data·and·add·a·constant·to·the·exogenous·(independent)·variables:
59 [4]:27 [·]:
60 data·=·sm.datasets.star98.load()28 data·=·sm.datasets.star98.load()
61 data.exog·=·sm.add_constant(data.exog,·prepend=False)29 data.exog·=·sm.add_constant(data.exog,·prepend=False)
62 The·dependent·variable·is·N·by·2·(Success:·NABOVE,·Failure:·NBELOW):30 The·dependent·variable·is·N·by·2·(Success:·NABOVE,·Failure:·NBELOW):
63 [5]:31 [·]:
64 print(data.endog.head())32 print(data.endog.head())
65 ···NABOVE··NBELOW 
66 0···452.0···355.0 
67 1···144.0····40.0 
68 2···337.0···234.0 
69 3···395.0···178.0 
70 4·····8.0····57.0 
71 The·independent·variables·include·all·the·other·variables·described·above,·as33 The·independent·variables·include·all·the·other·variables·described·above,·as
72 well·as·the·interaction·terms:34 well·as·the·interaction·terms:
73 [6]:35 [·]:
74 print(data.exog.head())36 print(data.exog.head())
75 ·····LOWINC···PERASIAN···PERBLACK····PERHISP··PERMINTE··AVYRSEXP····AVSALK··\ 
76 0··34.39730··23.299300··14.235280··11.411120··15.91837··14.70646··59.15732 
77 1··17.36507··29.328380···8.234897···9.314884··13.63636··16.08324··59.50397 
78 2··32.64324···9.226386··42.406310··13.543720··28.83436··14.59559··60.56992 
79 3··11.90953··13.883090···3.796973··11.443110··11.11111··14.38939··58.33411 
80 4··36.88889··12.187500··76.875000···7.604167··43.58974··13.90568··63.15364 
  
81 ···PERSPENK···PTRATIO·····PCTAF··...···PCTYRRND··PERMINTE_AVYRSEXP··\ 
82 0··4.445207··21.71025··57.03276··...··22.222220·········234.102872 
83 1··5.267598··20.44278··64.62264··...···0.000000·········219.316851 
84 2··5.482922··18.95419··53.94191··...···0.000000·········420.854496 
85 3··4.165093··21.63539··49.06103··...···7.142857·········159.882095 
86 4··4.324902··18.77984··52.38095··...···0.000000·········606.144976 
  
87 ···PERMINTE_AVSAL··AVYRSEXP_AVSAL··PERSPEN_PTRATIO··PERSPEN_PCTAF··\ 
88 0·······941.68811········869.9948·········96.50656······253.52242 
89 1·······811.41756········957.0166········107.68435······340.40609 
90 2······1746.49488········884.0537········103.92435······295.75929 
91 3·······648.15671········839.3923·········90.11341······204.34375 
92 4······2752.85075········878.1943·········81.22097······226.54248 
  
93 ···PTRATIO_PCTAF··PERMINTE_AVYRSEXP_AVSAL··PERSPEN_PTRATIO_PCTAF··const 
94 0······1238.1955···············13848.8985··············5504.0352····1.0 
95 1······1321.0664···············13050.2233··············6958.8468····1.0 
96 2······1022.4252···············25491.1232··············5605.8777····1.0 
97 3······1061.4545················9326.5797··············4421.0568····1.0 
98 4·······983.7059···············38280.2616··············4254.4314····1.0 
  
99 [5·rows·x·21·columns] 
100 *\x8**\x8**\x8**\x8*·F\x8Fi\x8it\x8t·a\x8an\x8nd\x8d·s\x8su\x8um\x8mm\x8ma\x8ar\x8ry\x8y_\x8?\x8·*\x8**\x8**\x8**\x8*37 *\x8**\x8**\x8**\x8*·F\x8Fi\x8it\x8t·a\x8an\x8nd\x8d·s\x8su\x8um\x8mm\x8ma\x8ar\x8ry\x8y_\x8?\x8·*\x8**\x8**\x8**\x8*
101 [7]:38 [·]:
102 glm_binom·=·sm.GLM(data.endog,·data.exog,·family=sm.families.Binomial())39 glm_binom·=·sm.GLM(data.endog,·data.exog,·family=sm.families.Binomial())
103 res·=·glm_binom.fit()40 res·=·glm_binom.fit()
104 print(res.summary())41 print(res.summary())
105 ··················Generalized·Linear·Model·Regression·Results 
106 ================================================================================ 
107 Dep.·Variable:·····['NABOVE',·'NBELOW']···No.·Observations: 
108 303 
109 Model:······························GLM···Df·Residuals: 
110 282 
111 Model·Family:··················Binomial···Df·Model: 
112 20 
113 Link·Function:····················Logit···Scale: 
114 1.0000 
115 Method:····························IRLS···Log-Likelihood:················- 
116 2998.6 
117 Date:··················Sun,·10·Aug·2025···Deviance: 
118 4078.8 
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57 ······<div·class="documentwrapper">57 ······<div·class="documentwrapper">
58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Weighted-Generalized-Linear-Models">61 ··<section·id="Weighted-Generalized-Linear-Models">
62 <h1>Weighted·Generalized·Linear·Models<a·class="headerlink"·href="#Weighted-Generalized-Linear-Models"·title="Link·to·this·heading">¶</a></h1>62 <h1>Weighted·Generalized·Linear·Models<a·class="headerlink"·href="#Weighted-Generalized-Linear-Models"·title="Link·to·this·heading">¶</a></h1>
63 <div·class="nbinput·nblast·docutils·container">63 <div·class="nbinput·nblast·docutils·container">
64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
65 </pre></div>65 </pre></div>
66 </div>66 </div>
67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
68 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>68 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
69 <span·class="kn">import</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="k">as</span>·<span·class="nn">smf</span>69 <span·class="kn">import</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="k">as</span>·<span·class="nn">smf</span>
70 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>70 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
71 </pre></div>71 </pre></div>
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73 </div>73 </div>
74 <section·id="Weighted-GLM:-Poisson-response-data">74 <section·id="Weighted-GLM:-Poisson-response-data">
75 <h2>Weighted·GLM:·Poisson·response·data<a·class="headerlink"·href="#Weighted-GLM:-Poisson-response-data"·title="Link·to·this·heading">¶</a></h2>75 <h2>Weighted·GLM:·Poisson·response·data<a·class="headerlink"·href="#Weighted-GLM:-Poisson-response-data"·title="Link·to·this·heading">¶</a></h2>
76 <section·id="Load-data">76 <section·id="Load-data">
77 <h3>Load·data<a·class="headerlink"·href="#Load-data"·title="Link·to·this·heading">¶</a></h3>77 <h3>Load·data<a·class="headerlink"·href="#Load-data"·title="Link·to·this·heading">¶</a></h3>
78 <p>In·this·example,·we’ll·use·the·affair·dataset·using·a·handful·of·exogenous·variables·to·predict·the·extra-marital·affair·rate.</p>78 <p>In·this·example,·we’ll·use·the·affair·dataset·using·a·handful·of·exogenous·variables·to·predict·the·extra-marital·affair·rate.</p>
79 <p>Weights·will·be·generated·to·show·that·<code·class="docutils·literal·notranslate"><span·class="pre">freq_weights</span></code>·are·equivalent·to·repeating·records·of·data.·On·the·other·hand,·<code·class="docutils·literal·notranslate"><span·class="pre">var_weights</span></code>·is·equivalent·to·aggregating·data.</p>79 <p>Weights·will·be·generated·to·show·that·<code·class="docutils·literal·notranslate"><span·class="pre">freq_weights</span></code>·are·equivalent·to·repeating·records·of·data.·On·the·other·hand,·<code·class="docutils·literal·notranslate"><span·class="pre">var_weights</span></code>·is·equivalent·to·aggregating·data.</p>
80 <div·class="nbinput·docutils·container">80 <div·class="nbinput·nblast·docutils·container">
81 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:81 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
82 </pre></div>82 </pre></div>
83 </div>83 </div>
84 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">fair</span><span·class="o">.</span><span·class="n">NOTE</span><span·class="p">)</span>84 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">fair</span><span·class="o">.</span><span·class="n">NOTE</span><span·class="p">)</span>
85 </pre></div>85 </pre></div>
86 </div>86 </div>
87 </div>87 </div>
88 <div·class="nboutput·nblast·docutils·container"> 
89 <div·class="prompt·empty·docutils·container"> 
90 </div> 
91 <div·class="output_area·docutils·container"> 
92 <div·class="highlight"><pre> 
93 :: 
  
94 ····Number·of·observations:·6366 
95 ····Number·of·variables:·9 
96 ····Variable·name·definitions: 
  
97 ········rate_marriage···:·How·rate·marriage,·1·=·very·poor,·2·=·poor,·3·=·fair, 
98 ························4·=·good,·5·=·very·good 
99 ········age·············:·Age 
100 ········yrs_married·····:·No.·years·married.·Interval·approximations.·See 
101 ························original·paper·for·detailed·explanation. 
102 ········children········:·No.·children 
103 ········religious·······:·How·relgious,·1·=·not,·2·=·mildly,·3·=·fairly, 
104 ························4·=·strongly 
105 ········educ············:·Level·of·education,·9·=·grade·school,·12·=·high 
106 ························school,·14·=·some·college,·16·=·college·graduate, 
107 ························17·=·some·graduate·school,·20·=·advanced·degree 
108 ········occupation······:·1·=·student,·2·=·farming,·agriculture;·semi-skilled, 
109 ························or·unskilled·worker;·3·=·white-colloar;·4·=·teacher 
110 ························counselor·social·worker,·nurse;·artist,·writers; 
111 ························technician,·skilled·worker,·5·=·managerial, 
112 ························administrative,·business,·6·=·professional·with 
113 ························advanced·degree 
114 ········occupation_husb·:·Husband&#39;s·occupation.·Same·as·occupation. 
115 ········affairs·········:·measure·of·time·spent·in·extramarital·affairs 
  
116 ····See·the·original·paper·for·more·details. 
  
117 </pre></div></div> 
118 </div> 
119 <p>Load·the·data·into·a·pandas·dataframe.</p>88 <p>Load·the·data·into·a·pandas·dataframe.</p>
120 <div·class="nbinput·nblast·docutils·container">89 <div·class="nbinput·nblast·docutils·container">
121 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:90 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
122 </pre></div>91 </pre></div>
123 </div>92 </div>
124 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">fair</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>93 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">fair</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>
125 </pre></div>94 </pre></div>
126 </div>95 </div>
127 </div>96 </div>
128 <p>The·dependent·(endogenous)·variable·is·<code·class="docutils·literal·notranslate"><span·class="pre">affairs</span></code></p>97 <p>The·dependent·(endogenous)·variable·is·<code·class="docutils·literal·notranslate"><span·class="pre">affairs</span></code></p>
129 <div·class="nbinput·docutils·container">98 <div·class="nbinput·nblast·docutils·container">
130 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:99 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
131 </pre></div>100 </pre></div>
132 </div>101 </div>
133 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span><span·class="o">.</span><span·class="n">describe</span><span·class="p">()</span>102 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span><span·class="o">.</span><span·class="n">describe</span><span·class="p">()</span>
134 </pre></div>103 </pre></div>
135 </div>104 </div>
136 </div>105 </div>
137 <div·class="nboutput·nblast·docutils·container">106 <div·class="nbinput·nblast·docutils·container">
138 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:107 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
139 </pre></div> 
140 </div> 
141 <div·class="output_area·rendered_html·docutils·container"> 
142 <div> 
143 <style·scoped> 
144 ····.dataframe·tbody·tr·th:only-of-type·{ 
145 ········vertical-align:·middle; 
146 ····} 
  
147 ····.dataframe·tbody·tr·th·{ 
148 ········vertical-align:·top; 
149 ····} 
  
150 ····.dataframe·thead·th·{ 
151 ········text-align:·right; 
152 ····} 
153 </style> 
154 <table·border="1"·class="dataframe"> 
155 ··<thead> 
156 ····<tr·style="text-align:·right;"> 
157 ······<th></th> 
158 ······<th>rate_marriage</th> 
159 ······<th>age</th> 
160 ······<th>yrs_married</th> 
161 ······<th>children</th> 
162 ······<th>religious</th> 
163 ······<th>educ</th> 
164 ······<th>occupation</th> 
165 ······<th>occupation_husb</th> 
166 ······<th>affairs</th> 
167 ····</tr> 
168 ··</thead> 
169 ··<tbody> 
170 ····<tr> 
171 ······<th>count</th> 
172 ······<td>6366.000000</td> 
173 ······<td>6366.000000</td> 
174 ······<td>6366.000000</td> 
175 ······<td>6366.000000</td> 
176 ······<td>6366.000000</td> 
177 ······<td>6366.000000</td> 
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Weighted·Generalized·Linear·Models8 ····*·Weighted·Generalized·Linear·Models
9 *\x8**\x8**\x8**\x8**\x8**\x8*·W\x8We\x8ei\x8ig\x8gh\x8ht\x8te\x8ed\x8d·G\x8Ge\x8en\x8ne\x8er\x8ra\x8al\x8li\x8iz\x8ze\x8ed\x8d·L\x8Li\x8in\x8ne\x8ea\x8ar\x8r·M\x8Mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·W\x8We\x8ei\x8ig\x8gh\x8ht\x8te\x8ed\x8d·G\x8Ge\x8en\x8ne\x8er\x8ra\x8al\x8li\x8iz\x8ze\x8ed\x8d·L\x8Li\x8in\x8ne\x8ea\x8ar\x8r·M\x8Mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 import·numpy·as·np11 import·numpy·as·np
12 import·pandas·as·pd12 import·pandas·as·pd
13 import·statsmodels.formula.api·as·smf13 import·statsmodels.formula.api·as·smf
14 import·statsmodels.api·as·sm14 import·statsmodels.api·as·sm
15 *\x8**\x8**\x8**\x8**\x8*·W\x8We\x8ei\x8ig\x8gh\x8ht\x8te\x8ed\x8d·G\x8GL\x8LM\x8M:\x8:·P\x8Po\x8oi\x8is\x8ss\x8so\x8on\x8n·r\x8re\x8es\x8sp\x8po\x8on\x8ns\x8se\x8e·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*15 *\x8**\x8**\x8**\x8**\x8*·W\x8We\x8ei\x8ig\x8gh\x8ht\x8te\x8ed\x8d·G\x8GL\x8LM\x8M:\x8:·P\x8Po\x8oi\x8is\x8ss\x8so\x8on\x8n·r\x8re\x8es\x8sp\x8po\x8on\x8ns\x8se\x8e·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
16 *\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8d·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8d·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*
17 In·this·example,·we’ll·use·the·affair·dataset·using·a·handful·of·exogenous17 In·this·example,·we’ll·use·the·affair·dataset·using·a·handful·of·exogenous
18 variables·to·predict·the·extra-marital·affair·rate.18 variables·to·predict·the·extra-marital·affair·rate.
19 Weights·will·be·generated·to·show·that·freq_weights·are·equivalent·to·repeating19 Weights·will·be·generated·to·show·that·freq_weights·are·equivalent·to·repeating
20 records·of·data.·On·the·other·hand,·var_weights·is·equivalent·to·aggregating20 records·of·data.·On·the·other·hand,·var_weights·is·equivalent·to·aggregating
21 data.21 data.
22 [2]:22 [·]:
23 print(sm.datasets.fair.NOTE)23 print(sm.datasets.fair.NOTE)
24 :: 
  
25 ····Number·of·observations:·6366 
26 ····Number·of·variables:·9 
27 ····Variable·name·definitions: 
  
28 ········rate_marriage···:·How·rate·marriage,·1·=·very·poor,·2·=·poor,·3·=·fair, 
29 ························4·=·good,·5·=·very·good 
30 ········age·············:·Age 
31 ········yrs_married·····:·No.·years·married.·Interval·approximations.·See 
32 ························original·paper·for·detailed·explanation. 
33 ········children········:·No.·children 
34 ········religious·······:·How·relgious,·1·=·not,·2·=·mildly,·3·=·fairly, 
35 ························4·=·strongly 
36 ········educ············:·Level·of·education,·9·=·grade·school,·12·=·high 
37 ························school,·14·=·some·college,·16·=·college·graduate, 
38 ························17·=·some·graduate·school,·20·=·advanced·degree 
39 ········occupation······:·1·=·student,·2·=·farming,·agriculture;·semi-skilled, 
40 ························or·unskilled·worker;·3·=·white-colloar;·4·=·teacher 
41 ························counselor·social·worker,·nurse;·artist,·writers; 
42 ························technician,·skilled·worker,·5·=·managerial, 
43 ························administrative,·business,·6·=·professional·with 
44 ························advanced·degree 
45 ········occupation_husb·:·Husband's·occupation.·Same·as·occupation. 
46 ········affairs·········:·measure·of·time·spent·in·extramarital·affairs 
  
47 ····See·the·original·paper·for·more·details. 
48 Load·the·data·into·a·pandas·dataframe.24 Load·the·data·into·a·pandas·dataframe.
49 [3]:25 [·]:
50 data·=·sm.datasets.fair.load_pandas().data26 data·=·sm.datasets.fair.load_pandas().data
51 The·dependent·(endogenous)·variable·is·affairs27 The·dependent·(endogenous)·variable·is·affairs
52 [4]:28 [·]:
53 data.describe()29 data.describe()
54 [4]:30 [·]:
55 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
56 |_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8r\x8r_\x8a\x8a_\x8t\x8t_\x8e\x8e_\x8_\x8__\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8y\x8y_\x8r\x8r_\x8s\x8s_\x8_\x8__\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8e\x8e_\x8d\x8d_\x8|_\x8·_\x8·_\x8·_\x8c\x8c_\x8h\x8h_\x8i\x8i_\x8l\x8l_\x8d\x8d_\x8r\x8r_\x8e\x8e_\x8n\x8n_\x8|_\x8·_\x8·_\x8r\x8r_\x8e\x8e_\x8l\x8l_\x8i\x8i_\x8g\x8g_\x8i\x8i_\x8o\x8o_\x8u\x8u_\x8s\x8s_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8e\x8e_\x8d\x8d_\x8u\x8u_\x8c\x8c_\x8|_\x8·_\x8o\x8o_\x8c\x8c_\x8c\x8c_\x8u\x8u_\x8p\x8p_\x8a\x8a_\x8t\x8t_\x8i\x8i_\x8o\x8o_\x8n\x8n_\x8|_\x8o\x8o_\x8c\x8c_\x8c\x8c_\x8u\x8u_\x8p\x8p_\x8a\x8a_\x8t\x8t_\x8i\x8i_\x8o\x8o_\x8n\x8n_\x8_\x8__\x8h\x8h_\x8u\x8u_\x8s\x8s_\x8b\x8b_\x8|_\x8·_\x8·_\x8·_\x8·_\x8a\x8a_\x8f\x8f_\x8f\x8f_\x8a\x8a_\x8i\x8i_\x8r\x8r_\x8s\x8s| 
57 |_\x8c\x8c_\x8o\x8o_\x8u\x8u_\x8n\x8n_\x8t\x8t_\x8|_\x86_\x83_\x86_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x86_\x83_\x86_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8|_\x86_\x83_\x86_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8|_\x86_\x83_\x86_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8|_\x86_\x83_\x86_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8|_\x86_\x83_\x86_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8|_\x86_\x83_\x86_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8|_\x86_\x83_\x86_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x86_\x83_\x86_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80| 
58 |_\x8m\x8m_\x8e\x8e_\x8a\x8a_\x8n\x8n_\x8·_\x8|_\x84_\x8._\x81_\x80_\x89_\x86_\x84_\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x89_\x8._\x80_\x88_\x82_\x88_\x86_\x82_\x8·_\x8·_\x8|_\x89_\x8._\x80_\x80_\x89_\x84_\x82_\x85_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x83_\x89_\x86_\x88_\x87_\x84_\x8·_\x8·_\x8·_\x8|_\x82_\x8._\x84_\x82_\x86_\x81_\x87_\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x84_\x8._\x82_\x80_\x89_\x88_\x86_\x85_\x8·_\x8·_\x8|_\x83_\x8._\x84_\x82_\x84_\x81_\x82_\x88_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x88_\x85_\x80_\x81_\x84_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x87_\x80_\x85_\x83_\x87_\x84_\x8·_\x8·_\x8·| 
59 |_\x8s\x8s_\x8t\x8t_\x8d\x8d_\x8·_\x8·_\x8|_\x80_\x8._\x89_\x86_\x81_\x84_\x83_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x86_\x8._\x88_\x84_\x87_\x88_\x88_\x82_\x8·_\x8·_\x8·_\x8|_\x87_\x8._\x82_\x88_\x80_\x81_\x82_\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x84_\x83_\x83_\x84_\x87_\x81_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x88_\x87_\x88_\x83_\x86_\x89_\x8·_\x8·_\x8·_\x8|_\x82_\x8._\x81_\x87_\x88_\x80_\x80_\x83_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x89_\x84_\x82_\x83_\x89_\x89_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x83_\x84_\x86_\x84_\x83_\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x8._\x82_\x80_\x83_\x83_\x87_\x84_\x8·_\x8·_\x8·| 
60 |_\x8m\x8m_\x8i\x8i_\x8n\x8n_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x87_\x8._\x85_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x80_\x8._\x85_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x89_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·| 
61 |_\x82\x82_\x85\x85_\x8%\x8%_\x8·_\x8·_\x8|_\x84_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x82_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x82_\x8._\x85_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x82_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x82_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·| 
62 |_\x85\x85_\x80\x80_\x8%\x8%_\x8·_\x8·_\x8|_\x84_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x87_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x82_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x84_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x84_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·| 
63 |_\x87\x87_\x85\x85_\x8%\x8%_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x82_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x81_\x86_\x8._\x85_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x82_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x81_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x84_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x84_\x88_\x84_\x88_\x84_\x88_\x8·_\x8·_\x8·| 
64 |_\x8m\x8m_\x8a\x8a_\x8x\x8x_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x84_\x82_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x82_\x83_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x85_\x8._\x85_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x84_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x82_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8|_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8|_\x86_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x85_\x87_\x8._\x85_\x89_\x89_\x89_\x89_\x81_\x8·_\x8·| 
65 [5]: 
66 data[:3]31 data[:3]
67 [5]: 
68 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
69 |_\x8·_\x8|_\x8r\x8r_\x8a\x8a_\x8t\x8t_\x8e\x8e_\x8_\x8__\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8·_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8y\x8y_\x8r\x8r_\x8s\x8s_\x8_\x8__\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8e\x8e_\x8d\x8d_\x8|_\x8c\x8c_\x8h\x8h_\x8i\x8i_\x8l\x8l_\x8d\x8d_\x8r\x8r_\x8e\x8e_\x8n\x8n_\x8|_\x8r\x8r_\x8e\x8e_\x8l\x8l_\x8i\x8i_\x8g\x8g_\x8i\x8i_\x8o\x8o_\x8u\x8u_\x8s\x8s_\x8|_\x8e\x8e_\x8d\x8d_\x8u\x8u_\x8c\x8c_\x8|_\x8o\x8o_\x8c\x8c_\x8c\x8c_\x8u\x8u_\x8p\x8p_\x8a\x8a_\x8t\x8t_\x8i\x8i_\x8o\x8o_\x8n\x8n_\x8|_\x8o\x8o_\x8c\x8c_\x8c\x8c_\x8u\x8u_\x8p\x8p_\x8a\x8a_\x8t\x8t_\x8i\x8i_\x8o\x8o_\x8n\x8n_\x8_\x8__\x8h\x8h_\x8u\x8u_\x8s\x8s_\x8b\x8b_\x8|_\x8·_\x8a\x8a_\x8f\x8f_\x8f\x8f_\x8a\x8a_\x8i\x8i_\x8r\x8r_\x8s\x8s| 
70 |_\x80\x80_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x82_\x8._\x80_\x8|_\x89_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x87_\x8._\x80_\x8|_\x82_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x81_\x81_\x81_\x81_\x81_\x81| 
71 |_\x81\x81_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x87_\x8._\x80_\x8|_\x81_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x84_\x8._\x80_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x84_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x82_\x83_\x80_\x87_\x86_\x89| 
72 |_\x82\x82_\x8|_\x84_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x82_\x8._\x80_\x8|_\x82_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x86_\x8._\x80_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x84_\x80_\x80_\x80_\x80_\x80| 
73 In·the·following·we·will·work·mostly·with·Poisson.·While·using·decimal·affairs32 In·the·following·we·will·work·mostly·with·Poisson.·While·using·decimal·affairs
74 works,·we·convert·them·to·integers·to·have·a·count·distribution.33 works,·we·convert·them·to·integers·to·have·a·count·distribution.
75 [6]:34 [·]:
76 data["affairs"]·=·np.ceil(data["affairs"])35 data["affairs"]·=·np.ceil(data["affairs"])
77 data[:3]36 data[:3]
78 [6]:37 [·]:
79 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
80 |_\x8·_\x8|_\x8r\x8r_\x8a\x8a_\x8t\x8t_\x8e\x8e_\x8_\x8__\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8·_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8y\x8y_\x8r\x8r_\x8s\x8s_\x8_\x8__\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8e\x8e_\x8d\x8d_\x8|_\x8c\x8c_\x8h\x8h_\x8i\x8i_\x8l\x8l_\x8d\x8d_\x8r\x8r_\x8e\x8e_\x8n\x8n_\x8|_\x8r\x8r_\x8e\x8e_\x8l\x8l_\x8i\x8i_\x8g\x8g_\x8i\x8i_\x8o\x8o_\x8u\x8u_\x8s\x8s_\x8|_\x8e\x8e_\x8d\x8d_\x8u\x8u_\x8c\x8c_\x8|_\x8o\x8o_\x8c\x8c_\x8c\x8c_\x8u\x8u_\x8p\x8p_\x8a\x8a_\x8t\x8t_\x8i\x8i_\x8o\x8o_\x8n\x8n_\x8|_\x8o\x8o_\x8c\x8c_\x8c\x8c_\x8u\x8u_\x8p\x8p_\x8a\x8a_\x8t\x8t_\x8i\x8i_\x8o\x8o_\x8n\x8n_\x8_\x8__\x8h\x8h_\x8u\x8u_\x8s\x8s_\x8b\x8b_\x8|_\x8a\x8a_\x8f\x8f_\x8f\x8f_\x8a\x8a_\x8i\x8i_\x8r\x8r_\x8s\x8s| 
81 |_\x80\x80_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x82_\x8._\x80_\x8|_\x89_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x87_\x8._\x80_\x8|_\x82_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·| 
82 |_\x81\x81_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x87_\x8._\x80_\x8|_\x81_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x84_\x8._\x80_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x84_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x84_\x8._\x80_\x8·_\x8·_\x8·_\x8·| 
83 |_\x82\x82_\x8|_\x84_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x82_\x8._\x80_\x8|_\x82_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x86_\x8._\x80_\x8|_\x83_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x85_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x8._\x80_\x8·_\x8·_\x8·_\x8·| 
84 [7]: 
85 (data["affairs"]·==·0).mean()38 (data["affairs"]·==·0).mean()
86 [7]:39 [·]:
87 np.float64(0.6775054979579014) 
88 [8]: 
89 np.bincount(data["affairs"].astype(int))40 np.bincount(data["affairs"].astype(int))
90 [8]: 
91 array([4313,··934,··488,··180,··130,··172,····7,···21,···67,····2,····0, 
92 ··········0,···17,····0,····0,····0,····3,···12,····8,····0,····0,····0, 
93 ··········0,····0,····2,····2,····2,····3,····0,····0,····0,····0,····0, 
94 ··········0,····0,····0,····0,····0,····0,····1,····1,····0,····0,····0, 
95 ··········0,····0,····0,····0,····0,····0,····0,····0,····0,····0,····0, 
96 ··········0,····0,····0,····1]) 
97 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nd\x8de\x8en\x8ns\x8si\x8in\x8ng\x8g·a\x8an\x8nd\x8d·A\x8Ag\x8gg\x8gr\x8re\x8eg\x8ga\x8at\x8ti\x8in\x8ng\x8g·o\x8ob\x8bs\x8se\x8er\x8rv\x8va\x8at\x8ti\x8io\x8on\x8ns\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*41 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nd\x8de\x8en\x8ns\x8si\x8in\x8ng\x8g·a\x8an\x8nd\x8d·A\x8Ag\x8gg\x8gr\x8re\x8eg\x8ga\x8at\x8ti\x8in\x8ng\x8g·o\x8ob\x8bs\x8se\x8er\x8rv\x8va\x8at\x8ti\x8io\x8on\x8ns\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
98 We·have·6366·observations·in·our·original·dataset.·When·we·consider·only·some42 We·have·6366·observations·in·our·original·dataset.·When·we·consider·only·some
99 selected·variables,·then·we·have·fewer·unique·observations.·In·the·following·we43 selected·variables,·then·we·have·fewer·unique·observations.·In·the·following·we
100 combine·observations·in·two·ways,·first·we·combine·observations·that·have44 combine·observations·in·two·ways,·first·we·combine·observations·that·have
101 values·for·all·variables·identical,·and·secondly·we·combine·observations·that45 values·for·all·variables·identical,·and·secondly·we·combine·observations·that
102 have·the·same·explanatory·variables.46 have·the·same·explanatory·variables.
103 *\x8**\x8**\x8**\x8*·D\x8Da\x8at\x8ta\x8as\x8se\x8et\x8t·w\x8wi\x8it\x8th\x8h·u\x8un\x8ni\x8iq\x8qu\x8ue\x8e·o\x8ob\x8bs\x8se\x8er\x8rv\x8va\x8at\x8ti\x8io\x8on\x8ns\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*47 *\x8**\x8**\x8**\x8*·D\x8Da\x8at\x8ta\x8as\x8se\x8et\x8t·w\x8wi\x8it\x8th\x8h·u\x8un\x8ni\x8iq\x8qu\x8ue\x8e·o\x8ob\x8bs\x8se\x8er\x8rv\x8va\x8at\x8ti\x8io\x8on\x8ns\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*
104 We·use·pandas’s·groupby·to·combine·identical·observations·and·create·a·new48 We·use·pandas’s·groupby·to·combine·identical·observations·and·create·a·new
105 variable·freq·that·count·how·many·observation·have·the·values·in·the49 variable·freq·that·count·how·many·observation·have·the·values·in·the
106 corresponding·row.50 corresponding·row.
107 [9]:51 [·]:
108 data2·=·data.copy()52 data2·=·data.copy()
109 data2["const"]·=·153 data2["const"]·=·1
110 dc·=·(54 dc·=·(
111 ····data2["affairs·rate_marriage·age·yrs_married·const".split()]55 ····data2["affairs·rate_marriage·age·yrs_married·const".split()]
112 ····.groupby("affairs·rate_marriage·age·yrs_married".split())56 ····.groupby("affairs·rate_marriage·age·yrs_married".split())
113 ····.count()57 ····.count()
114 )58 )
115 dc.reset_index(inplace=True)59 dc.reset_index(inplace=True)
116 dc.rename(columns={"const":·"freq"},·inplace=True)60 dc.rename(columns={"const":·"freq"},·inplace=True)
117 print(dc.shape)61 print(dc.shape)
118 dc.head()62 dc.head()
119 (476,·5) 
120 [9]: 
121 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
122 |_\x8·_\x8|_\x8a\x8a_\x8f\x8f_\x8f\x8f_\x8a\x8a_\x8i\x8i_\x8r\x8r_\x8s\x8s_\x8|_\x8r\x8r_\x8a\x8a_\x8t\x8t_\x8e\x8e_\x8_\x8__\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8·_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8y\x8y_\x8r\x8r_\x8s\x8s_\x8_\x8__\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8e\x8e_\x8d\x8d_\x8|_\x8f\x8f_\x8r\x8r_\x8e\x8e_\x8q\x8q| 
123 |_\x80\x80_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x87_\x8._\x85_\x8|_\x80_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·| 
124 |_\x81\x81_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x82_\x8._\x80_\x8|_\x82_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8·_\x8·_\x8·| 
125 |_\x82\x82_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x87_\x8._\x80_\x8|_\x82_\x8._\x85_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·| 
126 |_\x83\x83_\x8|_\x80_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x87_\x8._\x80_\x8|_\x86_\x8._\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x85_\x8·_\x8·_\x8·| 
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194 <span·class="nb">print</span><span·class="p">(</span><span·class="n">glsar_results</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>194 <span·class="nb">print</span><span·class="p">(</span><span·class="n">glsar_results</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
195 </pre></div>195 </pre></div>
196 </div>196 </div>
197 </div>197 </div>
198 <div·class="nboutput·docutils·container">198 <div·class="nboutput·docutils·container">
199 <div·class="prompt·empty·docutils·container">199 <div·class="prompt·empty·docutils·container">
200 </div>200 </div>
 201 <div·class="output_area·stderr·docutils·container">
 202 <div·class="highlight"><pre>
 203 /usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430:·UserWarning:·`kurtosistest`·p-value·may·be·inaccurate·with·fewer·than·20·observations;·only·n=15·observations·were·given.
 204 ··return·hypotest_fun_in(*args,·**kwds)
 205 </pre></div></div>
 206 </div>
 207 <div·class="nboutput·nblast·docutils·container">
 208 <div·class="prompt·empty·docutils·container">
 209 </div>
201 <div·class="output_area·docutils·container">210 <div·class="output_area·docutils·container">
202 <div·class="highlight"><pre>211 <div·class="highlight"><pre>
203 ···························GLSAR·Regression·Results212 ···························GLSAR·Regression·Results
204 ==============================================================================213 ==============================================================================
205 Dep.·Variable:·················TOTEMP···R-squared:·······················0.996214 Dep.·Variable:·················TOTEMP···R-squared:·······················0.996
206 Model:··························GLSAR···Adj.·R-squared:··················0.992215 Model:··························GLSAR···Adj.·R-squared:··················0.992
207 Method:·················Least·Squares···F-statistic:·····················295.2216 Method:·················Least·Squares···F-statistic:·····················295.2
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230 Notes:239 Notes:
231 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified.240 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified.
232 [2]·The·condition·number·is·large,·4.8e+09.·This·might·indicate·that·there·are241 [2]·The·condition·number·is·large,·4.8e+09.·This·might·indicate·that·there·are
233 strong·multicollinearity·or·other·numerical·problems.242 strong·multicollinearity·or·other·numerical·problems.
234 </pre></div></div>243 </pre></div></div>
235 </div>244 </div>
236 <div·class="nboutput·nblast·docutils·container"> 
237 <div·class="prompt·empty·docutils·container"> 
238 </div> 
239 <div·class="output_area·stderr·docutils·container"> 
240 <div·class="highlight"><pre> 
241 /usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430:·UserWarning:·`kurtosistest`·p-value·may·be·inaccurate·with·fewer·than·20·observations;·only·n=15·observations·were·given. 
242 ··return·hypotest_fun_in(*args,·**kwds) 
243 </pre></div></div> 
244 </div> 
245 <p>Comparing·gls·and·glsar·results,·we·see·that·there·are·some·small·differences·in·the·parameter·estimates·and·the·resulting·standard·errors·of·the·parameter·estimate.·This·might·be·do·to·the·numerical·differences·in·the·algorithm,·e.g.·the·treatment·of·initial·conditions,·because·of·the·small·number·of·observations·in·the·longley·dataset.</p>245 <p>Comparing·gls·and·glsar·results,·we·see·that·there·are·some·small·differences·in·the·parameter·estimates·and·the·resulting·standard·errors·of·the·parameter·estimate.·This·might·be·do·to·the·numerical·differences·in·the·algorithm,·e.g.·the·treatment·of·initial·conditions,·because·of·the·small·number·of·observations·in·the·longley·dataset.</p>
246 <div·class="nbinput·docutils·container">246 <div·class="nbinput·docutils·container">
247 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[10]:247 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[10]:
248 </pre></div>248 </pre></div>
249 </div>249 </div>
250 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">gls_results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>250 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">gls_results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>
251 <span·class="nb">print</span><span·class="p">(</span><span·class="n">glsar_results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>251 <span·class="nb">print</span><span·class="p">(</span><span·class="n">glsar_results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>
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68 Of·course,·the·exact·rho·in·this·instance·is·not·known·so·it·it·might·make·more68 Of·course,·the·exact·rho·in·this·instance·is·not·known·so·it·it·might·make·more
69 sense·to·use·feasible·gls,·which·currently·only·has·experimental·support.69 sense·to·use·feasible·gls,·which·currently·only·has·experimental·support.
70 We·can·use·the·GLSAR·model·with·one·lag,·to·get·to·a·similar·result:70 We·can·use·the·GLSAR·model·with·one·lag,·to·get·to·a·similar·result:
71 [9]:71 [9]:
72 glsar_model·=·sm.GLSAR(data.endog,·data.exog,·1)72 glsar_model·=·sm.GLSAR(data.endog,·data.exog,·1)
73 glsar_results·=·glsar_model.iterative_fit(1)73 glsar_results·=·glsar_model.iterative_fit(1)
74 print(glsar_results.summary())74 print(glsar_results.summary())
 75 /usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430:
 76 UserWarning:·`kurtosistest`·p-value·may·be·inaccurate·with·fewer·than·20
 77 observations;·only·n=15·observations·were·given.
 78 ··return·hypotest_fun_in(*args,·**kwds)
75 ···························GLSAR·Regression·Results79 ···························GLSAR·Regression·Results
76 ==============================================================================80 ==============================================================================
77 Dep.·Variable:·················TOTEMP···R-squared:·······················0.99681 Dep.·Variable:·················TOTEMP···R-squared:·······················0.996
78 Model:··························GLSAR···Adj.·R-squared:··················0.99282 Model:··························GLSAR···Adj.·R-squared:··················0.992
79 Method:·················Least·Squares···F-statistic:·····················295.283 Method:·················Least·Squares···F-statistic:·····················295.2
80 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········6.09e-0984 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········6.09e-09
81 Time:························13:13:47···Log-Likelihood:················-102.0485 Time:························13:13:47···Log-Likelihood:················-102.04
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101 ==============================================================================105 ==============================================================================
  
102 Notes:106 Notes:
103 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is107 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is
104 correctly·specified.108 correctly·specified.
105 [2]·The·condition·number·is·large,·4.8e+09.·This·might·indicate·that·there·are109 [2]·The·condition·number·is·large,·4.8e+09.·This·might·indicate·that·there·are
106 strong·multicollinearity·or·other·numerical·problems.110 strong·multicollinearity·or·other·numerical·problems.
107 /usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430: 
108 UserWarning:·`kurtosistest`·p-value·may·be·inaccurate·with·fewer·than·20 
109 observations;·only·n=15·observations·were·given. 
110 ··return·hypotest_fun_in(*args,·**kwds) 
111 Comparing·gls·and·glsar·results,·we·see·that·there·are·some·small·differences111 Comparing·gls·and·glsar·results,·we·see·that·there·are·some·small·differences
112 in·the·parameter·estimates·and·the·resulting·standard·errors·of·the·parameter112 in·the·parameter·estimates·and·the·resulting·standard·errors·of·the·parameter
113 estimate.·This·might·be·do·to·the·numerical·differences·in·the·algorithm,·e.g.113 estimate.·This·might·be·do·to·the·numerical·differences·in·the·algorithm,·e.g.
114 the·treatment·of·initial·conditions,·because·of·the·small·number·of114 the·treatment·of·initial·conditions,·because·of·the·small·number·of
115 observations·in·the·longley·dataset.115 observations·in·the·longley·dataset.
116 [10]:116 [10]:
117 print(gls_results.params)117 print(gls_results.params)
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Similarity: 0.9997807017543859% Differences: {"'cells'": "{16: {'outputs': {0: {'name': 'stderr', 'text': " "['/usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430: UserWarning: " '`kurtosistest` p-value may be inaccurate with fewer than 20 observations; only n=15 ' "observations were given.\\n', ' return hypotest_fun_in(*args, **kwds)\\n']}, 1: " "{'name': 'stdout', 'text': [' GLSAR Regression " "Results \\n', " " […]
    
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234 ············"cell_type":·"code",234 ············"cell_type":·"code",
235 ············"execution_count":·9,235 ············"execution_count":·9,
236 ············"metadata":·{236 ············"metadata":·{
237 ················"execution":·{}237 ················"execution":·{}
238 ············},238 ············},
239 ············"outputs":·[239 ············"outputs":·[
240 ················{240 ················{
 241 ····················"name":·"stderr",
 242 ····················"output_type":·"stream",
 243 ····················"text":·[
 244 ························"/usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430:·UserWarning:·`kurtosistest`·p-value·may·be·inaccurate·with·fewer·than·20·observations;·only·n=15·observations·were·given.\n",
 245 ························"··return·hypotest_fun_in(*args,·**kwds)\n"
 246 ····················]
 247 ················},
 248 ················{
241 ····················"name":·"stdout",249 ····················"name":·"stdout",
242 ····················"output_type":·"stream",250 ····················"output_type":·"stream",
243 ····················"text":·[251 ····················"text":·[
244 ························"···························GLSAR·Regression·Results···························\n",252 ························"···························GLSAR·Regression·Results···························\n",
245 ························"==============================================================================\n",253 ························"==============================================================================\n",
246 ························"Dep.·Variable:·················TOTEMP···R-squared:·······················0.996\n",254 ························"Dep.·Variable:·················TOTEMP···R-squared:·······················0.996\n",
247 ························"Model:··························GLSAR···Adj.·R-squared:··················0.992\n",255 ························"Model:··························GLSAR···Adj.·R-squared:··················0.992\n",
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270 ························"==============================================================================\n",278 ························"==============================================================================\n",
271 ························"\n",279 ························"\n",
272 ························"Notes:\n",280 ························"Notes:\n",
273 ························"[1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified.\n",281 ························"[1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified.\n",
274 ························"[2]·The·condition·number·is·large,·4.8e+09.·This·might·indicate·that·there·are\n",282 ························"[2]·The·condition·number·is·large,·4.8e+09.·This·might·indicate·that·there·are\n",
275 ························"strong·multicollinearity·or·other·numerical·problems.\n"283 ························"strong·multicollinearity·or·other·numerical·problems.\n"
276 ····················]284 ····················]
277 ················}, 
278 ················{ 
279 ····················"name":·"stderr", 
280 ····················"output_type":·"stream", 
281 ····················"text":·[ 
282 ························"/usr/lib/python3/dist-packages/scipy/stats/_axis_nan_policy.py:430:·UserWarning:·`kurtosistest`·p-value·may·be·inaccurate·with·fewer·than·20·observations;·only·n=15·observations·were·given.\n", 
283 ························"··return·hypotest_fun_in(*args,·**kwds)\n" 
284 ····················] 
285 ················}285 ················}
286 ············],286 ············],
287 ············"source":·[287 ············"source":·[
288 ················"glsar_model·=·sm.GLSAR(data.endog,·data.exog,·1)\n",288 ················"glsar_model·=·sm.GLSAR(data.endog,·data.exog,·1)\n",
289 ················"glsar_results·=·glsar_model.iterative_fit(1)\n",289 ················"glsar_results·=·glsar_model.iterative_fit(1)\n",
290 ················"print(glsar_results.summary())"290 ················"print(glsar_results.summary())"
291 ············]291 ············]
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59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="LOWESS-Smoother">61 ··<section·id="LOWESS-Smoother">
62 <h1>LOWESS·Smoother<a·class="headerlink"·href="#LOWESS-Smoother"·title="Link·to·this·heading">¶</a></h1>62 <h1>LOWESS·Smoother<a·class="headerlink"·href="#LOWESS-Smoother"·title="Link·to·this·heading">¶</a></h1>
63 <p>This·notebook·introduces·the·LOWESS·smoother·in·the·<code·class="docutils·literal·notranslate"><span·class="pre">nonparametric</span></code>·package.·LOWESS·performs·weighted·local·linear·fits.</p>63 <p>This·notebook·introduces·the·LOWESS·smoother·in·the·<code·class="docutils·literal·notranslate"><span·class="pre">nonparametric</span></code>·package.·LOWESS·performs·weighted·local·linear·fits.</p>
64 <p>We·generated·some·non-linear·data·and·perform·a·LOWESS·fit,·then·compute·a·95%·confidence·interval·around·the·LOWESS·fit·by·performing·bootstrap·resampling.</p>64 <p>We·generated·some·non-linear·data·and·perform·a·LOWESS·fit,·then·compute·a·95%·confidence·interval·around·the·LOWESS·fit·by·performing·bootstrap·resampling.</p>
65 <div·class="nbinput·nblast·docutils·container">65 <div·class="nbinput·nblast·docutils·container">
66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
67 </pre></div>67 </pre></div>
68 </div>68 </div>
69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
70 <span·class="kn">import</span>·<span·class="nn">pylab</span>70 <span·class="kn">import</span>·<span·class="nn">pylab</span>
71 <span·class="kn">import</span>·<span·class="nn">seaborn</span>·<span·class="k">as</span>·<span·class="nn">sns</span>71 <span·class="kn">import</span>·<span·class="nn">seaborn</span>·<span·class="k">as</span>·<span·class="nn">sns</span>
72 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>72 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
  
73 <span·class="n">sns</span><span·class="o">.</span><span·class="n">set_style</span><span·class="p">(</span><span·class="s2">&quot;darkgrid&quot;</span><span·class="p">)</span>73 <span·class="n">sns</span><span·class="o">.</span><span·class="n">set_style</span><span·class="p">(</span><span·class="s2">&quot;darkgrid&quot;</span><span·class="p">)</span>
74 <span·class="n">pylab</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;figure&quot;</span><span·class="p">,</span>·<span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">16</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>74 <span·class="n">pylab</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;figure&quot;</span><span·class="p">,</span>·<span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">16</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>
75 <span·class="n">pylab</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;font&quot;</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">14</span><span·class="p">)</span>75 <span·class="n">pylab</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;font&quot;</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">14</span><span·class="p">)</span>
76 </pre></div>76 </pre></div>
77 </div>77 </div>
78 </div>78 </div>
79 <div·class="nbinput·nblast·docutils·container">79 <div·class="nbinput·nblast·docutils·container">
80 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:80 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
81 </pre></div>81 </pre></div>
82 </div>82 </div>
83 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Seed·for·consistency</span>83 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Seed·for·consistency</span>
84 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1</span><span·class="p">)</span>84 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1</span><span·class="p">)</span>
85 </pre></div>85 </pre></div>
86 </div>86 </div>
87 </div>87 </div>
88 <div·class="nbinput·nblast·docutils·container">88 <div·class="nbinput·nblast·docutils·container">
89 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:89 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
90 </pre></div>90 </pre></div>
91 </div>91 </div>
92 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Generate·data·looking·like·cosine</span>92 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Generate·data·looking·like·cosine</span>
93 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">4</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">200</span><span·class="p">)</span>93 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">4</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">200</span><span·class="p">)</span>
94 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">cos</span><span·class="p">(</span><span·class="n">x</span><span·class="p">)</span>·<span·class="o">+</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">random</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="nb">len</span><span·class="p">(</span><span·class="n">x</span><span·class="p">))</span>94 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">cos</span><span·class="p">(</span><span·class="n">x</span><span·class="p">)</span>·<span·class="o">+</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">random</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="nb">len</span><span·class="p">(</span><span·class="n">x</span><span·class="p">))</span>
  
95 <span·class="c1">#·Compute·a·lowess·smoothing·of·the·data</span>95 <span·class="c1">#·Compute·a·lowess·smoothing·of·the·data</span>
96 <span·class="n">smoothed</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">nonparametric</span><span·class="o">.</span><span·class="n">lowess</span><span·class="p">(</span><span·class="n">exog</span><span·class="o">=</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">endog</span><span·class="o">=</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">frac</span><span·class="o">=</span><span·class="mf">0.2</span><span·class="p">)</span>96 <span·class="n">smoothed</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">nonparametric</span><span·class="o">.</span><span·class="n">lowess</span><span·class="p">(</span><span·class="n">exog</span><span·class="o">=</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">endog</span><span·class="o">=</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">frac</span><span·class="o">=</span><span·class="mf">0.2</span><span·class="p">)</span>
97 </pre></div>97 </pre></div>
98 </div>98 </div>
99 </div>99 </div>
100 <div·class="nbinput·docutils·container">100 <div·class="nbinput·nblast·docutils·container">
101 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:101 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
102 </pre></div>102 </pre></div>
103 </div>103 </div>
104 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Plot·the·fit·line</span>104 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Plot·the·fit·line</span>
105 <span·class="n">fig</span><span·class="p">,</span>·<span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">pylab</span><span·class="o">.</span><span·class="n">subplots</span><span·class="p">()</span>105 <span·class="n">fig</span><span·class="p">,</span>·<span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">pylab</span><span·class="o">.</span><span·class="n">subplots</span><span·class="p">()</span>
  
106 <span·class="n">ax</span><span·class="o">.</span><span·class="n">scatter</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">)</span>106 <span·class="n">ax</span><span·class="o">.</span><span·class="n">scatter</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">)</span>
107 <span·class="n">ax</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">smoothed</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">],</span>·<span·class="n">smoothed</span><span·class="p">[:,</span>·<span·class="mi">1</span><span·class="p">],</span>·<span·class="n">c</span><span·class="o">=</span><span·class="s2">&quot;k&quot;</span><span·class="p">)</span>107 <span·class="n">ax</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">smoothed</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">],</span>·<span·class="n">smoothed</span><span·class="p">[:,</span>·<span·class="mi">1</span><span·class="p">],</span>·<span·class="n">c</span><span·class="o">=</span><span·class="s2">&quot;k&quot;</span><span·class="p">)</span>
108 <span·class="n">pylab</span><span·class="o">.</span><span·class="n">autoscale</span><span·class="p">(</span><span·class="n">enable</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="s2">&quot;x&quot;</span><span·class="p">,</span>·<span·class="n">tight</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>108 <span·class="n">pylab</span><span·class="o">.</span><span·class="n">autoscale</span><span·class="p">(</span><span·class="n">enable</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="s2">&quot;x&quot;</span><span·class="p">,</span>·<span·class="n">tight</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>
109 </pre></div>109 </pre></div>
110 </div>110 </div>
111 </div>111 </div>
112 <div·class="nboutput·nblast·docutils·container"> 
113 <div·class="prompt·empty·docutils·container"> 
114 </div> 
115 <div·class="output_area·docutils·container"> 
116 <img·alt="../../../_images/examples_notebooks_generated_lowess_4_0.png"·src="../../../_images/examples_notebooks_generated_lowess_4_0.png"·/> 
117 </div> 
118 </div> 
119 <section·id="Confidence-interval">112 <section·id="Confidence-interval">
120 <h2>Confidence·interval<a·class="headerlink"·href="#Confidence-interval"·title="Link·to·this·heading">¶</a></h2>113 <h2>Confidence·interval<a·class="headerlink"·href="#Confidence-interval"·title="Link·to·this·heading">¶</a></h2>
121 <p>Now·that·we·have·performed·a·fit,·we·may·want·to·know·how·precise·it·is.·Bootstrap·resampling·gives·one·way·of·estimating·confidence·intervals·around·a·LOWESS·fit·by·recomputing·the·LOWESS·fit·for·a·large·number·of·random·resamplings·from·our·data.</p>114 <p>Now·that·we·have·performed·a·fit,·we·may·want·to·know·how·precise·it·is.·Bootstrap·resampling·gives·one·way·of·estimating·confidence·intervals·around·a·LOWESS·fit·by·recomputing·the·LOWESS·fit·for·a·large·number·of·random·resamplings·from·our·data.</p>
122 <div·class="nbinput·nblast·docutils·container">115 <div·class="nbinput·nblast·docutils·container">
123 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:116 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
124 </pre></div>117 </pre></div>
125 </div>118 </div>
126 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Now·create·a·bootstrap·confidence·interval·around·the·a·LOWESS·fit</span>119 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Now·create·a·bootstrap·confidence·interval·around·the·a·LOWESS·fit</span>
  
  
127 <span·class="k">def</span>·<span·class="nf">lowess_with_confidence_bounds</span><span·class="p">(</span>120 <span·class="k">def</span>·<span·class="nf">lowess_with_confidence_bounds</span><span·class="p">(</span>
128 ····<span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">,</span>·<span·class="n">eval_x</span><span·class="p">,</span>·<span·class="n">N</span><span·class="o">=</span><span·class="mi">200</span><span·class="p">,</span>·<span·class="n">conf_interval</span><span·class="o">=</span><span·class="mf">0.95</span><span·class="p">,</span>·<span·class="n">lowess_kw</span><span·class="o">=</span><span·class="kc">None</span>121 ····<span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">,</span>·<span·class="n">eval_x</span><span·class="p">,</span>·<span·class="n">N</span><span·class="o">=</span><span·class="mi">200</span><span·class="p">,</span>·<span·class="n">conf_interval</span><span·class="o">=</span><span·class="mf">0.95</span><span·class="p">,</span>·<span·class="n">lowess_kw</span><span·class="o">=</span><span·class="kc">None</span>
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163 <span·class="n">eval_x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">4</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span><span·class="p">,</span>·<span·class="mi">31</span><span·class="p">)</span>156 <span·class="n">eval_x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">4</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span><span·class="p">,</span>·<span·class="mi">31</span><span·class="p">)</span>
164 <span·class="n">smoothed</span><span·class="p">,</span>·<span·class="n">bottom</span><span·class="p">,</span>·<span·class="n">top</span>·<span·class="o">=</span>·<span·class="n">lowess_with_confidence_bounds</span><span·class="p">(</span>157 <span·class="n">smoothed</span><span·class="p">,</span>·<span·class="n">bottom</span><span·class="p">,</span>·<span·class="n">top</span>·<span·class="o">=</span>·<span·class="n">lowess_with_confidence_bounds</span><span·class="p">(</span>
165 ····<span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">,</span>·<span·class="n">eval_x</span><span·class="p">,</span>·<span·class="n">lowess_kw</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;frac&quot;</span><span·class="p">:</span>·<span·class="mf">0.1</span><span·class="p">}</span>158 ····<span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">,</span>·<span·class="n">eval_x</span><span·class="p">,</span>·<span·class="n">lowess_kw</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;frac&quot;</span><span·class="p">:</span>·<span·class="mf">0.1</span><span·class="p">}</span>
166 <span·class="p">)</span>159 <span·class="p">)</span>
167 </pre></div>160 </pre></div>
168 </div>161 </div>
169 </div>162 </div>
170 <div·class="nbinput·docutils·container">163 <div·class="nbinput·nblast·docutils·container">
171 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:164 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
172 </pre></div>165 </pre></div>
173 </div>166 </div>
174 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Plot·the·confidence·interval·and·fit</span>167 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Plot·the·confidence·interval·and·fit</span>
175 <span·class="n">fig</span><span·class="p">,</span>·<span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">pylab</span><span·class="o">.</span><span·class="n">subplots</span><span·class="p">()</span>168 <span·class="n">fig</span><span·class="p">,</span>·<span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">pylab</span><span·class="o">.</span><span·class="n">subplots</span><span·class="p">()</span>
176 <span·class="n">ax</span><span·class="o">.</span><span·class="n">scatter</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">)</span>169 <span·class="n">ax</span><span·class="o">.</span><span·class="n">scatter</span><span·class="p">(</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">y</span><span·class="p">)</span>
177 <span·class="n">ax</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">eval_x</span><span·class="p">,</span>·<span·class="n">smoothed</span><span·class="p">,</span>·<span·class="n">c</span><span·class="o">=</span><span·class="s2">&quot;k&quot;</span><span·class="p">)</span>170 <span·class="n">ax</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">eval_x</span><span·class="p">,</span>·<span·class="n">smoothed</span><span·class="p">,</span>·<span·class="n">c</span><span·class="o">=</span><span·class="s2">&quot;k&quot;</span><span·class="p">)</span>
178 <span·class="n">ax</span><span·class="o">.</span><span·class="n">fill_between</span><span·class="p">(</span><span·class="n">eval_x</span><span·class="p">,</span>·<span·class="n">bottom</span><span·class="p">,</span>·<span·class="n">top</span><span·class="p">,</span>·<span·class="n">alpha</span><span·class="o">=</span><span·class="mf">0.5</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;b&quot;</span><span·class="p">)</span>171 <span·class="n">ax</span><span·class="o">.</span><span·class="n">fill_between</span><span·class="p">(</span><span·class="n">eval_x</span><span·class="p">,</span>·<span·class="n">bottom</span><span·class="p">,</span>·<span·class="n">top</span><span·class="p">,</span>·<span·class="n">alpha</span><span·class="o">=</span><span·class="mf">0.5</span><span·class="p">,</span>·<span·class="n">color</span><span·class="o">=</span><span·class="s2">&quot;b&quot;</span><span·class="p">)</span>
179 <span·class="n">pylab</span><span·class="o">.</span><span·class="n">autoscale</span><span·class="p">(</span><span·class="n">enable</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="s2">&quot;x&quot;</span><span·class="p">,</span>·<span·class="n">tight</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>172 <span·class="n">pylab</span><span·class="o">.</span><span·class="n">autoscale</span><span·class="p">(</span><span·class="n">enable</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="s2">&quot;x&quot;</span><span·class="p">,</span>·<span·class="n">tight</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>
180 </pre></div>173 </pre></div>
181 </div>174 </div>
182 </div>175 </div>
183 <div·class="nboutput·nblast·docutils·container"> 
184 <div·class="prompt·empty·docutils·container"> 
185 </div> 
186 <div·class="output_area·docutils·container"> 
187 <img·alt="../../../_images/examples_notebooks_generated_lowess_7_0.png"·src="../../../_images/examples_notebooks_generated_lowess_7_0.png"·/> 
188 </div> 
189 </div> 
190 </section>176 </section>
191 </section>177 </section>
  
  
192 ············<div·class="clearer"></div>178 ············<div·class="clearer"></div>
193 ··········</div>179 ··········</div>
194 ········</div>180 ········</div>
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7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·LOWESS·Smoother8 ····*·LOWESS·Smoother
9 *\x8**\x8**\x8**\x8**\x8**\x8*·L\x8LO\x8OW\x8WE\x8ES\x8SS\x8S·S\x8Sm\x8mo\x8oo\x8ot\x8th\x8he\x8er\x8r_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·L\x8LO\x8OW\x8WE\x8ES\x8SS\x8S·S\x8Sm\x8mo\x8oo\x8ot\x8th\x8he\x8er\x8r_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 This·notebook·introduces·the·LOWESS·smoother·in·the·nonparametric·package.10 This·notebook·introduces·the·LOWESS·smoother·in·the·nonparametric·package.
11 LOWESS·performs·weighted·local·linear·fits.11 LOWESS·performs·weighted·local·linear·fits.
12 We·generated·some·non-linear·data·and·perform·a·LOWESS·fit,·then·compute·a·95%12 We·generated·some·non-linear·data·and·perform·a·LOWESS·fit,·then·compute·a·95%
13 confidence·interval·around·the·LOWESS·fit·by·performing·bootstrap·resampling.13 confidence·interval·around·the·LOWESS·fit·by·performing·bootstrap·resampling.
14 [1]:14 [·]:
15 import·numpy·as·np15 import·numpy·as·np
16 import·pylab16 import·pylab
17 import·seaborn·as·sns17 import·seaborn·as·sns
18 import·statsmodels.api·as·sm18 import·statsmodels.api·as·sm
  
19 sns.set_style("darkgrid")19 sns.set_style("darkgrid")
20 pylab.rc("figure",·figsize=(16,·8))20 pylab.rc("figure",·figsize=(16,·8))
21 pylab.rc("font",·size=14)21 pylab.rc("font",·size=14)
22 [2]:22 [·]:
23 #·Seed·for·consistency23 #·Seed·for·consistency
24 np.random.seed(1)24 np.random.seed(1)
25 [3]:25 [·]:
26 #·Generate·data·looking·like·cosine26 #·Generate·data·looking·like·cosine
27 x·=·np.random.uniform(0,·4·*·np.pi,·size=200)27 x·=·np.random.uniform(0,·4·*·np.pi,·size=200)
28 y·=·np.cos(x)·+·np.random.random(size=len(x))28 y·=·np.cos(x)·+·np.random.random(size=len(x))
  
29 #·Compute·a·lowess·smoothing·of·the·data29 #·Compute·a·lowess·smoothing·of·the·data
30 smoothed·=·sm.nonparametric.lowess(exog=x,·endog=y,·frac=0.2)30 smoothed·=·sm.nonparametric.lowess(exog=x,·endog=y,·frac=0.2)
31 [4]:31 [·]:
32 #·Plot·the·fit·line32 #·Plot·the·fit·line
33 fig,·ax·=·pylab.subplots()33 fig,·ax·=·pylab.subplots()
  
34 ax.scatter(x,·y)34 ax.scatter(x,·y)
35 ax.plot(smoothed[:,·0],·smoothed[:,·1],·c="k")35 ax.plot(smoothed[:,·0],·smoothed[:,·1],·c="k")
36 pylab.autoscale(enable=True,·axis="x",·tight=True)36 pylab.autoscale(enable=True,·axis="x",·tight=True)
37 [../../../_images/examples_notebooks_generated_lowess_4_0.png] 
38 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nf\x8fi\x8id\x8de\x8en\x8nc\x8ce\x8e·i\x8in\x8nt\x8te\x8er\x8rv\x8va\x8al\x8l_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*37 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nf\x8fi\x8id\x8de\x8en\x8nc\x8ce\x8e·i\x8in\x8nt\x8te\x8er\x8rv\x8va\x8al\x8l_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
39 Now·that·we·have·performed·a·fit,·we·may·want·to·know·how·precise·it·is.38 Now·that·we·have·performed·a·fit,·we·may·want·to·know·how·precise·it·is.
40 Bootstrap·resampling·gives·one·way·of·estimating·confidence·intervals·around·a39 Bootstrap·resampling·gives·one·way·of·estimating·confidence·intervals·around·a
41 LOWESS·fit·by·recomputing·the·LOWESS·fit·for·a·large·number·of·random40 LOWESS·fit·by·recomputing·the·LOWESS·fit·for·a·large·number·of·random
42 resamplings·from·our·data.41 resamplings·from·our·data.
43 [5]:42 [·]:
44 #·Now·create·a·bootstrap·confidence·interval·around·the·a·LOWESS·fit43 #·Now·create·a·bootstrap·confidence·interval·around·the·a·LOWESS·fit
  
  
45 def·lowess_with_confidence_bounds(44 def·lowess_with_confidence_bounds(
46 ····x,·y,·eval_x,·N=200,·conf_interval=0.95,·lowess_kw=None45 ····x,·y,·eval_x,·N=200,·conf_interval=0.95,·lowess_kw=None
47 ):46 ):
48 ····"""47 ····"""
Offset 80, 22 lines modifiedOffset 79, 21 lines modified
  
  
80 #·Compute·the·95%·confidence·interval79 #·Compute·the·95%·confidence·interval
81 eval_x·=·np.linspace(0,·4·*·np.pi,·31)80 eval_x·=·np.linspace(0,·4·*·np.pi,·31)
82 smoothed,·bottom,·top·=·lowess_with_confidence_bounds(81 smoothed,·bottom,·top·=·lowess_with_confidence_bounds(
83 ····x,·y,·eval_x,·lowess_kw={"frac":·0.1}82 ····x,·y,·eval_x,·lowess_kw={"frac":·0.1}
84 )83 )
85 [6]:84 [·]:
86 #·Plot·the·confidence·interval·and·fit85 #·Plot·the·confidence·interval·and·fit
87 fig,·ax·=·pylab.subplots()86 fig,·ax·=·pylab.subplots()
88 ax.scatter(x,·y)87 ax.scatter(x,·y)
89 ax.plot(eval_x,·smoothed,·c="k")88 ax.plot(eval_x,·smoothed,·c="k")
90 ax.fill_between(eval_x,·bottom,·top,·alpha=0.5,·color="b")89 ax.fill_between(eval_x,·bottom,·top,·alpha=0.5,·color="b")
91 pylab.autoscale(enable=True,·axis="x",·tight=True)90 pylab.autoscale(enable=True,·axis="x",·tight=True)
92 [../../../_images/examples_notebooks_generated_lowess_7_0.png] 
93 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]91 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
94 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*92 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*
95 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s93 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s
96 ····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d94 ····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d
97 ····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e95 ····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e
98 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s96 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s
99 ····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e97 ····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e
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60 ········<div·class="bodywrapper">60 ········<div·class="bodywrapper">
61 ··········<div·class="body"·role="main">61 ··········<div·class="body"·role="main">
62 ············62 ············
63 ··<section·id="Markov-switching-dynamic-regression-models">63 ··<section·id="Markov-switching-dynamic-regression-models">
64 <h1>Markov·switching·dynamic·regression·models<a·class="headerlink"·href="#Markov-switching-dynamic-regression-models"·title="Link·to·this·heading">¶</a></h1>64 <h1>Markov·switching·dynamic·regression·models<a·class="headerlink"·href="#Markov-switching-dynamic-regression-models"·title="Link·to·this·heading">¶</a></h1>
65 <p>This·notebook·provides·an·example·of·the·use·of·Markov·switching·models·in·statsmodels·to·estimate·dynamic·regression·models·with·changes·in·regime.·It·follows·the·examples·in·the·Stata·Markov·switching·documentation,·which·can·be·found·at·<a·class="reference·external"·href="http://www.stata.com/manuals14/tsmswitch.pdf">http://www.stata.com/manuals14/tsmswitch.pdf</a>.</p>65 <p>This·notebook·provides·an·example·of·the·use·of·Markov·switching·models·in·statsmodels·to·estimate·dynamic·regression·models·with·changes·in·regime.·It·follows·the·examples·in·the·Stata·Markov·switching·documentation,·which·can·be·found·at·<a·class="reference·external"·href="http://www.stata.com/manuals14/tsmswitch.pdf">http://www.stata.com/manuals14/tsmswitch.pdf</a>.</p>
66 <div·class="nbinput·nblast·docutils·container">66 <div·class="nbinput·nblast·docutils·container">
67 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:67 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline70 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
  
71 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>71 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
72 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>72 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
73 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>73 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
Offset 87, 16 lines modifiedOffset 87, 16 lines modified
87 \[\begin{split}·P(S_t·=·s_t·|·S_{t-1}·=·s_{t-1})·=87 \[\begin{split}·P(S_t·=·s_t·|·S_{t-1}·=·s_{t-1})·=
88 \begin{bmatrix}88 \begin{bmatrix}
89 p_{00}·&amp;·p_{10}·\\89 p_{00}·&amp;·p_{10}·\\
90 1·-·p_{00}·&amp;·1·-·p_{10}90 1·-·p_{00}·&amp;·1·-·p_{10}
91 \end{bmatrix}\end{split}\]</div>91 \end{bmatrix}\end{split}\]</div>
92 <p>We·will·estimate·the·parameters·of·this·model·by·maximum·likelihood:·<span·class="math·notranslate·nohighlight">\(p_{00},·p_{10},·\mu_0,·\mu_1,·\sigma^2\)</span>.</p>92 <p>We·will·estimate·the·parameters·of·this·model·by·maximum·likelihood:·<span·class="math·notranslate·nohighlight">\(p_{00},·p_{10},·\mu_0,·\mu_1,·\sigma^2\)</span>.</p>
93 <p>The·data·used·in·this·example·can·be·found·at·<a·class="reference·external"·href="https://www.stata-press.com/data/r14/usmacro">https://www.stata-press.com/data/r14/usmacro</a>.</p>93 <p>The·data·used·in·this·example·can·be·found·at·<a·class="reference·external"·href="https://www.stata-press.com/data/r14/usmacro">https://www.stata-press.com/data/r14/usmacro</a>.</p>
94 <div·class="nbinput·docutils·container">94 <div·class="nbinput·nblast·docutils·container">
95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
96 </pre></div>96 </pre></div>
97 </div>97 </div>
98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Get·the·federal·funds·rate·data</span>98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Get·the·federal·funds·rate·data</span>
99 <span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.regime_switching.tests.test_markov_regression</span>·<span·class="kn">import</span>·<span·class="n">fedfunds</span>99 <span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.regime_switching.tests.test_markov_regression</span>·<span·class="kn">import</span>·<span·class="n">fedfunds</span>
  
100 <span·class="n">dta_fedfunds</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">Series</span><span·class="p">(</span>100 <span·class="n">dta_fedfunds</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">Series</span><span·class="p">(</span>
101 ····<span·class="n">fedfunds</span><span·class="p">,</span>·<span·class="n">index</span><span·class="o">=</span><span·class="n">pd</span><span·class="o">.</span><span·class="n">date_range</span><span·class="p">(</span><span·class="s2">&quot;1954-07-01&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;2010-10-01&quot;</span><span·class="p">,</span>·<span·class="n">freq</span><span·class="o">=</span><span·class="s2">&quot;QS&quot;</span><span·class="p">)</span>101 ····<span·class="n">fedfunds</span><span·class="p">,</span>·<span·class="n">index</span><span·class="o">=</span><span·class="n">pd</span><span·class="o">.</span><span·class="n">date_range</span><span·class="p">(</span><span·class="s2">&quot;1954-07-01&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;2010-10-01&quot;</span><span·class="p">,</span>·<span·class="n">freq</span><span·class="o">=</span><span·class="s2">&quot;QS&quot;</span><span·class="p">)</span>
Offset 108, 142 lines modifiedOffset 108, 42 lines modified
108 <span·class="c1">#·Fit·the·model</span>108 <span·class="c1">#·Fit·the·model</span>
109 <span·class="c1">#·(a·switching·mean·is·the·default·of·the·MarkovRegession·model)</span>109 <span·class="c1">#·(a·switching·mean·is·the·default·of·the·MarkovRegession·model)</span>
110 <span·class="n">mod_fedfunds</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">MarkovRegression</span><span·class="p">(</span><span·class="n">dta_fedfunds</span><span·class="p">,</span>·<span·class="n">k_regimes</span><span·class="o">=</span><span·class="mi">2</span><span·class="p">)</span>110 <span·class="n">mod_fedfunds</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">MarkovRegression</span><span·class="p">(</span><span·class="n">dta_fedfunds</span><span·class="p">,</span>·<span·class="n">k_regimes</span><span·class="o">=</span><span·class="mi">2</span><span·class="p">)</span>
111 <span·class="n">res_fedfunds</span>·<span·class="o">=</span>·<span·class="n">mod_fedfunds</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>111 <span·class="n">res_fedfunds</span>·<span·class="o">=</span>·<span·class="n">mod_fedfunds</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
112 </pre></div>112 </pre></div>
113 </div>113 </div>
114 </div>114 </div>
115 <div·class="nboutput·nblast·docutils·container">115 <div·class="nbinput·nblast·docutils·container">
116 <div·class="prompt·empty·docutils·container"> 
117 </div> 
118 <div·class="output_area·docutils·container"> 
119 <img·alt="../../../_images/examples_notebooks_generated_markov_regression_4_0.png"·src="../../../_images/examples_notebooks_generated_markov_regression_4_0.png"·/> 
120 </div> 
121 </div> 
122 <div·class="nbinput·docutils·container"> 
123 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:116 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
124 </pre></div>117 </pre></div>
125 </div>118 </div>
126 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res_fedfunds</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">()</span>119 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res_fedfunds</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">()</span>
127 </pre></div>120 </pre></div>
128 </div>121 </div>
129 </div>122 </div>
130 <div·class="nboutput·nblast·docutils·container"> 
131 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]: 
132 </pre></div> 
133 </div> 
134 <div·class="output_area·rendered_html·docutils·container"> 
135 <table·class="simpletable"> 
136 <caption>Markov·Switching·Model·Results</caption> 
137 <tr> 
138 ··<th>Dep.·Variable:</th>···········<td>y</td>········<th>··No.·Observations:··</th>····<td>226</td> 
139 </tr> 
140 <tr> 
141 ··<th>Model:</th>···········<td>MarkovRegression</td>·<th>··Log·Likelihood·····</th>·<td>-508.636</td> 
142 </tr> 
143 <tr> 
144 ··<th>Date:</th>············<td>Sun,·10·Aug·2025</td>·<th>··AIC················</th>·<td>1027.272</td> 
145 </tr> 
146 <tr> 
147 ··<th>Time:</th>················<td>13:13:47</td>·····<th>··BIC················</th>·<td>1044.375</td> 
148 </tr> 
149 <tr> 
150 ··<th>Sample:</th>·············<td>07-01-1954</td>····<th>··HQIC···············</th>·<td>1034.174</td> 
151 </tr> 
152 <tr> 
153 ··<th></th>···················<td>-·10-01-2010</td>···<th>·····················</th>·····<td>·</td> 
154 </tr> 
155 <tr> 
156 ··<th>Covariance·Type:</th>······<td>approx</td>······<th>·····················</th>·····<td>·</td> 
157 </tr> 
158 </table> 
159 <table·class="simpletable"> 
160 <caption>Regime·0·parameters</caption> 
161 <tr> 
162 ····<td></td>·······<th>coef</th>·····<th>std·err</th>······<th>z</th>······<th>P>|z|</th>··<th>[0.025</th>····<th>0.975]</th> 
163 </tr> 
164 <tr> 
165 ··<th>const</th>·<td>····3.7088</td>·<td>····0.177</td>·<td>···20.988</td>·<td>·0.000</td>·<td>····3.362</td>·<td>····4.055</td> 
166 </tr> 
167 </table> 
168 <table·class="simpletable"> 
169 <caption>Regime·1·parameters</caption> 
170 <tr> 
171 ····<td></td>·······<th>coef</th>·····<th>std·err</th>······<th>z</th>······<th>P>|z|</th>··<th>[0.025</th>····<th>0.975]</th> 
172 </tr> 
173 <tr> 
174 ··<th>const</th>·<td>····9.5568</td>·<td>····0.300</td>·<td>···31.857</td>·<td>·0.000</td>·<td>····8.969</td>·<td>···10.145</td> 
175 </tr> 
176 </table> 
177 <table·class="simpletable"> 
178 <caption>Non-switching·parameters</caption> 
179 <tr> 
180 ·····<td></td>·······<th>coef</th>·····<th>std·err</th>······<th>z</th>······<th>P>|z|</th>··<th>[0.025</th>····<th>0.975]</th> 
181 </tr> 
182 <tr> 
183 ··<th>sigma2</th>·<td>····4.4418</td>·<td>····0.425</td>·<td>···10.447</td>·<td>·0.000</td>·<td>····3.608</td>·<td>····5.275</td> 
184 </tr> 
185 </table> 
186 <table·class="simpletable"> 
187 <caption>Regime·transition·parameters</caption> 
188 <tr> 
189 ·····<td></td>········<th>coef</th>·····<th>std·err</th>······<th>z</th>······<th>P>|z|</th>··<th>[0.025</th>····<th>0.975]</th> 
190 </tr> 
191 <tr> 
192 ··<th>p[0->0]</th>·<td>····0.9821</td>·<td>····0.010</td>·<td>···94.443</td>·<td>·0.000</td>·<td>····0.962</td>·<td>····1.002</td> 
193 </tr> 
194 <tr> 
195 ··<th>p[1->0]</th>·<td>····0.0504</td>·<td>····0.027</td>·<td>····1.876</td>·<td>·0.061</td>·<td>···-0.002</td>·<td>····0.103</td> 
196 </tr> 
197 </table><br/><br/>Warnings:<br/>[1]·Covariance·matrix·calculated·using·numerical·(complex-step)·differentiation.</div> 
198 </div> 
199 <p>From·the·summary·output,·the·mean·federal·funds·rate·in·the·first·regime·(the·“low·regime”)·is·estimated·to·be·<span·class="math·notranslate·nohighlight">\(3.7\)</span>·whereas·in·the·“high·regime”·it·is·<span·class="math·notranslate·nohighlight">\(9.6\)</span>.·Below·we·plot·the·smoothed·probabilities·of·being·in·the·high·regime.·The·model·suggests·that·the·1980’s·was·a·time-period·in·which·a·high·federal·funds·rate·existed.</p>123 <p>From·the·summary·output,·the·mean·federal·funds·rate·in·the·first·regime·(the·“low·regime”)·is·estimated·to·be·<span·class="math·notranslate·nohighlight">\(3.7\)</span>·whereas·in·the·“high·regime”·it·is·<span·class="math·notranslate·nohighlight">\(9.6\)</span>.·Below·we·plot·the·smoothed·probabilities·of·being·in·the·high·regime.·The·model·suggests·that·the·1980’s·was·a·time-period·in·which·a·high·federal·funds·rate·existed.</p>
200 <div·class="nbinput·docutils·container">124 <div·class="nbinput·nblast·docutils·container">
201 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:125 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
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7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Markov·switching·dynamic·regression·models8 ····*·Markov·switching·dynamic·regression·models
9 *\x8**\x8**\x8**\x8**\x8**\x8*·M\x8Ma\x8ar\x8rk\x8ko\x8ov\x8v·s\x8sw\x8wi\x8it\x8tc\x8ch\x8hi\x8in\x8ng\x8g·d\x8dy\x8yn\x8na\x8am\x8mi\x8ic\x8c·r\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·m\x8mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·M\x8Ma\x8ar\x8rk\x8ko\x8ov\x8v·s\x8sw\x8wi\x8it\x8tc\x8ch\x8hi\x8in\x8ng\x8g·d\x8dy\x8yn\x8na\x8am\x8mi\x8ic\x8c·r\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·m\x8mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 This·notebook·provides·an·example·of·the·use·of·Markov·switching·models·in10 This·notebook·provides·an·example·of·the·use·of·Markov·switching·models·in
11 statsmodels·to·estimate·dynamic·regression·models·with·changes·in·regime.·It11 statsmodels·to·estimate·dynamic·regression·models·with·changes·in·regime.·It
12 follows·the·examples·in·the·Stata·Markov·switching·documentation,·which·can·be12 follows·the·examples·in·the·Stata·Markov·switching·documentation,·which·can·be
13 found·at·_\x8h_\x8t_\x8t_\x8p_\x8:_\x8/_\x8/_\x8w_\x8w_\x8w_\x8._\x8s_\x8t_\x8a_\x8t_\x8a_\x8._\x8c_\x8o_\x8m_\x8/_\x8m_\x8a_\x8n_\x8u_\x8a_\x8l_\x8s_\x81_\x84_\x8/_\x8t_\x8s_\x8m_\x8s_\x8w_\x8i_\x8t_\x8c_\x8h_\x8._\x8p_\x8d_\x8f.13 found·at·_\x8h_\x8t_\x8t_\x8p_\x8:_\x8/_\x8/_\x8w_\x8w_\x8w_\x8._\x8s_\x8t_\x8a_\x8t_\x8a_\x8._\x8c_\x8o_\x8m_\x8/_\x8m_\x8a_\x8n_\x8u_\x8a_\x8l_\x8s_\x81_\x84_\x8/_\x8t_\x8s_\x8m_\x8s_\x8w_\x8i_\x8t_\x8c_\x8h_\x8._\x8p_\x8d_\x8f.
14 [1]:14 [·]:
15 %matplotlib·inline15 %matplotlib·inline
  
16 import·numpy·as·np16 import·numpy·as·np
17 import·pandas·as·pd17 import·pandas·as·pd
18 import·statsmodels.api·as·sm18 import·statsmodels.api·as·sm
19 import·matplotlib.pyplot·as·plt19 import·matplotlib.pyplot·as·plt
20 from·datetime·import·datetime20 from·datetime·import·datetime
Offset 28, 15 lines modifiedOffset 28, 15 lines modified
28 where·\(S_t·\in·\{0,·1\}\),·and·the·regime·transitions·according·to28 where·\(S_t·\in·\{0,·1\}\),·and·the·regime·transitions·according·to
29 \[\begin{split}·P(S_t·=·s_t·|·S_{t-1}·=·s_{t-1})·=·\begin{bmatrix}·p_{00}·&·p_29 \[\begin{split}·P(S_t·=·s_t·|·S_{t-1}·=·s_{t-1})·=·\begin{bmatrix}·p_{00}·&·p_
30 {10}·\\·1·-·p_{00}·&·1·-·p_{10}·\end{bmatrix}\end{split}\]30 {10}·\\·1·-·p_{00}·&·1·-·p_{10}·\end{bmatrix}\end{split}\]
31 We·will·estimate·the·parameters·of·this·model·by·maximum·likelihood:·\(p_{00},31 We·will·estimate·the·parameters·of·this·model·by·maximum·likelihood:·\(p_{00},
32 p_{10},·\mu_0,·\mu_1,·\sigma^2\).32 p_{10},·\mu_0,·\mu_1,·\sigma^2\).
33 The·data·used·in·this·example·can·be·found·at·_\x8h_\x8t_\x8t_\x8p_\x8s_\x8:_\x8/_\x8/_\x8w_\x8w_\x8w_\x8._\x8s_\x8t_\x8a_\x8t_\x8a_\x8-_\x8p_\x8r_\x8e_\x8s_\x8s_\x8._\x8c_\x8o_\x8m_\x8/_\x8d_\x8a_\x8t_\x8a_\x8/33 The·data·used·in·this·example·can·be·found·at·_\x8h_\x8t_\x8t_\x8p_\x8s_\x8:_\x8/_\x8/_\x8w_\x8w_\x8w_\x8._\x8s_\x8t_\x8a_\x8t_\x8a_\x8-_\x8p_\x8r_\x8e_\x8s_\x8s_\x8._\x8c_\x8o_\x8m_\x8/_\x8d_\x8a_\x8t_\x8a_\x8/
34 _\x8r_\x81_\x84_\x8/_\x8u_\x8s_\x8m_\x8a_\x8c_\x8r_\x8o.34 _\x8r_\x81_\x84_\x8/_\x8u_\x8s_\x8m_\x8a_\x8c_\x8r_\x8o.
35 [2]:35 [·]:
36 #·Get·the·federal·funds·rate·data36 #·Get·the·federal·funds·rate·data
37 from·statsmodels.tsa.regime_switching.tests.test_markov_regression·import37 from·statsmodels.tsa.regime_switching.tests.test_markov_regression·import
38 fedfunds38 fedfunds
  
39 dta_fedfunds·=·pd.Series(39 dta_fedfunds·=·pd.Series(
40 ····fedfunds,·index=pd.date_range("1954-07-01",·"2010-10-01",·freq="QS")40 ····fedfunds,·index=pd.date_range("1954-07-01",·"2010-10-01",·freq="QS")
41 )41 )
Offset 44, 138 lines modifiedOffset 44, 73 lines modified
44 #·Plot·the·data44 #·Plot·the·data
45 dta_fedfunds.plot(title="Federal·funds·rate",·figsize=(12,·3))45 dta_fedfunds.plot(title="Federal·funds·rate",·figsize=(12,·3))
  
46 #·Fit·the·model46 #·Fit·the·model
47 #·(a·switching·mean·is·the·default·of·the·MarkovRegession·model)47 #·(a·switching·mean·is·the·default·of·the·MarkovRegession·model)
48 mod_fedfunds·=·sm.tsa.MarkovRegression(dta_fedfunds,·k_regimes=2)48 mod_fedfunds·=·sm.tsa.MarkovRegression(dta_fedfunds,·k_regimes=2)
49 res_fedfunds·=·mod_fedfunds.fit()49 res_fedfunds·=·mod_fedfunds.fit()
50 [../../../_images/examples_notebooks_generated_markov_regression_4_0.png] 
51 [3]:50 [·]:
52 res_fedfunds.summary()51 res_fedfunds.summary()
53 [3]: 
54 ···············M\x8Ma\x8ar\x8rk\x8ko\x8ov\x8v·S\x8Sw\x8wi\x8it\x8tc\x8ch\x8hi\x8in\x8ng\x8g·M\x8Mo\x8od\x8de\x8el\x8l·R\x8Re\x8es\x8su\x8ul\x8lt\x8ts\x8s 
55 D\x8De\x8ep\x8p.\x8.·V\x8Va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8e:\x8:···y················N\x8No\x8o.\x8.·O\x8Ob\x8bs\x8se\x8er\x8rv\x8va\x8at\x8ti\x8io\x8on\x8ns\x8s:\x8:·226 
56 M\x8Mo\x8od\x8de\x8el\x8l:\x8:···········MarkovRegression·L\x8Lo\x8og\x8g·L\x8Li\x8ik\x8ke\x8el\x8li\x8ih\x8ho\x8oo\x8od\x8d····-508.636 
57 D\x8Da\x8at\x8te\x8e:\x8:············Sun,·10·Aug·2025·A\x8AI\x8IC\x8C···············1027.272 
58 T\x8Ti\x8im\x8me\x8e:\x8:············13:13:47·········B\x8BI\x8IC\x8C···············1044.375 
59 S\x8Sa\x8am\x8mp\x8pl\x8le\x8e:\x8:··········07-01-1954·······H\x8HQ\x8QI\x8IC\x8C··············1034.174 
60 ·················-·10-01-2010 
61 C\x8Co\x8ov\x8va\x8ar\x8ri\x8ia\x8an\x8nc\x8ce\x8e·T\x8Ty\x8yp\x8pe\x8e:\x8:·approx 
62 ··············R\x8Re\x8eg\x8gi\x8im\x8me\x8e·0\x80·p\x8pa\x8ar\x8ra\x8am\x8me\x8et\x8te\x8er\x8rs\x8s 
63 ······c\x8co\x8oe\x8ef\x8f···s\x8st\x8td\x8d·e\x8er\x8rr\x8r·z\x8z······P\x8P>\x8>|\x8|z\x8z|\x8|·[\x8[0\x80.\x8.0\x802\x825\x85·0\x80.\x8.9\x897\x875\x85]\x8] 
64 c\x8co\x8on\x8ns\x8st\x8t·3.7088·0.177···20.988·0.000·3.362··4.055 
65 ··············R\x8Re\x8eg\x8gi\x8im\x8me\x8e·1\x81·p\x8pa\x8ar\x8ra\x8am\x8me\x8et\x8te\x8er\x8rs\x8s 
66 ······c\x8co\x8oe\x8ef\x8f···s\x8st\x8td\x8d·e\x8er\x8rr\x8r·z\x8z······P\x8P>\x8>|\x8|z\x8z|\x8|·[\x8[0\x80.\x8.0\x802\x825\x85·0\x80.\x8.9\x897\x875\x85]\x8] 
67 c\x8co\x8on\x8ns\x8st\x8t·9.5568·0.300···31.857·0.000·8.969··10.145 
68 ············N\x8No\x8on\x8n-\x8-s\x8sw\x8wi\x8it\x8tc\x8ch\x8hi\x8in\x8ng\x8g·p\x8pa\x8ar\x8ra\x8am\x8me\x8et\x8te\x8er\x8rs\x8s 
69 ·······c\x8co\x8oe\x8ef\x8f···s\x8st\x8td\x8d·e\x8er\x8rr\x8r·z\x8z······P\x8P>\x8>|\x8|z\x8z|\x8|·[\x8[0\x80.\x8.0\x802\x825\x85·0\x80.\x8.9\x897\x875\x85]\x8] 
70 s\x8si\x8ig\x8gm\x8ma\x8a2\x82·4.4418·0.425···10.447·0.000·3.608··5.275 
71 ··········R\x8Re\x8eg\x8gi\x8im\x8me\x8e·t\x8tr\x8ra\x8an\x8ns\x8si\x8it\x8ti\x8io\x8on\x8n·p\x8pa\x8ar\x8ra\x8am\x8me\x8et\x8te\x8er\x8rs\x8s 
72 ········c\x8co\x8oe\x8ef\x8f···s\x8st\x8td\x8d·e\x8er\x8rr\x8r·z\x8z······P\x8P>\x8>|\x8|z\x8z|\x8|·[\x8[0\x80.\x8.0\x802\x825\x85·0\x80.\x8.9\x897\x875\x85]\x8] 
73 p\x8p[\x8[0\x80-\x8->\x8>0\x80]\x8]·0.9821·0.010···94.443·0.000·0.962··1.002 
74 p\x8p[\x8[1\x81-\x8->\x8>0\x80]\x8]·0.0504·0.027···1.876··0.061·-0.002·0.103 
  
  
75 Warnings: 
76 [1]·Covariance·matrix·calculated·using·numerical·(complex-step) 
77 differentiation. 
78 From·the·summary·output,·the·mean·federal·funds·rate·in·the·first·regime·(the52 From·the·summary·output,·the·mean·federal·funds·rate·in·the·first·regime·(the
79 “low·regime”)·is·estimated·to·be·\(3.7\)·whereas·in·the·“high·regime”·it·is·\53 “low·regime”)·is·estimated·to·be·\(3.7\)·whereas·in·the·“high·regime”·it·is·\
80 (9.6\).·Below·we·plot·the·smoothed·probabilities·of·being·in·the·high·regime.54 (9.6\).·Below·we·plot·the·smoothed·probabilities·of·being·in·the·high·regime.
81 The·model·suggests·that·the·1980’s·was·a·time-period·in·which·a·high·federal55 The·model·suggests·that·the·1980’s·was·a·time-period·in·which·a·high·federal
82 funds·rate·existed.56 funds·rate·existed.
83 [4]:57 [·]:
84 res_fedfunds.smoothed_marginal_probabilities[1].plot(58 res_fedfunds.smoothed_marginal_probabilities[1].plot(
85 ····title="Probability·of·being·in·the·high·regime",·figsize=(12,·3)59 ····title="Probability·of·being·in·the·high·regime",·figsize=(12,·3)
86 )60 )
87 [4]: 
88 <Axes:·title={'center':·'Probability·of·being·in·the·high·regime'}> 
89 [../../../_images/examples_notebooks_generated_markov_regression_7_1.png] 
90 From·the·estimated·transition·matrix·we·can·calculate·the·expected·duration·of61 From·the·estimated·transition·matrix·we·can·calculate·the·expected·duration·of
91 a·low·regime·versus·a·high·regime.62 a·low·regime·versus·a·high·regime.
92 [5]:63 [·]:
93 print(res_fedfunds.expected_durations)64 print(res_fedfunds.expected_durations)
94 [55.85400626·19.85506546] 
95 A·low·regime·is·expected·to·persist·for·about·fourteen·years,·whereas·the·high65 A·low·regime·is·expected·to·persist·for·about·fourteen·years,·whereas·the·high
96 regime·is·expected·to·persist·for·only·about·five·years.66 regime·is·expected·to·persist·for·only·about·five·years.
97 *\x8**\x8**\x8**\x8**\x8*·F\x8Fe\x8ed\x8de\x8er\x8ra\x8al\x8l·f\x8fu\x8un\x8nd\x8ds\x8s·r\x8ra\x8at\x8te\x8e·w\x8wi\x8it\x8th\x8h·s\x8sw\x8wi\x8it\x8tc\x8ch\x8hi\x8in\x8ng\x8g·i\x8in\x8nt\x8te\x8er\x8rc\x8ce\x8ep\x8pt\x8t·a\x8an\x8nd\x8d·l\x8la\x8ag\x8gg\x8ge\x8ed\x8d·d\x8de\x8ep\x8pe\x8en\x8nd\x8de\x8en\x8nt\x8t67 *\x8**\x8**\x8**\x8**\x8*·F\x8Fe\x8ed\x8de\x8er\x8ra\x8al\x8l·f\x8fu\x8un\x8nd\x8ds\x8s·r\x8ra\x8at\x8te\x8e·w\x8wi\x8it\x8th\x8h·s\x8sw\x8wi\x8it\x8tc\x8ch\x8hi\x8in\x8ng\x8g·i\x8in\x8nt\x8te\x8er\x8rc\x8ce\x8ep\x8pt\x8t·a\x8an\x8nd\x8d·l\x8la\x8ag\x8gg\x8ge\x8ed\x8d·d\x8de\x8ep\x8pe\x8en\x8nd\x8de\x8en\x8nt\x8t
98 v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*68 v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
99 The·second·example·augments·the·previous·model·to·include·the·lagged·value·of69 The·second·example·augments·the·previous·model·to·include·the·lagged·value·of
100 the·federal·funds·rate.70 the·federal·funds·rate.
101 \[r_t·=·\mu_{S_t}·+·r_{t-1}·\beta_{S_t}·+·\varepsilon_t·\qquad·\varepsilon_t71 \[r_t·=·\mu_{S_t}·+·r_{t-1}·\beta_{S_t}·+·\varepsilon_t·\qquad·\varepsilon_t
102 \sim·N(0,·\sigma^2)\]72 \sim·N(0,·\sigma^2)\]
103 where·\(S_t·\in·\{0,·1\}\),·and·the·regime·transitions·according·to73 where·\(S_t·\in·\{0,·1\}\),·and·the·regime·transitions·according·to
104 \[\begin{split}·P(S_t·=·s_t·|·S_{t-1}·=·s_{t-1})·=·\begin{bmatrix}·p_{00}·&·p_74 \[\begin{split}·P(S_t·=·s_t·|·S_{t-1}·=·s_{t-1})·=·\begin{bmatrix}·p_{00}·&·p_
105 {10}·\\·1·-·p_{00}·&·1·-·p_{10}·\end{bmatrix}\end{split}\]75 {10}·\\·1·-·p_{00}·&·1·-·p_{10}·\end{bmatrix}\end{split}\]
106 We·will·estimate·the·parameters·of·this·model·by·maximum·likelihood:·\(p_{00},76 We·will·estimate·the·parameters·of·this·model·by·maximum·likelihood:·\(p_{00},
107 p_{10},·\mu_0,·\mu_1,·\beta_0,·\beta_1,·\sigma^2\).77 p_{10},·\mu_0,·\mu_1,·\beta_0,·\beta_1,·\sigma^2\).
108 [6]:78 [·]:
109 #·Fit·the·model79 #·Fit·the·model
110 mod_fedfunds2·=·sm.tsa.MarkovRegression(80 mod_fedfunds2·=·sm.tsa.MarkovRegression(
111 ····dta_fedfunds.iloc[1:],·k_regimes=2,·exog=dta_fedfunds.iloc[:-1]81 ····dta_fedfunds.iloc[1:],·k_regimes=2,·exog=dta_fedfunds.iloc[:-1]
112 )82 )
113 res_fedfunds2·=·mod_fedfunds2.fit()83 res_fedfunds2·=·mod_fedfunds2.fit()
114 [7]:84 [·]:
115 res_fedfunds2.summary()85 res_fedfunds2.summary()
116 [7]: 
117 ···············M\x8Ma\x8ar\x8rk\x8ko\x8ov\x8v·S\x8Sw\x8wi\x8it\x8tc\x8ch\x8hi\x8in\x8ng\x8g·M\x8Mo\x8od\x8de\x8el\x8l·R\x8Re\x8es\x8su\x8ul\x8lt\x8ts\x8s 
118 D\x8De\x8ep\x8p.\x8.·V\x8Va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8e:\x8:···y················N\x8No\x8o.\x8.·O\x8Ob\x8bs\x8se\x8er\x8rv\x8va\x8at\x8ti\x8io\x8on\x8ns\x8s:\x8:·225 
119 M\x8Mo\x8od\x8de\x8el\x8l:\x8:···········MarkovRegression·L\x8Lo\x8og\x8g·L\x8Li\x8ik\x8ke\x8el\x8li\x8ih\x8ho\x8oo\x8od\x8d····-264.711 
120 D\x8Da\x8at\x8te\x8e:\x8:············Sun,·10·Aug·2025·A\x8AI\x8IC\x8C···············543.421 
121 T\x8Ti\x8im\x8me\x8e:\x8:············13:13:47·········B\x8BI\x8IC\x8C···············567.334 
122 S\x8Sa\x8am\x8mp\x8pl\x8le\x8e:\x8:··········10-01-1954·······H\x8HQ\x8QI\x8IC\x8C··············553.073 
123 ·················-·10-01-2010 
124 C\x8Co\x8ov\x8va\x8ar\x8ri\x8ia\x8an\x8nc\x8ce\x8e·T\x8Ty\x8yp\x8pe\x8e:\x8:·approx 
125 ··············R\x8Re\x8eg\x8gi\x8im\x8me\x8e·0\x80·p\x8pa\x8ar\x8ra\x8am\x8me\x8et\x8te\x8er\x8rs\x8s 
126 ······c\x8co\x8oe\x8ef\x8f···s\x8st\x8td\x8d·e\x8er\x8rr\x8r·z\x8z······P\x8P>\x8>|\x8|z\x8z|\x8|·[\x8[0\x80.\x8.0\x802\x825\x85·0\x80.\x8.9\x897\x875\x85]\x8] 
127 c\x8co\x8on\x8ns\x8st\x8t·0.7245·0.289···2.510··0.012·0.159··1.290 
128 x\x8x1\x81····0.7631·0.034···22.629·0.000·0.697··0.829 
129 ··············R\x8Re\x8eg\x8gi\x8im\x8me\x8e·1\x81·p\x8pa\x8ar\x8ra\x8am\x8me\x8et\x8te\x8er\x8rs\x8s 
130 ······c\x8co\x8oe\x8ef\x8f····s\x8st\x8td\x8d·e\x8er\x8rr\x8r·z\x8z······P\x8P>\x8>|\x8|z\x8z|\x8|·[\x8[0\x80.\x8.0\x802\x825\x85·0\x80.\x8.9\x897\x875\x85]\x8] 
131 c\x8co\x8on\x8ns\x8st\x8t·-0.0989·0.118···-0.835·0.404·-0.331·0.133 
132 x\x8x1\x81····1.0612··0.019···57.351·0.000·1.025··1.097 
133 ···········N\x8No\x8on\x8n-\x8-s\x8sw\x8wi\x8it\x8tc\x8ch\x8hi\x8in\x8ng\x8g·p\x8pa\x8ar\x8ra\x8am\x8me\x8et\x8te\x8er\x8rs\x8s 
134 ·······c\x8co\x8oe\x8ef\x8f···s\x8st\x8td\x8d·e\x8er\x8rr\x8r·z\x8z·····P\x8P>\x8>|\x8|z\x8z|\x8|·[\x8[0\x80.\x8.0\x802\x825\x85·0\x80.\x8.9\x897\x875\x85]\x8] 
135 s\x8si\x8ig\x8gm\x8ma\x8a2\x82·0.4783·0.050···9.642·0.000·0.381··0.576 
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58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Mediation-analysis-with-duration-data">61 ··<section·id="Mediation-analysis-with-duration-data">
62 <h1>Mediation·analysis·with·duration·data<a·class="headerlink"·href="#Mediation-analysis-with-duration-data"·title="Link·to·this·heading">¶</a></h1>62 <h1>Mediation·analysis·with·duration·data<a·class="headerlink"·href="#Mediation-analysis-with-duration-data"·title="Link·to·this·heading">¶</a></h1>
63 <p>This·notebook·demonstrates·mediation·analysis·when·the·mediator·and·outcome·are·duration·variables,·modeled·using·proportional·hazards·regression.·These·examples·are·based·on·simulated·data.</p>63 <p>This·notebook·demonstrates·mediation·analysis·when·the·mediator·and·outcome·are·duration·variables,·modeled·using·proportional·hazards·regression.·These·examples·are·based·on·simulated·data.</p>
64 <div·class="nbinput·nblast·docutils·container">64 <div·class="nbinput·nblast·docutils·container">
65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
66 </pre></div>66 </pre></div>
67 </div>67 </div>
68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
69 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>69 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
70 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>70 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
71 <span·class="kn">from</span>·<span·class="nn">statsmodels.stats.mediation</span>·<span·class="kn">import</span>·<span·class="n">Mediation</span>71 <span·class="kn">from</span>·<span·class="nn">statsmodels.stats.mediation</span>·<span·class="kn">import</span>·<span·class="n">Mediation</span>
72 </pre></div>72 </pre></div>
73 </div>73 </div>
74 </div>74 </div>
75 <p>Make·the·notebook·reproducible.</p>75 <p>Make·the·notebook·reproducible.</p>
76 <div·class="nbinput·nblast·docutils·container">76 <div·class="nbinput·nblast·docutils·container">
77 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:77 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
78 </pre></div>78 </pre></div>
79 </div>79 </div>
80 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">3424</span><span·class="p">)</span>80 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">3424</span><span·class="p">)</span>
81 </pre></div>81 </pre></div>
82 </div>82 </div>
83 </div>83 </div>
84 <p>Specify·a·sample·size.</p>84 <p>Specify·a·sample·size.</p>
85 <div·class="nbinput·nblast·docutils·container">85 <div·class="nbinput·nblast·docutils·container">
86 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:86 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
87 </pre></div>87 </pre></div>
88 </div>88 </div>
89 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">n</span>·<span·class="o">=</span>·<span·class="mi">1000</span>89 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">n</span>·<span·class="o">=</span>·<span·class="mi">1000</span>
90 </pre></div>90 </pre></div>
91 </div>91 </div>
92 </div>92 </div>
93 <p>Generate·an·exposure·variable.</p>93 <p>Generate·an·exposure·variable.</p>
94 <div·class="nbinput·nblast·docutils·container">94 <div·class="nbinput·nblast·docutils·container">
95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
96 </pre></div>96 </pre></div>
97 </div>97 </div>
98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">exp</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">)</span>98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">exp</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">)</span>
99 </pre></div>99 </pre></div>
100 </div>100 </div>
101 </div>101 </div>
102 <p>Generate·a·mediator·variable.</p>102 <p>Generate·a·mediator·variable.</p>
103 <div·class="nbinput·nblast·docutils·container">103 <div·class="nbinput·nblast·docutils·container">
104 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:104 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
105 </pre></div>105 </pre></div>
106 </div>106 </div>
107 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">gen_mediator</span><span·class="p">():</span>107 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">gen_mediator</span><span·class="p">():</span>
108 ····<span·class="n">mn</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">exp</span><span·class="p">(</span><span·class="n">exp</span><span·class="p">)</span>108 ····<span·class="n">mn</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">exp</span><span·class="p">(</span><span·class="n">exp</span><span·class="p">)</span>
109 ····<span·class="n">mtime0</span>·<span·class="o">=</span>·<span·class="o">-</span><span·class="n">mn</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">log</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">))</span>109 ····<span·class="n">mtime0</span>·<span·class="o">=</span>·<span·class="o">-</span><span·class="n">mn</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">log</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">))</span>
110 ····<span·class="n">ctime</span>·<span·class="o">=</span>·<span·class="o">-</span><span·class="mi">2</span>·<span·class="o">*</span>·<span·class="n">mn</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">log</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">))</span>110 ····<span·class="n">ctime</span>·<span·class="o">=</span>·<span·class="o">-</span><span·class="mi">2</span>·<span·class="o">*</span>·<span·class="n">mn</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">log</span><span·class="p">(</span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">uniform</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">n</span><span·class="p">))</span>
111 ····<span·class="n">mstatus</span>·<span·class="o">=</span>·<span·class="p">(</span><span·class="n">ctime</span>·<span·class="o">&gt;=</span>·<span·class="n">mtime0</span><span·class="p">)</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>111 ····<span·class="n">mstatus</span>·<span·class="o">=</span>·<span·class="p">(</span><span·class="n">ctime</span>·<span·class="o">&gt;=</span>·<span·class="n">mtime0</span><span·class="p">)</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>
112 ····<span·class="n">mtime</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">where</span><span·class="p">(</span><span·class="n">mtime0</span>·<span·class="o">&lt;=</span>·<span·class="n">ctime</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">ctime</span><span·class="p">)</span>112 ····<span·class="n">mtime</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">where</span><span·class="p">(</span><span·class="n">mtime0</span>·<span·class="o">&lt;=</span>·<span·class="n">ctime</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">ctime</span><span·class="p">)</span>
113 ····<span·class="k">return</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span>113 ····<span·class="k">return</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span>
114 </pre></div>114 </pre></div>
115 </div>115 </div>
116 </div>116 </div>
117 <p>Generate·an·outcome·variable.</p>117 <p>Generate·an·outcome·variable.</p>
118 <div·class="nbinput·nblast·docutils·container">118 <div·class="nbinput·nblast·docutils·container">
119 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:119 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
120 </pre></div>120 </pre></div>
121 </div>121 </div>
122 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">gen_outcome</span><span·class="p">(</span><span·class="n">otype</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">):</span>122 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">gen_outcome</span><span·class="p">(</span><span·class="n">otype</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">):</span>
123 ····<span·class="k">if</span>·<span·class="n">otype</span>·<span·class="o">==</span>·<span·class="s2">&quot;full&quot;</span><span·class="p">:</span>123 ····<span·class="k">if</span>·<span·class="n">otype</span>·<span·class="o">==</span>·<span·class="s2">&quot;full&quot;</span><span·class="p">:</span>
124 ········<span·class="n">lp</span>·<span·class="o">=</span>·<span·class="mf">0.5</span>·<span·class="o">*</span>·<span·class="n">mtime0</span>124 ········<span·class="n">lp</span>·<span·class="o">=</span>·<span·class="mf">0.5</span>·<span·class="o">*</span>·<span·class="n">mtime0</span>
125 ····<span·class="k">elif</span>·<span·class="n">otype</span>·<span·class="o">==</span>·<span·class="s2">&quot;no&quot;</span><span·class="p">:</span>125 ····<span·class="k">elif</span>·<span·class="n">otype</span>·<span·class="o">==</span>·<span·class="s2">&quot;no&quot;</span><span·class="p">:</span>
126 ········<span·class="n">lp</span>·<span·class="o">=</span>·<span·class="n">exp</span>126 ········<span·class="n">lp</span>·<span·class="o">=</span>·<span·class="n">exp</span>
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133 ····<span·class="n">ytime</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">where</span><span·class="p">(</span><span·class="n">ytime0</span>·<span·class="o">&lt;=</span>·<span·class="n">ctime</span><span·class="p">,</span>·<span·class="n">ytime0</span><span·class="p">,</span>·<span·class="n">ctime</span><span·class="p">)</span>133 ····<span·class="n">ytime</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">where</span><span·class="p">(</span><span·class="n">ytime0</span>·<span·class="o">&lt;=</span>·<span·class="n">ctime</span><span·class="p">,</span>·<span·class="n">ytime0</span><span·class="p">,</span>·<span·class="n">ctime</span><span·class="p">)</span>
134 ····<span·class="k">return</span>·<span·class="n">ytime</span><span·class="p">,</span>·<span·class="n">ystatus</span>134 ····<span·class="k">return</span>·<span·class="n">ytime</span><span·class="p">,</span>·<span·class="n">ystatus</span>
135 </pre></div>135 </pre></div>
136 </div>136 </div>
137 </div>137 </div>
138 <p>Build·a·dataframe·containing·all·the·relevant·variables.</p>138 <p>Build·a·dataframe·containing·all·the·relevant·variables.</p>
139 <div·class="nbinput·nblast·docutils·container">139 <div·class="nbinput·nblast·docutils·container">
140 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:140 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
141 </pre></div>141 </pre></div>
142 </div>142 </div>
143 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">build_df</span><span·class="p">(</span><span·class="n">ytime</span><span·class="p">,</span>·<span·class="n">ystatus</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span><span·class="p">):</span>143 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">build_df</span><span·class="p">(</span><span·class="n">ytime</span><span·class="p">,</span>·<span·class="n">ystatus</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span><span·class="p">):</span>
144 ····<span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">DataFrame</span><span·class="p">(</span>144 ····<span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">DataFrame</span><span·class="p">(</span>
145 ········<span·class="p">{</span>145 ········<span·class="p">{</span>
146 ············<span·class="s2">&quot;ytime&quot;</span><span·class="p">:</span>·<span·class="n">ytime</span><span·class="p">,</span>146 ············<span·class="s2">&quot;ytime&quot;</span><span·class="p">:</span>·<span·class="n">ytime</span><span·class="p">,</span>
147 ············<span·class="s2">&quot;ystatus&quot;</span><span·class="p">:</span>·<span·class="n">ystatus</span><span·class="p">,</span>147 ············<span·class="s2">&quot;ystatus&quot;</span><span·class="p">:</span>·<span·class="n">ystatus</span><span·class="p">,</span>
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152 ····<span·class="p">)</span>152 ····<span·class="p">)</span>
153 ····<span·class="k">return</span>·<span·class="n">df</span>153 ····<span·class="k">return</span>·<span·class="n">df</span>
154 </pre></div>154 </pre></div>
155 </div>155 </div>
156 </div>156 </div>
157 <p>Run·the·full·simulation·and·analysis,·under·a·particular·population·structure·of·mediation.</p>157 <p>Run·the·full·simulation·and·analysis,·under·a·particular·population·structure·of·mediation.</p>
158 <div·class="nbinput·nblast·docutils·container">158 <div·class="nbinput·nblast·docutils·container">
159 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[8]:159 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
160 </pre></div>160 </pre></div>
161 </div>161 </div>
162 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">run</span><span·class="p">(</span><span·class="n">otype</span><span·class="p">):</span>162 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">run</span><span·class="p">(</span><span·class="n">otype</span><span·class="p">):</span>
  
163 ····<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span>·<span·class="o">=</span>·<span·class="n">gen_mediator</span><span·class="p">()</span>163 ····<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span>·<span·class="o">=</span>·<span·class="n">gen_mediator</span><span·class="p">()</span>
164 ····<span·class="n">ytime</span><span·class="p">,</span>·<span·class="n">ystatus</span>·<span·class="o">=</span>·<span·class="n">gen_outcome</span><span·class="p">(</span><span·class="n">otype</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">)</span>164 ····<span·class="n">ytime</span><span·class="p">,</span>·<span·class="n">ystatus</span>·<span·class="o">=</span>·<span·class="n">gen_outcome</span><span·class="p">(</span><span·class="n">otype</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">)</span>
165 ····<span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">build_df</span><span·class="p">(</span><span·class="n">ytime</span><span·class="p">,</span>·<span·class="n">ystatus</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span><span·class="p">)</span>165 ····<span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">build_df</span><span·class="p">(</span><span·class="n">ytime</span><span·class="p">,</span>·<span·class="n">ystatus</span><span·class="p">,</span>·<span·class="n">mtime0</span><span·class="p">,</span>·<span·class="n">mtime</span><span·class="p">,</span>·<span·class="n">mstatus</span><span·class="p">)</span>
Offset 179, 94 lines modifiedOffset 179, 40 lines modified
179 ····<span·class="p">)</span>179 ····<span·class="p">)</span>
180 ····<span·class="n">med_result</span>·<span·class="o">=</span>·<span·class="n">med</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">n_rep</span><span·class="o">=</span><span·class="mi">20</span><span·class="p">)</span>180 ····<span·class="n">med_result</span>·<span·class="o">=</span>·<span·class="n">med</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">n_rep</span><span·class="o">=</span><span·class="mi">20</span><span·class="p">)</span>
181 ····<span·class="nb">print</span><span·class="p">(</span><span·class="n">med_result</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>181 ····<span·class="nb">print</span><span·class="p">(</span><span·class="n">med_result</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
182 </pre></div>182 </pre></div>
183 </div>183 </div>
184 </div>184 </div>
185 <p>Run·the·example·with·full·mediation</p>185 <p>Run·the·example·with·full·mediation</p>
186 <div·class="nbinput·docutils·container">186 <div·class="nbinput·nblast·docutils·container">
187 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[9]:187 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
188 </pre></div>188 </pre></div>
189 </div>189 </div>
190 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">run</span><span·class="p">(</span><span·class="s2">&quot;full&quot;</span><span·class="p">)</span>190 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">run</span><span·class="p">(</span><span·class="s2">&quot;full&quot;</span><span·class="p">)</span>
191 </pre></div>191 </pre></div>
192 </div>192 </div>
193 </div>193 </div>
194 <div·class="nboutput·nblast·docutils·container"> 
195 <div·class="prompt·empty·docutils·container"> 
196 </div> 
197 <div·class="output_area·docutils·container"> 
198 <div·class="highlight"><pre> 
199 ··························Estimate··Lower·CI·bound··Upper·CI·bound··P-value 
200 ACME·(control)············0.742427········0.643339········0.862745······0.0 
201 ACME·(treated)············0.742427········0.643339········0.862745······0.0 
202 ADE·(control)·············0.073017·······-0.016189········0.155321······0.1 
203 ADE·(treated)·············0.073017·······-0.016189········0.155321······0.1 
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6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Mediation·analysis·with·duration·data8 ····*·Mediation·analysis·with·duration·data
9 *\x8**\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8ed\x8di\x8ia\x8at\x8ti\x8io\x8on\x8n·a\x8an\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s·w\x8wi\x8it\x8th\x8h·d\x8du\x8ur\x8ra\x8at\x8ti\x8io\x8on\x8n·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8ed\x8di\x8ia\x8at\x8ti\x8io\x8on\x8n·a\x8an\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s·w\x8wi\x8it\x8th\x8h·d\x8du\x8ur\x8ra\x8at\x8ti\x8io\x8on\x8n·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 This·notebook·demonstrates·mediation·analysis·when·the·mediator·and·outcome·are10 This·notebook·demonstrates·mediation·analysis·when·the·mediator·and·outcome·are
11 duration·variables,·modeled·using·proportional·hazards·regression.·These11 duration·variables,·modeled·using·proportional·hazards·regression.·These
12 examples·are·based·on·simulated·data.12 examples·are·based·on·simulated·data.
13 [1]:13 [·]:
14 import·pandas·as·pd14 import·pandas·as·pd
15 import·numpy·as·np15 import·numpy·as·np
16 import·statsmodels.api·as·sm16 import·statsmodels.api·as·sm
17 from·statsmodels.stats.mediation·import·Mediation17 from·statsmodels.stats.mediation·import·Mediation
18 Make·the·notebook·reproducible.18 Make·the·notebook·reproducible.
19 [2]:19 [·]:
20 np.random.seed(3424)20 np.random.seed(3424)
21 Specify·a·sample·size.21 Specify·a·sample·size.
22 [3]:22 [·]:
23 n·=·100023 n·=·1000
24 Generate·an·exposure·variable.24 Generate·an·exposure·variable.
25 [4]:25 [·]:
26 exp·=·np.random.normal(size=n)26 exp·=·np.random.normal(size=n)
27 Generate·a·mediator·variable.27 Generate·a·mediator·variable.
28 [5]:28 [·]:
29 def·gen_mediator():29 def·gen_mediator():
30 ····mn·=·np.exp(exp)30 ····mn·=·np.exp(exp)
31 ····mtime0·=·-mn·*·np.log(np.random.uniform(size=n))31 ····mtime0·=·-mn·*·np.log(np.random.uniform(size=n))
32 ····ctime·=·-2·*·mn·*·np.log(np.random.uniform(size=n))32 ····ctime·=·-2·*·mn·*·np.log(np.random.uniform(size=n))
33 ····mstatus·=·(ctime·>=·mtime0).astype(int)33 ····mstatus·=·(ctime·>=·mtime0).astype(int)
34 ····mtime·=·np.where(mtime0·<=·ctime,·mtime0,·ctime)34 ····mtime·=·np.where(mtime0·<=·ctime,·mtime0,·ctime)
35 ····return·mtime0,·mtime,·mstatus35 ····return·mtime0,·mtime,·mstatus
36 Generate·an·outcome·variable.36 Generate·an·outcome·variable.
37 [6]:37 [·]:
38 def·gen_outcome(otype,·mtime0):38 def·gen_outcome(otype,·mtime0):
39 ····if·otype·==·"full":39 ····if·otype·==·"full":
40 ········lp·=·0.5·*·mtime040 ········lp·=·0.5·*·mtime0
41 ····elif·otype·==·"no":41 ····elif·otype·==·"no":
42 ········lp·=·exp42 ········lp·=·exp
43 ····else:43 ····else:
44 ········lp·=·exp·+·mtime044 ········lp·=·exp·+·mtime0
45 ····mn·=·np.exp(-lp)45 ····mn·=·np.exp(-lp)
46 ····ytime0·=·-mn·*·np.log(np.random.uniform(size=n))46 ····ytime0·=·-mn·*·np.log(np.random.uniform(size=n))
47 ····ctime·=·-2·*·mn·*·np.log(np.random.uniform(size=n))47 ····ctime·=·-2·*·mn·*·np.log(np.random.uniform(size=n))
48 ····ystatus·=·(ctime·>=·ytime0).astype(int)48 ····ystatus·=·(ctime·>=·ytime0).astype(int)
49 ····ytime·=·np.where(ytime0·<=·ctime,·ytime0,·ctime)49 ····ytime·=·np.where(ytime0·<=·ctime,·ytime0,·ctime)
50 ····return·ytime,·ystatus50 ····return·ytime,·ystatus
51 Build·a·dataframe·containing·all·the·relevant·variables.51 Build·a·dataframe·containing·all·the·relevant·variables.
52 [7]:52 [·]:
53 def·build_df(ytime,·ystatus,·mtime0,·mtime,·mstatus):53 def·build_df(ytime,·ystatus,·mtime0,·mtime,·mstatus):
54 ····df·=·pd.DataFrame(54 ····df·=·pd.DataFrame(
55 ········{55 ········{
56 ············"ytime":·ytime,56 ············"ytime":·ytime,
57 ············"ystatus":·ystatus,57 ············"ystatus":·ystatus,
58 ············"mtime":·mtime,58 ············"mtime":·mtime,
59 ············"mstatus":·mstatus,59 ············"mstatus":·mstatus,
60 ············"exp":·exp,60 ············"exp":·exp,
61 ········}61 ········}
62 ····)62 ····)
63 ····return·df63 ····return·df
64 Run·the·full·simulation·and·analysis,·under·a·particular·population·structure64 Run·the·full·simulation·and·analysis,·under·a·particular·population·structure
65 of·mediation.65 of·mediation.
66 [8]:66 [·]:
67 def·run(otype):67 def·run(otype):
  
68 ····mtime0,·mtime,·mstatus·=·gen_mediator()68 ····mtime0,·mtime,·mstatus·=·gen_mediator()
69 ····ytime,·ystatus·=·gen_outcome(otype,·mtime0)69 ····ytime,·ystatus·=·gen_outcome(otype,·mtime0)
70 ····df·=·build_df(ytime,·ystatus,·mtime0,·mtime,·mstatus)70 ····df·=·build_df(ytime,·ystatus,·mtime0,·mtime,·mstatus)
  
71 ····outcome_model·=·sm.PHReg.from_formula(71 ····outcome_model·=·sm.PHReg.from_formula(
Offset 82, 55 lines modifiedOffset 82, 22 lines modified
82 ········"exp",82 ········"exp",
83 ········"mtime",83 ········"mtime",
84 ········outcome_predict_kwargs={"pred_only":·True},84 ········outcome_predict_kwargs={"pred_only":·True},
85 ····)85 ····)
86 ····med_result·=·med.fit(n_rep=20)86 ····med_result·=·med.fit(n_rep=20)
87 ····print(med_result.summary())87 ····print(med_result.summary())
88 Run·the·example·with·full·mediation88 Run·the·example·with·full·mediation
89 [9]:89 [·]:
90 run("full")90 run("full")
91 ··························Estimate··Lower·CI·bound··Upper·CI·bound··P-value 
92 ACME·(control)············0.742427········0.643339········0.862745······0.0 
93 ACME·(treated)············0.742427········0.643339········0.862745······0.0 
94 ADE·(control)·············0.073017·······-0.016189········0.155321······0.1 
95 ADE·(treated)·············0.073017·······-0.016189········0.155321······0.1 
96 Total·effect··············0.815444········0.675214········0.919580······0.0 
97 Prop.·mediated·(control)··0.912695········0.814965········1.025747······0.0 
98 Prop.·mediated·(treated)··0.912695········0.814965········1.025747······0.0 
99 ACME·(average)············0.742427········0.643339········0.862745······0.0 
100 ADE·(average)·············0.073017·······-0.016189········0.155321······0.1 
101 Prop.·mediated·(average)··0.912695········0.814965········1.025747······0.0 
102 Run·the·example·with·partial·mediation91 Run·the·example·with·partial·mediation
103 [10]:92 [·]:
104 run("partial")93 run("partial")
105 ··························Estimate··Lower·CI·bound··Upper·CI·bound··P-value 
106 ACME·(control)············0.987067········0.801560········1.192019······0.0 
107 ACME·(treated)············0.987067········0.801560········1.192019······0.0 
108 ADE·(control)·············1.071734········0.964214········1.150352······0.0 
109 ADE·(treated)·············1.071734········0.964214········1.150352······0.0 
110 Total·effect··············2.058801········1.862231········2.288170······0.0 
111 Prop.·mediated·(control)··0.481807········0.417501········0.533773······0.0 
112 Prop.·mediated·(treated)··0.481807········0.417501········0.533773······0.0 
113 ACME·(average)············0.987067········0.801560········1.192019······0.0 
114 ADE·(average)·············1.071734········0.964214········1.150352······0.0 
115 Prop.·mediated·(average)··0.481807········0.417501········0.533773······0.0 
116 Run·the·example·with·no·mediation94 Run·the·example·with·no·mediation
117 [11]:95 [·]:
118 run("no")96 run("no")
119 ··························Estimate··Lower·CI·bound··Upper·CI·bound··P-value 
120 ACME·(control)············0.010200·······-0.039434········0.065176······1.0 
121 ACME·(treated)············0.010200·······-0.039434········0.065176······1.0 
122 ADE·(control)·············0.902295········0.824526········0.984934······0.0 
123 ADE·(treated)·············0.902295········0.824526········0.984934······0.0 
124 Total·effect··············0.912495········0.834728········1.009958······0.0 
125 Prop.·mediated·(control)··0.003763·······-0.044186········0.065520······1.0 
126 Prop.·mediated·(treated)··0.003763·······-0.044186········0.065520······1.0 
127 ACME·(average)············0.010200·······-0.039434········0.065176······1.0 
128 ADE·(average)·············0.902295········0.824526········0.984934······0.0 
129 Prop.·mediated·(average)··0.003763·······-0.044186········0.065520······1.0 
130 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]97 _\x8[_\x8L_\x8o_\x8g_\x8o_\x8·_\x8o_\x8f_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g_\x8]
131 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*98 *\x8**\x8**\x8**\x8*·_\x8T\x8T_\x8a\x8a_\x8b\x8b_\x8l\x8l_\x8e\x8e_\x8·_\x8o\x8o_\x8f\x8f_\x8·_\x8C\x8C_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8e\x8e_\x8n\x8n_\x8t\x8t_\x8s\x8s·*\x8**\x8**\x8**\x8*
132 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s99 ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s
133 ····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d100 ····*·_\x8G_\x8e_\x8t_\x8t_\x8i_\x8n_\x8g_\x8·_\x8s_\x8t_\x8a_\x8r_\x8t_\x8e_\x8d
134 ····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e101 ····*·_\x8U_\x8s_\x8e_\x8r_\x8·_\x8G_\x8u_\x8i_\x8d_\x8e
135 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s102 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s
136 ····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e103 ····*·_\x8A_\x8P_\x8I_\x8·_\x8R_\x8e_\x8f_\x8e_\x8r_\x8e_\x8n_\x8c_\x8e
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59 ······<div·class="documentwrapper">59 ······<div·class="documentwrapper">
60 ········<div·class="bodywrapper">60 ········<div·class="bodywrapper">
61 ··········<div·class="body"·role="main">61 ··········<div·class="body"·role="main">
62 ············62 ············
63 ··<section·id="Ordinary-Least-Squares">63 ··<section·id="Ordinary-Least-Squares">
64 <h1>Ordinary·Least·Squares<a·class="headerlink"·href="#Ordinary-Least-Squares"·title="Link·to·this·heading">¶</a></h1>64 <h1>Ordinary·Least·Squares<a·class="headerlink"·href="#Ordinary-Least-Squares"·title="Link·to·this·heading">¶</a></h1>
65 <div·class="nbinput·nblast·docutils·container">65 <div·class="nbinput·nblast·docutils·container">
66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
67 </pre></div>67 </pre></div>
68 </div>68 </div>
69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
70 </pre></div>70 </pre></div>
71 </div>71 </div>
72 </div>72 </div>
73 <div·class="nbinput·nblast·docutils·container">73 <div·class="nbinput·nblast·docutils·container">
74 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:74 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
75 </pre></div>75 </pre></div>
76 </div>76 </div>
77 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>77 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
78 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>78 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
79 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>79 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
80 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>80 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
  
Offset 83, 193 lines modifiedOffset 83, 99 lines modified
83 </pre></div>83 </pre></div>
84 </div>84 </div>
85 </div>85 </div>
86 <section·id="OLS-estimation">86 <section·id="OLS-estimation">
87 <h2>OLS·estimation<a·class="headerlink"·href="#OLS-estimation"·title="Link·to·this·heading">¶</a></h2>87 <h2>OLS·estimation<a·class="headerlink"·href="#OLS-estimation"·title="Link·to·this·heading">¶</a></h2>
88 <p>Artificial·data:</p>88 <p>Artificial·data:</p>
89 <div·class="nbinput·nblast·docutils·container">89 <div·class="nbinput·nblast·docutils·container">
90 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:90 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
91 </pre></div>91 </pre></div>
92 </div>92 </div>
93 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">nsample</span>·<span·class="o">=</span>·<span·class="mi">100</span>93 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">nsample</span>·<span·class="o">=</span>·<span·class="mi">100</span>
94 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">10</span><span·class="p">,</span>·<span·class="mi">100</span><span·class="p">)</span>94 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">10</span><span·class="p">,</span>·<span·class="mi">100</span><span·class="p">)</span>
95 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">column_stack</span><span·class="p">((</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">x</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">))</span>95 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">column_stack</span><span·class="p">((</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">x</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">))</span>
96 <span·class="n">beta</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">array</span><span·class="p">([</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mf">0.1</span><span·class="p">,</span>·<span·class="mi">10</span><span·class="p">])</span>96 <span·class="n">beta</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">array</span><span·class="p">([</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mf">0.1</span><span·class="p">,</span>·<span·class="mi">10</span><span·class="p">])</span>
97 <span·class="n">e</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">nsample</span><span·class="p">)</span>97 <span·class="n">e</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">nsample</span><span·class="p">)</span>
98 </pre></div>98 </pre></div>
99 </div>99 </div>
100 </div>100 </div>
101 <p>Our·model·needs·an·intercept·so·we·add·a·column·of·1s:</p>101 <p>Our·model·needs·an·intercept·so·we·add·a·column·of·1s:</p>
102 <div·class="nbinput·nblast·docutils·container">102 <div·class="nbinput·nblast·docutils·container">
103 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:103 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
104 </pre></div>104 </pre></div>
105 </div>105 </div>
106 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">X</span><span·class="p">)</span>106 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">X</span><span·class="p">)</span>
107 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">dot</span><span·class="p">(</span><span·class="n">X</span><span·class="p">,</span>·<span·class="n">beta</span><span·class="p">)</span>·<span·class="o">+</span>·<span·class="n">e</span>107 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">dot</span><span·class="p">(</span><span·class="n">X</span><span·class="p">,</span>·<span·class="n">beta</span><span·class="p">)</span>·<span·class="o">+</span>·<span·class="n">e</span>
108 </pre></div>108 </pre></div>
109 </div>109 </div>
110 </div>110 </div>
111 <p>Fit·and·summary:</p>111 <p>Fit·and·summary:</p>
112 <div·class="nbinput·docutils·container">112 <div·class="nbinput·nblast·docutils·container">
113 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:113 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
114 </pre></div>114 </pre></div>
115 </div>115 </div>
116 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">model</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">OLS</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">X</span><span·class="p">)</span>116 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">model</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">OLS</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">X</span><span·class="p">)</span>
117 <span·class="n">results</span>·<span·class="o">=</span>·<span·class="n">model</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>117 <span·class="n">results</span>·<span·class="o">=</span>·<span·class="n">model</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
118 <span·class="nb">print</span><span·class="p">(</span><span·class="n">results</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>118 <span·class="nb">print</span><span·class="p">(</span><span·class="n">results</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
119 </pre></div>119 </pre></div>
120 </div>120 </div>
121 </div>121 </div>
122 <div·class="nboutput·nblast·docutils·container"> 
123 <div·class="prompt·empty·docutils·container"> 
124 </div> 
125 <div·class="output_area·docutils·container"> 
126 <div·class="highlight"><pre> 
127 ····························OLS·Regression·Results 
128 ============================================================================== 
129 Dep.·Variable:······················y···R-squared:·······················1.000 
130 Model:····························OLS···Adj.·R-squared:··················1.000 
131 Method:·················Least·Squares···F-statistic:·················4.020e+06 
132 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):··········2.83e-239 
133 Time:························13:13:47···Log-Likelihood:················-146.51 
134 No.·Observations:·················100···AIC:·····························299.0 
135 Df·Residuals:······················97···BIC:·····························306.8 
136 Df·Model:···························2 
137 Covariance·Type:············nonrobust 
138 ============================================================================== 
139 ·················coef····std·err··········t······P&gt;|t|······[0.025······0.975] 
140 ------------------------------------------------------------------------------ 
141 const··········1.3423······0.313······4.292······0.000·······0.722·······1.963 
142 x1············-0.0402······0.145·····-0.278······0.781······-0.327·······0.247 
143 x2············10.0103······0.014····715.745······0.000·······9.982······10.038 
144 ============================================================================== 
145 Omnibus:························2.042···Durbin-Watson:···················2.274 
146 Prob(Omnibus):··················0.360···Jarque-Bera·(JB):················1.875 
147 Skew:···························0.234···Prob(JB):························0.392 
148 Kurtosis:·······················2.519···Cond.·No.·························144. 
149 ============================================================================== 
  
150 Notes: 
151 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified. 
152 </pre></div></div> 
153 </div> 
154 <p>Quantities·of·interest·can·be·extracted·directly·from·the·fitted·model.·Type·<code·class="docutils·literal·notranslate"><span·class="pre">dir(results)</span></code>·for·a·full·list.·Here·are·some·examples:</p>122 <p>Quantities·of·interest·can·be·extracted·directly·from·the·fitted·model.·Type·<code·class="docutils·literal·notranslate"><span·class="pre">dir(results)</span></code>·for·a·full·list.·Here·are·some·examples:</p>
155 <div·class="nbinput·docutils·container">123 <div·class="nbinput·nblast·docutils·container">
156 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:124 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
157 </pre></div>125 </pre></div>
158 </div>126 </div>
159 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;Parameters:·&quot;</span><span·class="p">,</span>·<span·class="n">results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>127 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;Parameters:·&quot;</span><span·class="p">,</span>·<span·class="n">results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>
160 <span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;R2:·&quot;</span><span·class="p">,</span>·<span·class="n">results</span><span·class="o">.</span><span·class="n">rsquared</span><span·class="p">)</span>128 <span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;R2:·&quot;</span><span·class="p">,</span>·<span·class="n">results</span><span·class="o">.</span><span·class="n">rsquared</span><span·class="p">)</span>
161 </pre></div>129 </pre></div>
162 </div>130 </div>
163 </div>131 </div>
164 <div·class="nboutput·nblast·docutils·container"> 
165 <div·class="prompt·empty·docutils·container"> 
166 </div> 
167 <div·class="output_area·docutils·container"> 
168 <div·class="highlight"><pre> 
169 Parameters:··[·1.34233516·-0.04024948·10.01025357] 
170 R2:··0.9999879365025871 
171 </pre></div></div> 
172 </div> 
173 </section>132 </section>
174 <section·id="OLS-non-linear-curve-but-linear-in-parameters">133 <section·id="OLS-non-linear-curve-but-linear-in-parameters">
175 <h2>OLS·non-linear·curve·but·linear·in·parameters<a·class="headerlink"·href="#OLS-non-linear-curve-but-linear-in-parameters"·title="Link·to·this·heading">¶</a></h2>134 <h2>OLS·non-linear·curve·but·linear·in·parameters<a·class="headerlink"·href="#OLS-non-linear-curve-but-linear-in-parameters"·title="Link·to·this·heading">¶</a></h2>
176 <p>We·simulate·artificial·data·with·a·non-linear·relationship·between·x·and·y:</p>135 <p>We·simulate·artificial·data·with·a·non-linear·relationship·between·x·and·y:</p>
177 <div·class="nbinput·nblast·docutils·container">136 <div·class="nbinput·nblast·docutils·container">
178 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:137 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
179 </pre></div>138 </pre></div>
180 </div>139 </div>
181 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">nsample</span>·<span·class="o">=</span>·<span·class="mi">50</span>140 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">nsample</span>·<span·class="o">=</span>·<span·class="mi">50</span>
182 <span·class="n">sig</span>·<span·class="o">=</span>·<span·class="mf">0.5</span>141 <span·class="n">sig</span>·<span·class="o">=</span>·<span·class="mf">0.5</span>
183 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">20</span><span·class="p">,</span>·<span·class="n">nsample</span><span·class="p">)</span>142 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">20</span><span·class="p">,</span>·<span·class="n">nsample</span><span·class="p">)</span>
184 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">column_stack</span><span·class="p">((</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sin</span><span·class="p">(</span><span·class="n">x</span><span·class="p">),</span>·<span·class="p">(</span><span·class="n">x</span>·<span·class="o">-</span>·<span·class="mi">5</span><span·class="p">)</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">nsample</span><span·class="p">)))</span>143 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">column_stack</span><span·class="p">((</span><span·class="n">x</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sin</span><span·class="p">(</span><span·class="n">x</span><span·class="p">),</span>·<span·class="p">(</span><span·class="n">x</span>·<span·class="o">-</span>·<span·class="mi">5</span><span·class="p">)</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">ones</span><span·class="p">(</span><span·class="n">nsample</span><span·class="p">)))</span>
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Ordinary·Least·Squares8 ····*·Ordinary·Least·Squares
9 *\x8**\x8**\x8**\x8**\x8**\x8*·O\x8Or\x8rd\x8di\x8in\x8na\x8ar\x8ry\x8y·L\x8Le\x8ea\x8as\x8st\x8t·S\x8Sq\x8qu\x8ua\x8ar\x8re\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·O\x8Or\x8rd\x8di\x8in\x8na\x8ar\x8ry\x8y·L\x8Le\x8ea\x8as\x8st\x8t·S\x8Sq\x8qu\x8ua\x8ar\x8re\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 %matplotlib·inline11 %matplotlib·inline
12 [2]:12 [·]:
13 import·matplotlib.pyplot·as·plt13 import·matplotlib.pyplot·as·plt
14 import·numpy·as·np14 import·numpy·as·np
15 import·pandas·as·pd15 import·pandas·as·pd
16 import·statsmodels.api·as·sm16 import·statsmodels.api·as·sm
  
17 np.random.seed(9876789)17 np.random.seed(9876789)
18 *\x8**\x8**\x8**\x8**\x8*·O\x8OL\x8LS\x8S·e\x8es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*18 *\x8**\x8**\x8**\x8**\x8*·O\x8OL\x8LS\x8S·e\x8es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
19 Artificial·data:19 Artificial·data:
20 [3]:20 [·]:
21 nsample·=·10021 nsample·=·100
22 x·=·np.linspace(0,·10,·100)22 x·=·np.linspace(0,·10,·100)
23 X·=·np.column_stack((x,·x·**·2))23 X·=·np.column_stack((x,·x·**·2))
24 beta·=·np.array([1,·0.1,·10])24 beta·=·np.array([1,·0.1,·10])
25 e·=·np.random.normal(size=nsample)25 e·=·np.random.normal(size=nsample)
26 Our·model·needs·an·intercept·so·we·add·a·column·of·1s:26 Our·model·needs·an·intercept·so·we·add·a·column·of·1s:
27 [4]:27 [·]:
28 X·=·sm.add_constant(X)28 X·=·sm.add_constant(X)
29 y·=·np.dot(X,·beta)·+·e29 y·=·np.dot(X,·beta)·+·e
30 Fit·and·summary:30 Fit·and·summary:
31 [5]:31 [·]:
32 model·=·sm.OLS(y,·X)32 model·=·sm.OLS(y,·X)
33 results·=·model.fit()33 results·=·model.fit()
34 print(results.summary())34 print(results.summary())
35 ····························OLS·Regression·Results 
36 ============================================================================== 
37 Dep.·Variable:······················y···R-squared:·······················1.000 
38 Model:····························OLS···Adj.·R-squared:··················1.000 
39 Method:·················Least·Squares···F-statistic:·················4.020e+06 
40 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):··········2.83e-239 
41 Time:························13:13:47···Log-Likelihood:················-146.51 
42 No.·Observations:·················100···AIC:·····························299.0 
43 Df·Residuals:······················97···BIC:·····························306.8 
44 Df·Model:···························2 
45 Covariance·Type:············nonrobust 
46 ============================================================================== 
47 ·················coef····std·err··········t······P>|t|······[0.025······0.975] 
48 ------------------------------------------------------------------------------ 
49 const··········1.3423······0.313······4.292······0.000·······0.722·······1.963 
50 x1············-0.0402······0.145·····-0.278······0.781······-0.327·······0.247 
51 x2············10.0103······0.014····715.745······0.000·······9.982······10.038 
52 ============================================================================== 
53 Omnibus:························2.042···Durbin-Watson:···················2.274 
54 Prob(Omnibus):··················0.360···Jarque-Bera·(JB):················1.875 
55 Skew:···························0.234···Prob(JB):························0.392 
56 Kurtosis:·······················2.519···Cond.·No.·························144. 
57 ============================================================================== 
  
58 Notes: 
59 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is 
60 correctly·specified. 
61 Quantities·of·interest·can·be·extracted·directly·from·the·fitted·model.·Type35 Quantities·of·interest·can·be·extracted·directly·from·the·fitted·model.·Type
62 dir(results)·for·a·full·list.·Here·are·some·examples:36 dir(results)·for·a·full·list.·Here·are·some·examples:
63 [6]:37 [·]:
64 print("Parameters:·",·results.params)38 print("Parameters:·",·results.params)
65 print("R2:·",·results.rsquared)39 print("R2:·",·results.rsquared)
66 Parameters:··[·1.34233516·-0.04024948·10.01025357] 
67 R2:··0.9999879365025871 
68 *\x8**\x8**\x8**\x8**\x8*·O\x8OL\x8LS\x8S·n\x8no\x8on\x8n-\x8-l\x8li\x8in\x8ne\x8ea\x8ar\x8r·c\x8cu\x8ur\x8rv\x8ve\x8e·b\x8bu\x8ut\x8t·l\x8li\x8in\x8ne\x8ea\x8ar\x8r·i\x8in\x8n·p\x8pa\x8ar\x8ra\x8am\x8me\x8et\x8te\x8er\x8rs\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*40 *\x8**\x8**\x8**\x8**\x8*·O\x8OL\x8LS\x8S·n\x8no\x8on\x8n-\x8-l\x8li\x8in\x8ne\x8ea\x8ar\x8r·c\x8cu\x8ur\x8rv\x8ve\x8e·b\x8bu\x8ut\x8t·l\x8li\x8in\x8ne\x8ea\x8ar\x8r·i\x8in\x8n·p\x8pa\x8ar\x8ra\x8am\x8me\x8et\x8te\x8er\x8rs\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
69 We·simulate·artificial·data·with·a·non-linear·relationship·between·x·and·y:41 We·simulate·artificial·data·with·a·non-linear·relationship·between·x·and·y:
70 [7]:42 [·]:
71 nsample·=·5043 nsample·=·50
72 sig·=·0.544 sig·=·0.5
73 x·=·np.linspace(0,·20,·nsample)45 x·=·np.linspace(0,·20,·nsample)
74 X·=·np.column_stack((x,·np.sin(x),·(x·-·5)·**·2,·np.ones(nsample)))46 X·=·np.column_stack((x,·np.sin(x),·(x·-·5)·**·2,·np.ones(nsample)))
75 beta·=·[0.5,·0.5,·-0.02,·5.0]47 beta·=·[0.5,·0.5,·-0.02,·5.0]
  
76 y_true·=·np.dot(X,·beta)48 y_true·=·np.dot(X,·beta)
77 y·=·y_true·+·sig·*·np.random.normal(size=nsample)49 y·=·y_true·+·sig·*·np.random.normal(size=nsample)
78 Fit·and·summary:50 Fit·and·summary:
79 [8]:51 [·]:
80 res·=·sm.OLS(y,·X).fit()52 res·=·sm.OLS(y,·X).fit()
81 print(res.summary())53 print(res.summary())
82 ····························OLS·Regression·Results 
83 ============================================================================== 
84 Dep.·Variable:······················y···R-squared:·······················0.933 
85 Model:····························OLS···Adj.·R-squared:··················0.928 
86 Method:·················Least·Squares···F-statistic:·····················211.8 
87 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········6.30e-27 
88 Time:························13:13:47···Log-Likelihood:················-34.438 
89 No.·Observations:··················50···AIC:·····························76.88 
90 Df·Residuals:······················46···BIC:·····························84.52 
91 Df·Model:···························3 
92 Covariance·Type:············nonrobust 
93 ============================================================================== 
94 ·················coef····std·err··········t······P>|t|······[0.025······0.975] 
95 ------------------------------------------------------------------------------ 
96 x1·············0.4687······0.026·····17.751······0.000·······0.416·······0.522 
97 x2·············0.4836······0.104······4.659······0.000·······0.275·······0.693 
98 x3············-0.0174······0.002·····-7.507······0.000······-0.022······-0.013 
99 const··········5.2058······0.171·····30.405······0.000·······4.861·······5.550 
100 ============================================================================== 
101 Omnibus:························0.655···Durbin-Watson:···················2.896 
102 Prob(Omnibus):··················0.721···Jarque-Bera·(JB):················0.360 
103 Skew:···························0.207···Prob(JB):························0.835 
104 Kurtosis:·······················3.026···Cond.·No.·························221. 
105 ============================================================================== 
  
106 Notes: 
107 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is 
108 correctly·specified. 
109 Extract·other·quantities·of·interest:54 Extract·other·quantities·of·interest:
110 [9]:55 [·]:
111 print("Parameters:·",·res.params)56 print("Parameters:·",·res.params)
112 print("Standard·errors:·",·res.bse)57 print("Standard·errors:·",·res.bse)
113 print("Predicted·values:·",·res.predict())58 print("Predicted·values:·",·res.predict())
114 Parameters:··[·0.46872448··0.48360119·-0.01740479··5.20584496] 
115 Standard·errors:··[0.02640602·0.10380518·0.00231847·0.17121765] 
116 Predicted·values:··[·4.77072516··5.22213464··5.63620761··5.98658823··6.25643234 
117 6.44117491 
118 ··6.54928009··6.60085051··6.62432454··6.6518039···6.71377946··6.83412169 
119 ··7.02615877··7.29048685··7.61487206··7.97626054··8.34456611··8.68761335 
120 ··8.97642389··9.18997755··9.31866582··9.36587056··9.34740836··9.28893189 
121 ··9.22171529··9.17751587··9.1833565···9.25708583··9.40444579··9.61812821 
122 ··9.87897556·10.15912843·10.42660281·10.65054491·10.8063004··10.87946503 
123 ·10.86825119·10.78378163·10.64826203·10.49133265·10.34519853·10.23933827 
124 ·10.19566084·10.22490593·10.32487947·10.48081414·10.66779556·10.85485568 
125 ·11.01006072·11.10575781] 
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5 ············"metadata":·{},5 ············"metadata":·{},
6 ············"source":·[6 ············"source":·[
7 ················"#·Ordinary·Least·Squares"7 ················"#·Ordinary·Least·Squares"
8 ············]8 ············]
9 ········},9 ········},
10 ········{10 ········{
11 ············"cell_type":·"code",11 ············"cell_type":·"code",
12 ············"execution_count":·1,12 ············"execution_count":·null,
13 ············"metadata":·{13 ············"metadata":·{},
14 ················"execution":·{} 
15 ············}, 
16 ············"outputs":·[],14 ············"outputs":·[],
17 ············"source":·[15 ············"source":·[
18 ················"%matplotlib·inline"16 ················"%matplotlib·inline"
19 ············]17 ············]
20 ········},18 ········},
21 ········{19 ········{
22 ············"cell_type":·"code",20 ············"cell_type":·"code",
23 ············"execution_count":·2,21 ············"execution_count":·null,
24 ············"metadata":·{22 ············"metadata":·{},
25 ················"execution":·{} 
26 ············}, 
27 ············"outputs":·[],23 ············"outputs":·[],
28 ············"source":·[24 ············"source":·[
29 ················"import·matplotlib.pyplot·as·plt\n",25 ················"import·matplotlib.pyplot·as·plt\n",
30 ················"import·numpy·as·np\n",26 ················"import·numpy·as·np\n",
31 ················"import·pandas·as·pd\n",27 ················"import·pandas·as·pd\n",
32 ················"import·statsmodels.api·as·sm\n",28 ················"import·statsmodels.api·as·sm\n",
33 ················"\n",29 ················"\n",
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41 ················"##·OLS·estimation\n",37 ················"##·OLS·estimation\n",
42 ················"\n",38 ················"\n",
43 ················"Artificial·data:"39 ················"Artificial·data:"
44 ············]40 ············]
45 ········},41 ········},
46 ········{42 ········{
47 ············"cell_type":·"code",43 ············"cell_type":·"code",
48 ············"execution_count":·3,44 ············"execution_count":·null,
49 ············"metadata":·{45 ············"metadata":·{},
50 ················"execution":·{} 
51 ············}, 
52 ············"outputs":·[],46 ············"outputs":·[],
53 ············"source":·[47 ············"source":·[
54 ················"nsample·=·100\n",48 ················"nsample·=·100\n",
55 ················"x·=·np.linspace(0,·10,·100)\n",49 ················"x·=·np.linspace(0,·10,·100)\n",
56 ················"X·=·np.column_stack((x,·x·**·2))\n",50 ················"X·=·np.column_stack((x,·x·**·2))\n",
57 ················"beta·=·np.array([1,·0.1,·10])\n",51 ················"beta·=·np.array([1,·0.1,·10])\n",
58 ················"e·=·np.random.normal(size=nsample)"52 ················"e·=·np.random.normal(size=nsample)"
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63 ············"metadata":·{},57 ············"metadata":·{},
64 ············"source":·[58 ············"source":·[
65 ················"Our·model·needs·an·intercept·so·we·add·a·column·of·1s:"59 ················"Our·model·needs·an·intercept·so·we·add·a·column·of·1s:"
66 ············]60 ············]
67 ········},61 ········},
68 ········{62 ········{
69 ············"cell_type":·"code",63 ············"cell_type":·"code",
70 ············"execution_count":·4,64 ············"execution_count":·null,
71 ············"metadata":·{65 ············"metadata":·{},
72 ················"execution":·{} 
73 ············}, 
74 ············"outputs":·[],66 ············"outputs":·[],
75 ············"source":·[67 ············"source":·[
76 ················"X·=·sm.add_constant(X)\n",68 ················"X·=·sm.add_constant(X)\n",
77 ················"y·=·np.dot(X,·beta)·+·e"69 ················"y·=·np.dot(X,·beta)·+·e"
78 ············]70 ············]
79 ········},71 ········},
80 ········{72 ········{
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82 ············"metadata":·{},74 ············"metadata":·{},
83 ············"source":·[75 ············"source":·[
84 ················"Fit·and·summary:"76 ················"Fit·and·summary:"
85 ············]77 ············]
86 ········},78 ········},
87 ········{79 ········{
88 ············"cell_type":·"code",80 ············"cell_type":·"code",
89 ············"execution_count":·5,81 ············"execution_count":·null,
90 ············"metadata":·{82 ············"metadata":·{},
91 ················"execution":·{} 
92 ············}, 
93 ············"outputs":·[83 ············"outputs":·[],
94 ················{ 
95 ····················"name":·"stdout", 
96 ····················"output_type":·"stream", 
97 ····················"text":·[ 
98 ························"····························OLS·Regression·Results····························\n", 
99 ························"==============================================================================\n", 
100 ························"Dep.·Variable:······················y···R-squared:·······················1.000\n", 
101 ························"Model:····························OLS···Adj.·R-squared:··················1.000\n", 
102 ························"Method:·················Least·Squares···F-statistic:·················4.020e+06\n", 
103 ························"Date:················Sun,·10·Aug·2025···Prob·(F-statistic):··········2.83e-239\n", 
104 ························"Time:························13:13:47···Log-Likelihood:················-146.51\n", 
105 ························"No.·Observations:·················100···AIC:·····························299.0\n", 
106 ························"Df·Residuals:······················97···BIC:·····························306.8\n", 
107 ························"Df·Model:···························2·········································\n", 
108 ························"Covariance·Type:············nonrobust·········································\n", 
109 ························"==============================================================================\n", 
110 ························"·················coef····std·err··········t······P>|t|······[0.025······0.975]\n", 
111 ························"------------------------------------------------------------------------------\n", 
112 ························"const··········1.3423······0.313······4.292······0.000·······0.722·······1.963\n", 
113 ························"x1············-0.0402······0.145·····-0.278······0.781······-0.327·······0.247\n", 
114 ························"x2············10.0103······0.014····715.745······0.000·······9.982······10.038\n", 
115 ························"==============================================================================\n", 
116 ························"Omnibus:························2.042···Durbin-Watson:···················2.274\n", 
117 ························"Prob(Omnibus):··················0.360···Jarque-Bera·(JB):················1.875\n", 
118 ························"Skew:···························0.234···Prob(JB):························0.392\n", 
119 ························"Kurtosis:·······················2.519···Cond.·No.·························144.\n", 
120 ························"==============================================================================\n", 
121 ························"\n", 
122 ························"Notes:\n", 
123 ························"[1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified.\n" 
124 ····················] 
125 ················} 
126 ············], 
127 ············"source":·[84 ············"source":·[
128 ················"model·=·sm.OLS(y,·X)\n",85 ················"model·=·sm.OLS(y,·X)\n",
129 ················"results·=·model.fit()\n",86 ················"results·=·model.fit()\n",
130 ················"print(results.summary())"87 ················"print(results.summary())"
131 ············]88 ············]
132 ········},89 ········},
133 ········{90 ········{
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135 ············"metadata":·{},92 ············"metadata":·{},
136 ············"source":·[93 ············"source":·[
137 ················"Quantities·of·interest·can·be·extracted·directly·from·the·fitted·model.·Type·``dir(results)``·for·a·full·list.·Here·are·some·examples:··"94 ················"Quantities·of·interest·can·be·extracted·directly·from·the·fitted·model.·Type·``dir(results)``·for·a·full·list.·Here·are·some·examples:··"
138 ············]95 ············]
139 ········},96 ········},
140 ········{97 ········{
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60 ············60 ············
61 ··<section·id="statsmodels-Principal-Component-Analysis">61 ··<section·id="statsmodels-Principal-Component-Analysis">
62 <h1>statsmodels·Principal·Component·Analysis<a·class="headerlink"·href="#statsmodels-Principal-Component-Analysis"·title="Link·to·this·heading">¶</a></h1>62 <h1>statsmodels·Principal·Component·Analysis<a·class="headerlink"·href="#statsmodels-Principal-Component-Analysis"·title="Link·to·this·heading">¶</a></h1>
63 <p><em>Key·ideas:</em>·Principal·component·analysis,·world·bank·data,·fertility</p>63 <p><em>Key·ideas:</em>·Principal·component·analysis,·world·bank·data,·fertility</p>
64 <p>In·this·notebook,·we·use·principal·components·analysis·(PCA)·to·analyze·the·time·series·of·fertility·rates·in·192·countries,·using·data·obtained·from·the·World·Bank.·The·main·goal·is·to·understand·how·the·trends·in·fertility·over·time·differ·from·country·to·country.·This·is·a·slightly·atypical·illustration·of·PCA·because·the·data·are·time·series.·Methods·such·as·functional·PCA·have·been·developed·for·this·setting,·but·since·the·fertility·data·are·very·smooth,·there·is·no·real·disadvantage·to64 <p>In·this·notebook,·we·use·principal·components·analysis·(PCA)·to·analyze·the·time·series·of·fertility·rates·in·192·countries,·using·data·obtained·from·the·World·Bank.·The·main·goal·is·to·understand·how·the·trends·in·fertility·over·time·differ·from·country·to·country.·This·is·a·slightly·atypical·illustration·of·PCA·because·the·data·are·time·series.·Methods·such·as·functional·PCA·have·been·developed·for·this·setting,·but·since·the·fertility·data·are·very·smooth,·there·is·no·real·disadvantage·to
65 using·standard·PCA·in·this·case.</p>65 using·standard·PCA·in·this·case.</p>
66 <div·class="nbinput·nblast·docutils·container">66 <div·class="nbinput·nblast·docutils·container">
67 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:67 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline70 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
  
71 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>71 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
72 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>72 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
73 <span·class="kn">from</span>·<span·class="nn">statsmodels.multivariate.pca</span>·<span·class="kn">import</span>·<span·class="n">PCA</span>73 <span·class="kn">from</span>·<span·class="nn">statsmodels.multivariate.pca</span>·<span·class="kn">import</span>·<span·class="n">PCA</span>
  
74 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;figure&quot;</span><span·class="p">,</span>·<span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">16</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>74 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;figure&quot;</span><span·class="p">,</span>·<span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">16</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>
75 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;font&quot;</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">14</span><span·class="p">)</span>75 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;font&quot;</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">14</span><span·class="p">)</span>
76 </pre></div>76 </pre></div>
77 </div>77 </div>
78 </div>78 </div>
79 <p>The·data·can·be·obtained·from·the·<a·class="reference·external"·href="http://data.worldbank.org/indicator/SP.DYN.TFRT.IN">World·Bank·web·site</a>,·but·here·we·work·with·a·slightly·cleaned-up·version·of·the·data:</p>79 <p>The·data·can·be·obtained·from·the·<a·class="reference·external"·href="http://data.worldbank.org/indicator/SP.DYN.TFRT.IN">World·Bank·web·site</a>,·but·here·we·work·with·a·slightly·cleaned-up·version·of·the·data:</p>
80 <div·class="nbinput·docutils·container">80 <div·class="nbinput·nblast·docutils·container">
81 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:81 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
82 </pre></div>82 </pre></div>
83 </div>83 </div>
84 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">fertility</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>84 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">fertility</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>
85 <span·class="n">data</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>85 <span·class="n">data</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>
86 </pre></div>86 </pre></div>
87 </div>87 </div>
88 </div>88 </div>
89 <div·class="nboutput·nblast·docutils·container"> 
90 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]: 
91 </pre></div> 
92 </div> 
93 <div·class="output_area·rendered_html·docutils·container"> 
94 <div> 
95 <style·scoped> 
96 ····.dataframe·tbody·tr·th:only-of-type·{ 
97 ········vertical-align:·middle; 
98 ····} 
  
99 ····.dataframe·tbody·tr·th·{ 
100 ········vertical-align:·top; 
101 ····} 
  
102 ····.dataframe·thead·th·{ 
103 ········text-align:·right; 
104 ····} 
105 </style> 
106 <table·border="1"·class="dataframe"> 
107 ··<thead> 
108 ····<tr·style="text-align:·right;"> 
109 ······<th></th> 
110 ······<th>Country·Name</th> 
111 ······<th>Country·Code</th> 
112 ······<th>Indicator·Name</th> 
113 ······<th>Indicator·Code</th> 
114 ······<th>1960</th> 
115 ······<th>1961</th> 
116 ······<th>1962</th> 
117 ······<th>1963</th> 
118 ······<th>1964</th> 
119 ······<th>1965</th> 
120 ······<th>...</th> 
121 ······<th>2004</th> 
122 ······<th>2005</th> 
123 ······<th>2006</th> 
124 ······<th>2007</th> 
125 ······<th>2008</th> 
126 ······<th>2009</th> 
127 ······<th>2010</th> 
128 ······<th>2011</th> 
129 ······<th>2012</th> 
130 ······<th>2013</th> 
131 ····</tr> 
132 ··</thead> 
133 ··<tbody> 
134 ····<tr> 
135 ······<th>0</th> 
136 ······<td>Aruba</td> 
137 ······<td>ABW</td> 
138 ······<td>Fertility·rate,·total·(births·per·woman)</td> 
139 ······<td>SP.DYN.TFRT.IN</td> 
140 ······<td>4.820</td> 
141 ······<td>4.655</td> 
142 ······<td>4.471</td> 
143 ······<td>4.271</td> 
144 ······<td>4.059</td> 
145 ······<td>3.842</td> 
146 ······<td>...</td> 
147 ······<td>1.786</td> 
148 ······<td>1.769</td> 
149 ······<td>1.754</td> 
150 ······<td>1.739</td> 
151 ······<td>1.726</td> 
152 ······<td>1.713</td> 
153 ······<td>1.701</td> 
154 ······<td>1.690</td> 
155 ······<td>NaN</td> 
156 ······<td>NaN</td> 
157 ····</tr> 
158 ····<tr> 
159 ······<th>1</th> 
160 ······<td>Andorra</td> 
161 ······<td>AND</td> 
162 ······<td>Fertility·rate,·total·(births·per·woman)</td> 
163 ······<td>SP.DYN.TFRT.IN</td> 
164 ······<td>NaN</td> 
165 ······<td>NaN</td> 
166 ······<td>NaN</td> 
167 ······<td>NaN</td> 
168 ······<td>NaN</td> 
169 ······<td>NaN</td> 
170 ······<td>...</td> 
171 ······<td>NaN</td> 
172 ······<td>NaN</td> 
173 ······<td>1.240</td> 
174 ······<td>1.180</td> 
175 ······<td>1.250</td> 
176 ······<td>1.190</td> 
177 ······<td>1.220</td> 
178 ······<td>NaN</td> 
179 ······<td>NaN</td> 
180 ······<td>NaN</td> 
181 ····</tr> 
182 ····<tr> 
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11 In·this·notebook,·we·use·principal·components·analysis·(PCA)·to·analyze·the11 In·this·notebook,·we·use·principal·components·analysis·(PCA)·to·analyze·the
12 time·series·of·fertility·rates·in·192·countries,·using·data·obtained·from·the12 time·series·of·fertility·rates·in·192·countries,·using·data·obtained·from·the
13 World·Bank.·The·main·goal·is·to·understand·how·the·trends·in·fertility·over13 World·Bank.·The·main·goal·is·to·understand·how·the·trends·in·fertility·over
14 time·differ·from·country·to·country.·This·is·a·slightly·atypical·illustration14 time·differ·from·country·to·country.·This·is·a·slightly·atypical·illustration
15 of·PCA·because·the·data·are·time·series.·Methods·such·as·functional·PCA·have15 of·PCA·because·the·data·are·time·series.·Methods·such·as·functional·PCA·have
16 been·developed·for·this·setting,·but·since·the·fertility·data·are·very·smooth,16 been·developed·for·this·setting,·but·since·the·fertility·data·are·very·smooth,
17 there·is·no·real·disadvantage·to·using·standard·PCA·in·this·case.17 there·is·no·real·disadvantage·to·using·standard·PCA·in·this·case.
18 [1]:18 [·]:
19 %matplotlib·inline19 %matplotlib·inline
  
20 import·matplotlib.pyplot·as·plt20 import·matplotlib.pyplot·as·plt
21 import·statsmodels.api·as·sm21 import·statsmodels.api·as·sm
22 from·statsmodels.multivariate.pca·import·PCA22 from·statsmodels.multivariate.pca·import·PCA
  
23 plt.rc("figure",·figsize=(16,·8))23 plt.rc("figure",·figsize=(16,·8))
24 plt.rc("font",·size=14)24 plt.rc("font",·size=14)
25 The·data·can·be·obtained·from·the·_\x8W_\x8o_\x8r_\x8l_\x8d_\x8·_\x8B_\x8a_\x8n_\x8k_\x8·_\x8w_\x8e_\x8b_\x8·_\x8s_\x8i_\x8t_\x8e,·but·here·we·work·with·a25 The·data·can·be·obtained·from·the·_\x8W_\x8o_\x8r_\x8l_\x8d_\x8·_\x8B_\x8a_\x8n_\x8k_\x8·_\x8w_\x8e_\x8b_\x8·_\x8s_\x8i_\x8t_\x8e,·but·here·we·work·with·a
26 slightly·cleaned-up·version·of·the·data:26 slightly·cleaned-up·version·of·the·data:
27 [2]:27 [·]:
28 data·=·sm.datasets.fertility.load_pandas().data28 data·=·sm.datasets.fertility.load_pandas().data
29 data.head()29 data.head()
30 [2]: 
31 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
32 |·|····C\x8Co\x8ou\x8un\x8nt\x8tr\x8ry\x8y|C\x8Co\x8ou\x8un\x8nt\x8tr\x8ry\x8y|I\x8In\x8nd\x8di\x8ic\x8ca\x8at\x8to\x8or\x8r|I\x8In\x8nd\x8di\x8ic\x8ca\x8at\x8to\x8or\x8r·C\x8Co\x8od\x8de\x8e|·1\x819\x896\x860\x80|·1\x819\x896\x861\x81|·1\x819\x896\x862\x82|·1\x819\x896\x863\x83|·1\x819\x896\x864\x84|·1\x819\x896\x865\x85|.\x8..\x8..\x8.|·2\x820\x800\x804\x84|·2\x820\x800\x805\x85|·2\x820\x800\x806\x86|·2\x820\x800\x807\x87|·2\x820\x800\x808\x88|·2\x820\x800\x809\x89|·2\x820\x801\x810\x80|·2\x820\x801\x811\x81|2\x820\x801\x812\x82|2\x820\x801\x813\x83| 
33 |_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8N\x8N_\x8a\x8a_\x8m\x8m_\x8e\x8e_\x8|_\x8·_\x8·_\x8·_\x8C\x8C_\x8o\x8o_\x8d\x8d_\x8e\x8e_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8N\x8N_\x8a\x8a_\x8m\x8m_\x8e\x8e_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·| 
34 |·|···········|·······|Fertility|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
35 |·|···········|·······|rate,····|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
36 |0\x80|Aruba······|ABW····|total····|SP.DYN.TFRT.IN|4.820|4.655|4.471|4.271|4.059|3.842|...|1.786|1.769|1.754|1.739|1.726|1.713|1.701|1.690|NaN·|NaN·| 
37 |·|···········|·······|(births··|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
38 |·|···········|·······|per······|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
39 |_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8w_\x8o_\x8m_\x8a_\x8n_\x8)_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·| 
40 |·|···········|·······|Fertility|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
41 |·|···········|·······|rate,····|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
42 |1\x81|Andorra····|AND····|total····|SP.DYN.TFRT.IN|NaN··|NaN··|NaN··|NaN··|NaN··|NaN··|...|NaN··|NaN··|1.240|1.180|1.250|1.190|1.220|NaN··|NaN·|NaN·| 
43 |·|···········|·······|(births··|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
44 |·|···········|·······|per······|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
45 |_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8w_\x8o_\x8m_\x8a_\x8n_\x8)_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·| 
46 |·|···········|·······|Fertility|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
47 |·|···········|·······|rate,····|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
48 |2\x82|Afghanistan|AFG····|total····|SP.DYN.TFRT.IN|7.671|7.671|7.671|7.671|7.671|7.671|...|7.136|6.930|6.702|6.456|6.196|5.928|5.659|5.395|NaN·|NaN·| 
49 |·|···········|·······|(births··|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
50 |·|···········|·······|per······|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
51 |_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8w_\x8o_\x8m_\x8a_\x8n_\x8)_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·| 
52 |·|···········|·······|Fertility|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
53 |·|···········|·······|rate,····|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
54 |3\x83|Angola·····|AGO····|total····|SP.DYN.TFRT.IN|7.316|7.354|7.385|7.410|7.425|7.430|...|6.704|6.657|6.598|6.523|6.434|6.331|6.218|6.099|NaN·|NaN·| 
55 |·|···········|·······|(births··|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
56 |·|···········|·······|per······|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
57 |_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8w_\x8o_\x8m_\x8a_\x8n_\x8)_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·| 
58 |·|···········|·······|Fertility|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
59 |·|···········|·······|rate,····|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
60 |4\x84|Albania····|ALB····|total····|SP.DYN.TFRT.IN|6.186|6.076|5.956|5.833|5.711|5.594|...|2.004|1.919|1.849|1.796|1.761|1.744|1.741|1.748|NaN·|NaN·| 
61 |·|···········|·······|(births··|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
62 |·|···········|·······|per······|··············|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|····|····| 
63 |_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8w_\x8o_\x8m_\x8a_\x8n_\x8)_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·| 
64 5·rows·×·58·columns 
65 Here·we·construct·a·DataFrame·that·contains·only·the·numerical·fertility·rate30 Here·we·construct·a·DataFrame·that·contains·only·the·numerical·fertility·rate
66 data·and·set·the·index·to·the·country·names.·We·also·drop·all·the·countries31 data·and·set·the·index·to·the·country·names.·We·also·drop·all·the·countries
67 with·any·missing·data.32 with·any·missing·data.
68 [3]:33 [·]:
69 columns·=·list(map(str,·range(1960,·2012)))34 columns·=·list(map(str,·range(1960,·2012)))
70 data.set_index("Country·Name",·inplace=True)35 data.set_index("Country·Name",·inplace=True)
71 dta·=·data[columns]36 dta·=·data[columns]
72 dta·=·dta.dropna()37 dta·=·dta.dropna()
73 dta.head()38 dta.head()
74 [3]: 
75 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
76 |_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x80\x80_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x81\x81_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x82\x82_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x83\x83_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x84\x84_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x85\x85_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x86\x86_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x87\x87_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x88\x88_\x8|_\x8·_\x81\x81_\x89\x89_\x86\x86_\x89\x89_\x8|_\x8.\x8._\x8.\x8._\x8.\x8._\x8|_\x8·_\x82\x82_\x80\x80_\x80\x80_\x82\x82_\x8|_\x8·_\x82\x82_\x80\x80_\x80\x80_\x83\x83_\x8|_\x8·_\x82\x82_\x80\x80_\x80\x80_\x84\x84_\x8|_\x8·_\x82\x82_\x80\x80_\x80\x80_\x85\x85_\x8|_\x8·_\x82\x82_\x80\x80_\x80\x80_\x86\x86_\x8|_\x8·_\x82\x82_\x80\x80_\x80\x80_\x87\x87_\x8|_\x8·_\x82\x82_\x80\x80_\x80\x80_\x88\x88_\x8|_\x8·_\x82\x82_\x80\x80_\x80\x80_\x89\x89_\x8|_\x8·_\x82\x82_\x80\x80_\x81\x81_\x80\x80_\x8|_\x8·_\x82\x82_\x80\x80_\x81\x81_\x81\x81| 
77 |C\x8Co\x8ou\x8un\x8nt\x8tr\x8ry\x8y····|·····|·····|·····|·····|·····|·····|·····|·····|·····|·····|···|·····|·····|·····|·····|·····|·····|·····|·····|·····|·····| 
78 |_\x8N\x8N_\x8a\x8a_\x8m\x8m_\x8e\x8e_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·| 
79 |_\x8A\x8A_\x8r\x8r_\x8u\x8u_\x8b\x8b_\x8a\x8a_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x84_\x8._\x88_\x82_\x80_\x8|_\x84_\x8._\x86_\x85_\x85_\x8|_\x84_\x8._\x84_\x87_\x81_\x8|_\x84_\x8._\x82_\x87_\x81_\x8|_\x84_\x8._\x80_\x85_\x89_\x8|_\x83_\x8._\x88_\x84_\x82_\x8|_\x83_\x8._\x86_\x82_\x85_\x8|_\x83_\x8._\x84_\x81_\x87_\x8|_\x83_\x8._\x82_\x82_\x86_\x8|_\x83_\x8._\x80_\x85_\x84_\x8|_\x8._\x8._\x8._\x8|_\x81_\x8._\x88_\x82_\x85_\x8|_\x81_\x8._\x88_\x80_\x85_\x8|_\x81_\x8._\x87_\x88_\x86_\x8|_\x81_\x8._\x87_\x86_\x89_\x8|_\x81_\x8._\x87_\x85_\x84_\x8|_\x81_\x8._\x87_\x83_\x89_\x8|_\x81_\x8._\x87_\x82_\x86_\x8|_\x81_\x8._\x87_\x81_\x83_\x8|_\x81_\x8._\x87_\x80_\x81_\x8|_\x81_\x8._\x86_\x89_\x80| 
80 |_\x8A\x8A_\x8f\x8f_\x8g\x8g_\x8h\x8h_\x8a\x8a_\x8n\x8n_\x8i\x8i_\x8s\x8s_\x8t\x8t_\x8a\x8a_\x8n\x8n_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x87_\x8._\x86_\x87_\x81_\x8|_\x8._\x8._\x8._\x8|_\x87_\x8._\x84_\x88_\x84_\x8|_\x87_\x8._\x83_\x82_\x81_\x8|_\x87_\x8._\x81_\x83_\x86_\x8|_\x86_\x8._\x89_\x83_\x80_\x8|_\x86_\x8._\x87_\x80_\x82_\x8|_\x86_\x8._\x84_\x85_\x86_\x8|_\x86_\x8._\x81_\x89_\x86_\x8|_\x85_\x8._\x89_\x82_\x88_\x8|_\x85_\x8._\x86_\x85_\x89_\x8|_\x85_\x8._\x83_\x89_\x85| 
81 |_\x8A\x8A_\x8n\x8n_\x8g\x8g_\x8o\x8o_\x8l\x8l_\x8a\x8a_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x87_\x8._\x83_\x81_\x86_\x8|_\x87_\x8._\x83_\x85_\x84_\x8|_\x87_\x8._\x83_\x88_\x85_\x8|_\x87_\x8._\x84_\x81_\x80_\x8|_\x87_\x8._\x84_\x82_\x85_\x8|_\x87_\x8._\x84_\x83_\x80_\x8|_\x87_\x8._\x84_\x82_\x82_\x8|_\x87_\x8._\x84_\x80_\x83_\x8|_\x87_\x8._\x83_\x87_\x85_\x8|_\x87_\x8._\x83_\x83_\x89_\x8|_\x8._\x8._\x8._\x8|_\x86_\x8._\x87_\x87_\x88_\x8|_\x86_\x8._\x87_\x84_\x83_\x8|_\x86_\x8._\x87_\x80_\x84_\x8|_\x86_\x8._\x86_\x85_\x87_\x8|_\x86_\x8._\x85_\x89_\x88_\x8|_\x86_\x8._\x85_\x82_\x83_\x8|_\x86_\x8._\x84_\x83_\x84_\x8|_\x86_\x8._\x83_\x83_\x81_\x8|_\x86_\x8._\x82_\x81_\x88_\x8|_\x86_\x8._\x80_\x89_\x89| 
82 |_\x8A\x8A_\x8l\x8l_\x8b\x8b_\x8a\x8a_\x8n\x8n_\x8i\x8i_\x8a\x8a_\x8·_\x8·_\x8·_\x8·_\x8|_\x86_\x8._\x81_\x88_\x86_\x8|_\x86_\x8._\x80_\x87_\x86_\x8|_\x85_\x8._\x89_\x85_\x86_\x8|_\x85_\x8._\x88_\x83_\x83_\x8|_\x85_\x8._\x87_\x81_\x81_\x8|_\x85_\x8._\x85_\x89_\x84_\x8|_\x85_\x8._\x84_\x88_\x83_\x8|_\x85_\x8._\x83_\x87_\x86_\x8|_\x85_\x8._\x82_\x86_\x88_\x8|_\x85_\x8._\x81_\x86_\x80_\x8|_\x8._\x8._\x8._\x8|_\x82_\x8._\x81_\x89_\x85_\x8|_\x82_\x8._\x80_\x89_\x87_\x8|_\x82_\x8._\x80_\x80_\x84_\x8|_\x81_\x8._\x89_\x81_\x89_\x8|_\x81_\x8._\x88_\x84_\x89_\x8|_\x81_\x8._\x87_\x89_\x86_\x8|_\x81_\x8._\x87_\x86_\x81_\x8|_\x81_\x8._\x87_\x84_\x84_\x8|_\x81_\x8._\x87_\x84_\x81_\x8|_\x81_\x8._\x87_\x84_\x88| 
83 |U\x8Un\x8ni\x8it\x8te\x8ed\x8d·A\x8Ar\x8ra\x8ab\x8b|6.928|6.910|6.893|6.877|6.861|6.841|6.816|6.783|6.738|6.679|...|2.428|2.329|2.236|2.149|2.071|2.004|1.948|1.903|1.868|1.841| 
84 |_\x8E\x8E_\x8m\x8m_\x8i\x8i_\x8r\x8r_\x8a\x8a_\x8t\x8t_\x8e\x8e_\x8s\x8s_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·| 
85 5·rows·×·52·columns 
86 There·are·two·ways·to·use·PCA·to·analyze·a·rectangular·matrix:·we·can·treat·the39 There·are·two·ways·to·use·PCA·to·analyze·a·rectangular·matrix:·we·can·treat·the
87 rows·as·the·“objects”·and·the·columns·as·the·“variables”,·or·vice-versa.·Here40 rows·as·the·“objects”·and·the·columns·as·the·“variables”,·or·vice-versa.·Here
88 we·will·treat·the·fertility·measures·as·“variables”·used·to·measure·the41 we·will·treat·the·fertility·measures·as·“variables”·used·to·measure·the
89 countries·as·“objects”.·Thus·the·goal·will·be·to·reduce·the·yearly·fertility42 countries·as·“objects”.·Thus·the·goal·will·be·to·reduce·the·yearly·fertility
90 rate·values·to·a·small·number·of·fertility·rate·“profiles”·or·“basis·functions”43 rate·values·to·a·small·number·of·fertility·rate·“profiles”·or·“basis·functions”
91 that·capture·most·of·the·variation·over·time·in·the·different·countries.44 that·capture·most·of·the·variation·over·time·in·the·different·countries.
92 The·mean·trend·is·removed·in·PCA,·but·its·worthwhile·taking·a·look·at·it.·It45 The·mean·trend·is·removed·in·PCA,·but·its·worthwhile·taking·a·look·at·it.·It
93 shows·that·fertility·has·dropped·steadily·over·the·time·period·covered·in·this46 shows·that·fertility·has·dropped·steadily·over·the·time·period·covered·in·this
94 dataset.·Note·that·the·mean·is·calculated·using·a·country·as·the·unit·of47 dataset.·Note·that·the·mean·is·calculated·using·a·country·as·the·unit·of
95 analysis,·ignoring·population·size.·This·is·also·true·for·the·PC·analysis48 analysis,·ignoring·population·size.·This·is·also·true·for·the·PC·analysis
96 conducted·below.·A·more·sophisticated·analysis·might·weight·the·countries,·say49 conducted·below.·A·more·sophisticated·analysis·might·weight·the·countries,·say
97 by·population·in·1980.50 by·population·in·1980.
98 [4]:51 [·]:
99 ax·=·dta.mean().plot(grid=False)52 ax·=·dta.mean().plot(grid=False)
100 ax.set_xlabel("Year",·size=17)53 ax.set_xlabel("Year",·size=17)
101 ax.set_ylabel("Fertility·rate",·size=17)54 ax.set_ylabel("Fertility·rate",·size=17)
102 ax.set_xlim(0,·51)55 ax.set_xlim(0,·51)
103 [4]: 
104 (0.0,·51.0) 
105 [../../../_images/examples_notebooks_generated_pca_fertility_factors_9_1.png] 
106 Next·we·perform·the·PCA:56 Next·we·perform·the·PCA:
107 [5]:57 [·]:
108 pca_model·=·PCA(dta.T,·standardize=False,·demean=True)58 pca_model·=·PCA(dta.T,·standardize=False,·demean=True)
109 Based·on·the·eigenvalues,·we·see·that·the·first·PC·dominates,·with·perhaps·a59 Based·on·the·eigenvalues,·we·see·that·the·first·PC·dominates,·with·perhaps·a
110 small·amount·of·meaningful·variation·captured·in·the·second·and·third·PC’s.60 small·amount·of·meaningful·variation·captured·in·the·second·and·third·PC’s.
111 [6]:61 [·]:
112 fig·=·pca_model.plot_scree(log_scale=False)62 fig·=·pca_model.plot_scree(log_scale=False)
113 [../../../_images/examples_notebooks_generated_pca_fertility_factors_13_0.png] 
114 Next·we·will·plot·the·PC·factors.·The·dominant·factor·is·monotonically63 Next·we·will·plot·the·PC·factors.·The·dominant·factor·is·monotonically
115 increasing.·Countries·with·a·positive·score·on·the·first·factor·will·increase64 increasing.·Countries·with·a·positive·score·on·the·first·factor·will·increase
116 faster·(or·decrease·slower)·compared·to·the·mean·shown·above.·Countries·with·a65 faster·(or·decrease·slower)·compared·to·the·mean·shown·above.·Countries·with·a
117 negative·score·on·the·first·factor·will·decrease·faster·than·the·mean.·The66 negative·score·on·the·first·factor·will·decrease·faster·than·the·mean.·The
118 second·factor·is·U-shaped·with·a·positive·peak·at·around·1985.·Countries·with·a67 second·factor·is·U-shaped·with·a·positive·peak·at·around·1985.·Countries·with·a
119 large·positive·score·on·the·second·factor·will·have·lower·than·average68 large·positive·score·on·the·second·factor·will·have·lower·than·average
120 fertilities·at·the·beginning·and·end·of·the·data·range,·but·higher·than·average69 fertilities·at·the·beginning·and·end·of·the·data·range,·but·higher·than·average
121 fertility·in·the·middle·of·the·range.70 fertility·in·the·middle·of·the·range.
122 [7]:71 [·]:
123 fig,·ax·=·plt.subplots(figsize=(8,·4))72 fig,·ax·=·plt.subplots(figsize=(8,·4))
124 lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6)73 lines·=·ax.plot(pca_model.factors.iloc[:,·:3],·lw=4,·alpha=0.6)
125 ax.set_xticklabels(dta.columns.values[::10])74 ax.set_xticklabels(dta.columns.values[::10])
126 ax.set_xlim(0,·51)75 ax.set_xlim(0,·51)
127 ax.set_xlabel("Year",·size=17)76 ax.set_xlabel("Year",·size=17)
128 fig.subplots_adjust(0.1,·0.1,·0.85,·0.9)77 fig.subplots_adjust(0.1,·0.1,·0.85,·0.9)
129 legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right")78 legend·=·fig.legend(lines,·["PC·1",·"PC·2",·"PC·3"],·loc="center·right")
130 legend.draw_frame(False)79 legend.draw_frame(False)
131 /tmp/ipykernel_nnnnnnn/427128218.py:3:·UserWarning:·set_ticklabels()·should 
132 only·be·used·with·a·fixed·number·of·ticks,·i.e.·after·set_ticks()·or·using·a 
133 FixedLocator. 
134 ··ax.set_xticklabels(dta.columns.values[::10]) 
135 [../../../_images/examples_notebooks_generated_pca_fertility_factors_15_1.png] 
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58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Box-Plots">61 ··<section·id="Box-Plots">
62 <h1>Box·Plots<a·class="headerlink"·href="#Box-Plots"·title="Link·to·this·heading">¶</a></h1>62 <h1>Box·Plots<a·class="headerlink"·href="#Box-Plots"·title="Link·to·this·heading">¶</a></h1>
63 <p>The·following·illustrates·some·options·for·the·boxplot·in·statsmodels.·These·include·<code·class="docutils·literal·notranslate"><span·class="pre">violin_plot</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">bean_plot</span></code>.</p>63 <p>The·following·illustrates·some·options·for·the·boxplot·in·statsmodels.·These·include·<code·class="docutils·literal·notranslate"><span·class="pre">violin_plot</span></code>·and·<code·class="docutils·literal·notranslate"><span·class="pre">bean_plot</span></code>.</p>
64 <div·class="nbinput·nblast·docutils·container">64 <div·class="nbinput·nblast·docutils·container">
65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
66 </pre></div>66 </pre></div>
67 </div>67 </div>
68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
  
69 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>69 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
70 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>70 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
71 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>71 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
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75 </div>75 </div>
76 </div>76 </div>
77 <section·id="Bean-Plots">77 <section·id="Bean-Plots">
78 <h2>Bean·Plots<a·class="headerlink"·href="#Bean-Plots"·title="Link·to·this·heading">¶</a></h2>78 <h2>Bean·Plots<a·class="headerlink"·href="#Bean-Plots"·title="Link·to·this·heading">¶</a></h2>
79 <p>The·following·example·is·taken·from·the·docstring·of·<code·class="docutils·literal·notranslate"><span·class="pre">beanplot</span></code>.</p>79 <p>The·following·example·is·taken·from·the·docstring·of·<code·class="docutils·literal·notranslate"><span·class="pre">beanplot</span></code>.</p>
80 <p>We·use·the·American·National·Election·Survey·1996·dataset,·which·has·Party·Identification·of·respondents·as·independent·variable·and·(among·other·data)·age·as·dependent·variable.</p>80 <p>We·use·the·American·National·Election·Survey·1996·dataset,·which·has·Party·Identification·of·respondents·as·independent·variable·and·(among·other·data)·age·as·dependent·variable.</p>
81 <div·class="nbinput·nblast·docutils·container">81 <div·class="nbinput·nblast·docutils·container">
82 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:82 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
83 </pre></div>83 </pre></div>
84 </div>84 </div>
85 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">anes96</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span>85 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">anes96</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span>
86 <span·class="n">party_ID</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="mi">7</span><span·class="p">)</span>86 <span·class="n">party_ID</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="mi">7</span><span·class="p">)</span>
87 <span·class="n">labels</span>·<span·class="o">=</span>·<span·class="p">[</span>87 <span·class="n">labels</span>·<span·class="o">=</span>·<span·class="p">[</span>
88 ····<span·class="s2">&quot;Strong·Democrat&quot;</span><span·class="p">,</span>88 ····<span·class="s2">&quot;Strong·Democrat&quot;</span><span·class="p">,</span>
89 ····<span·class="s2">&quot;Weak·Democrat&quot;</span><span·class="p">,</span>89 ····<span·class="s2">&quot;Weak·Democrat&quot;</span><span·class="p">,</span>
Offset 93, 16 lines modifiedOffset 93, 16 lines modified
93 ····<span·class="s2">&quot;Weak·Republican&quot;</span><span·class="p">,</span>93 ····<span·class="s2">&quot;Weak·Republican&quot;</span><span·class="p">,</span>
94 ····<span·class="s2">&quot;Strong·Republican&quot;</span><span·class="p">,</span>94 ····<span·class="s2">&quot;Strong·Republican&quot;</span><span·class="p">,</span>
95 <span·class="p">]</span>95 <span·class="p">]</span>
96 </pre></div>96 </pre></div>
97 </div>97 </div>
98 </div>98 </div>
99 <p>Group·age·by·party·ID,·and·create·a·violin·plot·with·it:</p>99 <p>Group·age·by·party·ID,·and·create·a·violin·plot·with·it:</p>
100 <div·class="nbinput·docutils·container">100 <div·class="nbinput·nblast·docutils·container">
101 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:101 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
102 </pre></div>102 </pre></div>
103 </div>103 </div>
104 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">plt</span><span·class="o">.</span><span·class="n">rcParams</span><span·class="p">[</span><span·class="s2">&quot;figure.subplot.bottom&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="mf">0.23</span>··<span·class="c1">#·keep·labels·visible</span>104 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">plt</span><span·class="o">.</span><span·class="n">rcParams</span><span·class="p">[</span><span·class="s2">&quot;figure.subplot.bottom&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="mf">0.23</span>··<span·class="c1">#·keep·labels·visible</span>
105 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rcParams</span><span·class="p">[</span><span·class="s2">&quot;figure.figsize&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="p">(</span><span·class="mf">10.0</span><span·class="p">,</span>·<span·class="mf">8.0</span><span·class="p">)</span>··<span·class="c1">#·make·plot·larger·in·notebook</span>105 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rcParams</span><span·class="p">[</span><span·class="s2">&quot;figure.figsize&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="p">(</span><span·class="mf">10.0</span><span·class="p">,</span>·<span·class="mf">8.0</span><span·class="p">)</span>··<span·class="c1">#·make·plot·larger·in·notebook</span>
106 <span·class="n">age</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">[</span><span·class="s2">&quot;age&quot;</span><span·class="p">][</span><span·class="n">data</span><span·class="o">.</span><span·class="n">endog</span>·<span·class="o">==</span>·<span·class="nb">id</span><span·class="p">]</span>·<span·class="k">for</span>·<span·class="nb">id</span>·<span·class="ow">in</span>·<span·class="n">party_ID</span><span·class="p">]</span>106 <span·class="n">age</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">[</span><span·class="s2">&quot;age&quot;</span><span·class="p">][</span><span·class="n">data</span><span·class="o">.</span><span·class="n">endog</span>·<span·class="o">==</span>·<span·class="nb">id</span><span·class="p">]</span>·<span·class="k">for</span>·<span·class="nb">id</span>·<span·class="ow">in</span>·<span·class="n">party_ID</span><span·class="p">]</span>
107 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">()</span>107 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">()</span>
108 <span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">111</span><span·class="p">)</span>108 <span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">111</span><span·class="p">)</span>
Offset 115, 32 lines modifiedOffset 115, 16 lines modified
115 <span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">beanplot</span><span·class="p">(</span><span·class="n">age</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax</span><span·class="p">,</span>·<span·class="n">labels</span><span·class="o">=</span><span·class="n">labels</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="n">plot_opts</span><span·class="p">)</span>115 <span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">beanplot</span><span·class="p">(</span><span·class="n">age</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax</span><span·class="p">,</span>·<span·class="n">labels</span><span·class="o">=</span><span·class="n">labels</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="n">plot_opts</span><span·class="p">)</span>
116 <span·class="n">ax</span><span·class="o">.</span><span·class="n">set_xlabel</span><span·class="p">(</span><span·class="s2">&quot;Party·identification·of·respondent.&quot;</span><span·class="p">)</span>116 <span·class="n">ax</span><span·class="o">.</span><span·class="n">set_xlabel</span><span·class="p">(</span><span·class="s2">&quot;Party·identification·of·respondent.&quot;</span><span·class="p">)</span>
117 <span·class="n">ax</span><span·class="o">.</span><span·class="n">set_ylabel</span><span·class="p">(</span><span·class="s2">&quot;Age&quot;</span><span·class="p">)</span>117 <span·class="n">ax</span><span·class="o">.</span><span·class="n">set_ylabel</span><span·class="p">(</span><span·class="s2">&quot;Age&quot;</span><span·class="p">)</span>
118 <span·class="c1">#·plt.show()</span>118 <span·class="c1">#·plt.show()</span>
119 </pre></div>119 </pre></div>
120 </div>120 </div>
121 </div>121 </div>
122 <div·class="nboutput·docutils·container"> 
123 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]: 
124 </pre></div> 
125 </div> 
126 <div·class="output_area·docutils·container"> 
127 <div·class="highlight"><pre> 
128 Text(0,·0.5,·&#39;Age&#39;) 
129 </pre></div></div> 
130 </div> 
131 <div·class="nboutput·nblast·docutils·container"> 
132 <div·class="prompt·empty·docutils·container"> 
133 </div> 
134 <div·class="output_area·docutils·container"> 
135 <img·alt="../../../_images/examples_notebooks_generated_plots_boxplots_7_1.png"·src="../../../_images/examples_notebooks_generated_plots_boxplots_7_1.png"·/> 
136 </div> 
137 </div> 
138 <div·class="nbinput·nblast·docutils·container">122 <div·class="nbinput·nblast·docutils·container">
139 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:123 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
140 </pre></div>124 </pre></div>
141 </div>125 </div>
142 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">beanplot</span><span·class="p">(</span><span·class="n">data</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="p">{},</span>·<span·class="n">jitter</span><span·class="o">=</span><span·class="kc">False</span><span·class="p">):</span>126 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">beanplot</span><span·class="p">(</span><span·class="n">data</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="p">{},</span>·<span·class="n">jitter</span><span·class="o">=</span><span·class="kc">False</span><span·class="p">):</span>
143 <span·class="w">····</span><span·class="sd">&quot;&quot;&quot;helper·function·to·try·out·different·plot·options&quot;&quot;&quot;</span>127 <span·class="w">····</span><span·class="sd">&quot;&quot;&quot;helper·function·to·try·out·different·plot·options&quot;&quot;&quot;</span>
144 ····<span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">()</span>128 ····<span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">()</span>
145 ····<span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">111</span><span·class="p">)</span>129 ····<span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">111</span><span·class="p">)</span>
146 ····<span·class="n">plot_opts_</span>·<span·class="o">=</span>·<span·class="p">{</span>130 ····<span·class="n">plot_opts_</span>·<span·class="o">=</span>·<span·class="p">{</span>
Offset 154, 122 lines modifiedOffset 138, 80 lines modified
154 ········<span·class="n">data</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax</span><span·class="p">,</span>·<span·class="n">labels</span><span·class="o">=</span><span·class="n">labels</span><span·class="p">,</span>·<span·class="n">jitter</span><span·class="o">=</span><span·class="n">jitter</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="n">plot_opts_</span>138 ········<span·class="n">data</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax</span><span·class="p">,</span>·<span·class="n">labels</span><span·class="o">=</span><span·class="n">labels</span><span·class="p">,</span>·<span·class="n">jitter</span><span·class="o">=</span><span·class="n">jitter</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="n">plot_opts_</span>
155 ····<span·class="p">)</span>139 ····<span·class="p">)</span>
156 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">set_xlabel</span><span·class="p">(</span><span·class="s2">&quot;Party·identification·of·respondent.&quot;</span><span·class="p">)</span>140 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">set_xlabel</span><span·class="p">(</span><span·class="s2">&quot;Party·identification·of·respondent.&quot;</span><span·class="p">)</span>
157 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">set_ylabel</span><span·class="p">(</span><span·class="s2">&quot;Age&quot;</span><span·class="p">)</span>141 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">set_ylabel</span><span·class="p">(</span><span·class="s2">&quot;Age&quot;</span><span·class="p">)</span>
158 </pre></div>142 </pre></div>
159 </div>143 </div>
160 </div>144 </div>
161 <div·class="nbinput·docutils·container">145 <div·class="nbinput·nblast·docutils·container">
162 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:146 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
163 </pre></div>147 </pre></div>
164 </div>148 </div>
165 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">beanplot</span><span·class="p">(</span><span·class="n">age</span><span·class="p">,</span>·<span·class="n">jitter</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>149 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">beanplot</span><span·class="p">(</span><span·class="n">age</span><span·class="p">,</span>·<span·class="n">jitter</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>
166 </pre></div>150 </pre></div>
167 </div>151 </div>
168 </div>152 </div>
169 <div·class="nboutput·nblast·docutils·container">153 <div·class="nbinput·nblast·docutils·container">
170 <div·class="prompt·empty·docutils·container"> 
171 </div> 
172 <div·class="output_area·docutils·container"> 
173 <img·alt="../../../_images/examples_notebooks_generated_plots_boxplots_9_0.png"·src="../../../_images/examples_notebooks_generated_plots_boxplots_9_0.png"·/> 
174 </div> 
175 </div> 
176 <div·class="nbinput·docutils·container"> 
177 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:154 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
178 </pre></div>155 </pre></div>
179 </div>156 </div>
180 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">beanplot</span><span·class="p">(</span><span·class="n">age</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;violin_width&quot;</span><span·class="p">:</span>·<span·class="mf">0.5</span><span·class="p">,</span>·<span·class="s2">&quot;violin_fc&quot;</span><span·class="p">:</span>·<span·class="s2">&quot;#66c2a5&quot;</span><span·class="p">})</span>157 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">beanplot</span><span·class="p">(</span><span·class="n">age</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;violin_width&quot;</span><span·class="p">:</span>·<span·class="mf">0.5</span><span·class="p">,</span>·<span·class="s2">&quot;violin_fc&quot;</span><span·class="p">:</span>·<span·class="s2">&quot;#66c2a5&quot;</span><span·class="p">})</span>
181 </pre></div>158 </pre></div>
182 </div>159 </div>
183 </div>160 </div>
184 <div·class="nboutput·nblast·docutils·container">161 <div·class="nbinput·nblast·docutils·container">
185 <div·class="prompt·empty·docutils·container"> 
186 </div> 
187 <div·class="output_area·docutils·container"> 
188 <img·alt="../../../_images/examples_notebooks_generated_plots_boxplots_10_0.png"·src="../../../_images/examples_notebooks_generated_plots_boxplots_10_0.png"·/> 
189 </div> 
190 </div> 
191 <div·class="nbinput·docutils·container"> 
192 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:162 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
193 </pre></div>163 </pre></div>
194 </div>164 </div>
195 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">beanplot</span><span·class="p">(</span><span·class="n">age</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;violin_fc&quot;</span><span·class="p">:</span>·<span·class="s2">&quot;#66c2a5&quot;</span><span·class="p">})</span>165 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">beanplot</span><span·class="p">(</span><span·class="n">age</span><span·class="p">,</span>·<span·class="n">plot_opts</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;violin_fc&quot;</span><span·class="p">:</span>·<span·class="s2">&quot;#66c2a5&quot;</span><span·class="p">})</span>
196 </pre></div>166 </pre></div>
197 </div>167 </div>
198 </div>168 </div>
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5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Box·Plots8 ····*·Box·Plots
9 *\x8**\x8**\x8**\x8**\x8**\x8*·B\x8Bo\x8ox\x8x·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·B\x8Bo\x8ox\x8x·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 The·following·illustrates·some·options·for·the·boxplot·in·statsmodels.·These10 The·following·illustrates·some·options·for·the·boxplot·in·statsmodels.·These
11 include·violin_plot·and·bean_plot.11 include·violin_plot·and·bean_plot.
12 [1]:12 [·]:
13 %matplotlib·inline13 %matplotlib·inline
  
14 import·numpy·as·np14 import·numpy·as·np
15 import·matplotlib.pyplot·as·plt15 import·matplotlib.pyplot·as·plt
16 import·statsmodels.api·as·sm16 import·statsmodels.api·as·sm
17 np.random.seed(1234)·#·for·reproducibility17 np.random.seed(1234)·#·for·reproducibility
18 *\x8**\x8**\x8**\x8**\x8*·B\x8Be\x8ea\x8an\x8n·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*18 *\x8**\x8**\x8**\x8**\x8*·B\x8Be\x8ea\x8an\x8n·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
19 The·following·example·is·taken·from·the·docstring·of·beanplot.19 The·following·example·is·taken·from·the·docstring·of·beanplot.
20 We·use·the·American·National·Election·Survey·1996·dataset,·which·has·Party20 We·use·the·American·National·Election·Survey·1996·dataset,·which·has·Party
21 Identification·of·respondents·as·independent·variable·and·(among·other·data)21 Identification·of·respondents·as·independent·variable·and·(among·other·data)
22 age·as·dependent·variable.22 age·as·dependent·variable.
23 [2]:23 [·]:
24 data·=·sm.datasets.anes96.load_pandas()24 data·=·sm.datasets.anes96.load_pandas()
25 party_ID·=·np.arange(7)25 party_ID·=·np.arange(7)
26 labels·=·[26 labels·=·[
27 ····"Strong·Democrat",27 ····"Strong·Democrat",
28 ····"Weak·Democrat",28 ····"Weak·Democrat",
29 ····"Independent-Democrat",29 ····"Independent-Democrat",
30 ····"Independent-Independent",30 ····"Independent-Independent",
31 ····"Independent-Republican",31 ····"Independent-Republican",
32 ····"Weak·Republican",32 ····"Weak·Republican",
33 ····"Strong·Republican",33 ····"Strong·Republican",
34 ]34 ]
35 Group·age·by·party·ID,·and·create·a·violin·plot·with·it:35 Group·age·by·party·ID,·and·create·a·violin·plot·with·it:
36 [3]:36 [·]:
37 plt.rcParams["figure.subplot.bottom"]·=·0.23··#·keep·labels·visible37 plt.rcParams["figure.subplot.bottom"]·=·0.23··#·keep·labels·visible
38 plt.rcParams["figure.figsize"]·=·(10.0,·8.0)··#·make·plot·larger·in·notebook38 plt.rcParams["figure.figsize"]·=·(10.0,·8.0)··#·make·plot·larger·in·notebook
39 age·=·[data.exog["age"][data.endog·==·id]·for·id·in·party_ID]39 age·=·[data.exog["age"][data.endog·==·id]·for·id·in·party_ID]
40 fig·=·plt.figure()40 fig·=·plt.figure()
41 ax·=·fig.add_subplot(111)41 ax·=·fig.add_subplot(111)
42 plot_opts·=·{42 plot_opts·=·{
43 ····"cutoff_val":·5,43 ····"cutoff_val":·5,
Offset 46, 18 lines modifiedOffset 46, 15 lines modified
46 ····"label_fontsize":·"small",46 ····"label_fontsize":·"small",
47 ····"label_rotation":·30,47 ····"label_rotation":·30,
48 }48 }
49 sm.graphics.beanplot(age,·ax=ax,·labels=labels,·plot_opts=plot_opts)49 sm.graphics.beanplot(age,·ax=ax,·labels=labels,·plot_opts=plot_opts)
50 ax.set_xlabel("Party·identification·of·respondent.")50 ax.set_xlabel("Party·identification·of·respondent.")
51 ax.set_ylabel("Age")51 ax.set_ylabel("Age")
52 #·plt.show()52 #·plt.show()
53 [3]:53 [·]:
54 Text(0,·0.5,·'Age') 
55 [../../../_images/examples_notebooks_generated_plots_boxplots_7_1.png] 
56 [4]: 
57 def·beanplot(data,·plot_opts={},·jitter=False):54 def·beanplot(data,·plot_opts={},·jitter=False):
58 ····"""helper·function·to·try·out·different·plot·options"""55 ····"""helper·function·to·try·out·different·plot·options"""
59 ····fig·=·plt.figure()56 ····fig·=·plt.figure()
60 ····ax·=·fig.add_subplot(111)57 ····ax·=·fig.add_subplot(111)
61 ····plot_opts_·=·{58 ····plot_opts_·=·{
62 ········"cutoff_val":·5,59 ········"cutoff_val":·5,
63 ········"cutoff_type":·"abs",60 ········"cutoff_type":·"abs",
Offset 66, 41 lines modifiedOffset 63, 35 lines modified
66 ····}63 ····}
67 ····plot_opts_.update(plot_opts)64 ····plot_opts_.update(plot_opts)
68 ····sm.graphics.beanplot(65 ····sm.graphics.beanplot(
69 ········data,·ax=ax,·labels=labels,·jitter=jitter,·plot_opts=plot_opts_66 ········data,·ax=ax,·labels=labels,·jitter=jitter,·plot_opts=plot_opts_
70 ····)67 ····)
71 ····ax.set_xlabel("Party·identification·of·respondent.")68 ····ax.set_xlabel("Party·identification·of·respondent.")
72 ····ax.set_ylabel("Age")69 ····ax.set_ylabel("Age")
73 [5]:70 [·]:
74 fig·=·beanplot(age,·jitter=True)71 fig·=·beanplot(age,·jitter=True)
75 [../../../_images/examples_notebooks_generated_plots_boxplots_9_0.png] 
76 [6]:72 [·]:
77 fig·=·beanplot(age,·plot_opts={"violin_width":·0.5,·"violin_fc":·"#66c2a5"})73 fig·=·beanplot(age,·plot_opts={"violin_width":·0.5,·"violin_fc":·"#66c2a5"})
78 [../../../_images/examples_notebooks_generated_plots_boxplots_10_0.png] 
79 [7]:74 [·]:
80 fig·=·beanplot(age,·plot_opts={"violin_fc":·"#66c2a5"})75 fig·=·beanplot(age,·plot_opts={"violin_fc":·"#66c2a5"})
81 [../../../_images/examples_notebooks_generated_plots_boxplots_11_0.png] 
82 [8]:76 [·]:
83 fig·=·beanplot(77 fig·=·beanplot(
84 ····age,·plot_opts={"bean_size":·0.2,·"violin_width":·0.75,·"violin_fc":78 ····age,·plot_opts={"bean_size":·0.2,·"violin_width":·0.75,·"violin_fc":
85 "#66c2a5"}79 "#66c2a5"}
86 )80 )
87 [../../../_images/examples_notebooks_generated_plots_boxplots_12_0.png] 
88 [9]:81 [·]:
89 fig·=·beanplot(age,·jitter=True,·plot_opts={"violin_fc":·"#66c2a5"})82 fig·=·beanplot(age,·jitter=True,·plot_opts={"violin_fc":·"#66c2a5"})
 83 [·]:
90 [../../../_images/examples_notebooks_generated_plots_boxplots_13_0.png] 
91 [10]: 
92 fig·=·beanplot(84 fig·=·beanplot(
93 ····age,·jitter=True,·plot_opts={"violin_width":·0.5,·"violin_fc":·"#66c2a5"}85 ····age,·jitter=True,·plot_opts={"violin_width":·0.5,·"violin_fc":·"#66c2a5"}
94 )86 )
95 [../../../_images/examples_notebooks_generated_plots_boxplots_14_0.png] 
96 [·]:87 [·]:
97 *\x8**\x8**\x8**\x8**\x8*·A\x8Ad\x8dv\x8va\x8an\x8nc\x8ce\x8ed\x8d·B\x8Bo\x8ox\x8x·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*88 *\x8**\x8**\x8**\x8**\x8*·A\x8Ad\x8dv\x8va\x8an\x8nc\x8ce\x8ed\x8d·B\x8Bo\x8ox\x8x·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
98 Based·of·example·script·example_enhanced_boxplots.py·(by·Ralf·Gommers)89 Based·of·example·script·example_enhanced_boxplots.py·(by·Ralf·Gommers)
99 [11]:90 [·]:
100 import·numpy·as·np91 import·numpy·as·np
101 import·matplotlib.pyplot·as·plt92 import·matplotlib.pyplot·as·plt
  
102 import·statsmodels.api·as·sm93 import·statsmodels.api·as·sm
  
  
103 #·Necessary·to·make·horizontal·axis·labels·fit94 #·Necessary·to·make·horizontal·axis·labels·fit
Offset 116, 15 lines modifiedOffset 107, 15 lines modified
116 ····"Independent-Republican",107 ····"Independent-Republican",
117 ····"Weak·Republican",108 ····"Weak·Republican",
118 ····"Strong·Republican",109 ····"Strong·Republican",
119 ]110 ]
  
120 #·Group·age·by·party·ID.111 #·Group·age·by·party·ID.
121 age·=·[data.exog["age"][data.endog·==·id]·for·id·in·party_ID]112 age·=·[data.exog["age"][data.endog·==·id]·for·id·in·party_ID]
122 [12]:113 [·]:
123 #·Create·a·violin·plot.114 #·Create·a·violin·plot.
124 fig·=·plt.figure()115 fig·=·plt.figure()
125 ax·=·fig.add_subplot(111)116 ax·=·fig.add_subplot(111)
  
126 sm.graphics.violinplot(117 sm.graphics.violinplot(
127 ····age,118 ····age,
128 ····ax=ax,119 ····ax=ax,
Offset 136, 18 lines modifiedOffset 127, 15 lines modified
136 ········"label_rotation":·30,127 ········"label_rotation":·30,
137 ····},128 ····},
138 )129 )
  
139 ax.set_xlabel("Party·identification·of·respondent.")130 ax.set_xlabel("Party·identification·of·respondent.")
140 ax.set_ylabel("Age")131 ax.set_ylabel("Age")
141 ax.set_title("US·national·election·'96·-·Age·&·Party·Identification")132 ax.set_title("US·national·election·'96·-·Age·&·Party·Identification")
 133 [·]:
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77 <div·class="line"><strong>Warning</strong>·Recently·added·features·are·not·stable.</div>77 <div·class="line"><strong>Warning</strong>·Recently·added·features·are·not·stable.</div>
78 <div·class="line">The·main·features·have·been·unit·tested·and·verified·against·other·statistical·packages.·However,·not·every·option·is·fully·tested.·The·API,·options,·defaults·and·return·types·may·still·change·as·more·features·are·added.·(The·current·emphasis·is·on·adding·features·and·not·on·finding·a·convenient·and·futureproof·interface.)</div>78 <div·class="line">The·main·features·have·been·unit·tested·and·verified·against·other·statistical·packages.·However,·not·every·option·is·fully·tested.·The·API,·options,·defaults·and·return·types·may·still·change·as·more·features·are·added.·(The·current·emphasis·is·on·adding·features·and·not·on·finding·a·convenient·and·futureproof·interface.)</div>
79 </div>79 </div>
80 <section·id="A-simulated-example">80 <section·id="A-simulated-example">
81 <h2>A·simulated·example<a·class="headerlink"·href="#A-simulated-example"·title="Link·to·this·heading">¶</a></h2>81 <h2>A·simulated·example<a·class="headerlink"·href="#A-simulated-example"·title="Link·to·this·heading">¶</a></h2>
82 <p>For·the·illustration·we·simulate·data·for·the·Poisson·regression,·that·is·correctly·specified·and·has·a·relatively·large·sample.·One·regressor·is·categorical·with·two·levels,·The·second·regressor·is·uniformly·distributed·on·the·unit·interval.</p>82 <p>For·the·illustration·we·simulate·data·for·the·Poisson·regression,·that·is·correctly·specified·and·has·a·relatively·large·sample.·One·regressor·is·categorical·with·two·levels,·The·second·regressor·is·uniformly·distributed·on·the·unit·interval.</p>
83 <div·class="nbinput·nblast·docutils·container">83 <div·class="nbinput·nblast·docutils·container">
84 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:84 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
85 </pre></div>85 </pre></div>
86 </div>86 </div>
87 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>87 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
88 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>88 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
89 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>89 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>
90 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>90 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
  
91 <span·class="kn">from</span>·<span·class="nn">statsmodels.discrete.discrete_model</span>·<span·class="kn">import</span>·<span·class="n">Poisson</span>91 <span·class="kn">from</span>·<span·class="nn">statsmodels.discrete.discrete_model</span>·<span·class="kn">import</span>·<span·class="n">Poisson</span>
92 <span·class="kn">from</span>·<span·class="nn">statsmodels.discrete.diagnostic</span>·<span·class="kn">import</span>·<span·class="n">PoissonDiagnostic</span>92 <span·class="kn">from</span>·<span·class="nn">statsmodels.discrete.diagnostic</span>·<span·class="kn">import</span>·<span·class="n">PoissonDiagnostic</span>
93 </pre></div>93 </pre></div>
94 </div>94 </div>
95 </div>95 </div>
96 <div·class="nbinput·docutils·container">96 <div·class="nbinput·nblast·docutils·container">
97 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:97 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
98 </pre></div>98 </pre></div>
99 </div>99 </div>
100 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">983154356</span><span·class="p">)</span>100 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">983154356</span><span·class="p">)</span>
  
101 <span·class="n">nr</span>·<span·class="o">=</span>·<span·class="mi">10</span>101 <span·class="n">nr</span>·<span·class="o">=</span>·<span·class="mi">10</span>
102 <span·class="n">n_groups</span>·<span·class="o">=</span>·<span·class="mi">2</span>102 <span·class="n">n_groups</span>·<span·class="o">=</span>·<span·class="mi">2</span>
103 <span·class="n">labels</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n_groups</span><span·class="p">)</span>103 <span·class="n">labels</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">arange</span><span·class="p">(</span><span·class="n">n_groups</span><span·class="p">)</span>
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118 <span·class="nb">len</span><span·class="p">(</span><span·class="n">y</span><span·class="p">),</span>·<span·class="n">y</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(),</span>·<span·class="p">(</span><span·class="n">y</span>·<span·class="o">==</span>·<span·class="mi">0</span><span·class="p">)</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">()</span>118 <span·class="nb">len</span><span·class="p">(</span><span·class="n">y</span><span·class="p">),</span>·<span·class="n">y</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">(),</span>·<span·class="p">(</span><span·class="n">y</span>·<span·class="o">==</span>·<span·class="mi">0</span><span·class="p">)</span><span·class="o">.</span><span·class="n">mean</span><span·class="p">()</span>
  
119 <span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">Poisson</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">exog</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">disp</span><span·class="o">=</span><span·class="mi">0</span><span·class="p">)</span>119 <span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">Poisson</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">exog</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">disp</span><span·class="o">=</span><span·class="mi">0</span><span·class="p">)</span>
120 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>120 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
121 </pre></div>121 </pre></div>
122 </div>122 </div>
123 </div>123 </div>
124 <div·class="nboutput·nblast·docutils·container"> 
125 <div·class="prompt·empty·docutils·container"> 
126 </div> 
127 <div·class="output_area·docutils·container"> 
128 <div·class="highlight"><pre> 
129 ··························Poisson·Regression·Results 
130 ============================================================================== 
131 Dep.·Variable:······················y···No.·Observations:·················1000 
132 Model:························Poisson···Df·Residuals:······················997 
133 Method:···························MLE···Df·Model:····························2 
134 Date:················Sun,·10·Aug·2025···Pseudo·R-squ.:·················0.01258 
135 Time:························13:13:47···Log-Likelihood:················-1618.3 
136 converged:·······················True···LL-Null:·······················-1638.9 
137 Covariance·Type:············nonrobust···LLR·p-value:·················1.120e-09 
138 ============================================================================== 
139 ·················coef····std·err··········z······P&gt;|z|······[0.025······0.975] 
140 ------------------------------------------------------------------------------ 
141 x1·············0.2386······0.061······3.926······0.000·······0.120·······0.358 
142 x2·············0.3229······0.055······5.873······0.000·······0.215·······0.431 
143 x3·············0.5109······0.083······6.186······0.000·······0.349·······0.673 
144 ============================================================================== 
145 </pre></div></div> 
146 </div> 
147 <div·class="nbinput·nblast·docutils·container">124 <div·class="nbinput·nblast·docutils·container">
148 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:125 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
149 </pre></div>126 </pre></div>
150 </div>127 </div>
151 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span>128 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span>
152 </pre></div>129 </pre></div>
153 </div>130 </div>
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164 <ul·class="simple">141 <ul·class="simple">
165 <li><p>t_test</p></li>142 <li><p>t_test</p></li>
166 <li><p>wald_test</p></li>143 <li><p>wald_test</p></li>
167 <li><p>t_test_pairwise</p></li>144 <li><p>t_test_pairwise</p></li>
168 <li><p>wald_test_terms</p></li>145 <li><p>wald_test_terms</p></li>
169 </ul>146 </ul>
170 <p><code·class="docutils·literal·notranslate"><span·class="pre">f_test</span></code>·is·available·as·legacy·method.·It·is·the·same·as·<code·class="docutils·literal·notranslate"><span·class="pre">wald_test</span></code>·with·keyword·option·<code·class="docutils·literal·notranslate"><span·class="pre">use_f=True</span></code>.</p>147 <p><code·class="docutils·literal·notranslate"><span·class="pre">f_test</span></code>·is·available·as·legacy·method.·It·is·the·same·as·<code·class="docutils·literal·notranslate"><span·class="pre">wald_test</span></code>·with·keyword·option·<code·class="docutils·literal·notranslate"><span·class="pre">use_f=True</span></code>.</p>
171 <div·class="nbinput·docutils·container">148 <div·class="nbinput·nblast·docutils·container">
172 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:149 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
173 </pre></div>150 </pre></div>
174 </div>151 </div>
175 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res</span><span·class="o">.</span><span·class="n">t_test</span><span·class="p">(</span><span·class="s2">&quot;x1=x2&quot;</span><span·class="p">)</span>152 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res</span><span·class="o">.</span><span·class="n">t_test</span><span·class="p">(</span><span·class="s2">&quot;x1=x2&quot;</span><span·class="p">)</span>
176 </pre></div>153 </pre></div>
177 </div>154 </div>
178 </div>155 </div>
179 <div·class="nboutput·nblast·docutils·container">156 <div·class="nbinput·nblast·docutils·container">
180 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:157 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
181 </pre></div> 
182 </div> 
183 <div·class="output_area·docutils·container"> 
184 <div·class="highlight"><pre> 
185 &lt;class·&#39;statsmodels.stats.contrast.ContrastResults&#39;&gt; 
186 ·····························Test·for·Constraints 
187 ============================================================================== 
188 ·················coef····std·err··········z······P&gt;|z|······[0.025······0.975] 
189 ------------------------------------------------------------------------------ 
190 c0············-0.0843······0.049·····-1.717······0.086······-0.181·······0.012 
191 ============================================================================== 
192 </pre></div></div> 
193 </div> 
194 <div·class="nbinput·docutils·container"> 
195 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]: 
196 </pre></div>158 </pre></div>
197 </div>159 </div>
198 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res</span><span·class="o">.</span><span·class="n">wald_test</span><span·class="p">(</span><span·class="s2">&quot;x1=x2,·x3&quot;</span><span·class="p">,</span>·<span·class="n">scalar</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>160 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res</span><span·class="o">.</span><span·class="n">wald_test</span><span·class="p">(</span><span·class="s2">&quot;x1=x2,·x3&quot;</span><span·class="p">,</span>·<span·class="n">scalar</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span>
199 </pre></div>161 </pre></div>
200 </div>162 </div>
201 </div>163 </div>
202 <div·class="nboutput·nblast·docutils·container"> 
203 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]: 
204 </pre></div> 
205 </div> 
206 <div·class="output_area·docutils·container"> 
207 <div·class="highlight"><pre> 
208 &lt;class·&#39;statsmodels.stats.contrast.ContrastResults&#39;&gt; 
209 &lt;Wald·test·(chi2):·statistic=40.772322944293165,·p-value=1.400885259219231e-09,·df_denom=2&gt; 
210 </pre></div></div> 
211 </div> 
212 </section>164 </section>
213 <section·id="Inference---score_test">165 <section·id="Inference---score_test">
214 <h2>Inference·-·score_test<a·class="headerlink"·href="#Inference---score_test"·title="Link·to·this·heading">¶</a></h2>166 <h2>Inference·-·score_test<a·class="headerlink"·href="#Inference---score_test"·title="Link·to·this·heading">¶</a></h2>
215 <p>new·in·statsmodels·0.14·for·most·discrete·models·and·for·GLM.</p>167 <p>new·in·statsmodels·0.14·for·most·discrete·models·and·for·GLM.</p>
216 <p>Score·or·lagrange·multiplier·(LM)·tests·are·based·on·the·model·estimated·under·the·null·hypothesis.·A·common·example·are·variable·addition·tests·for·which·we·estimate·the·model·parameters·under·null·restrictions·but·evaluate·the·score·and·hessian·under·for·the·full·model·to·test·whether·an·additional·variable·is·statistically·significant.</p>168 <p>Score·or·lagrange·multiplier·(LM)·tests·are·based·on·the·model·estimated·under·the·null·hypothesis.·A·common·example·are·variable·addition·tests·for·which·we·estimate·the·model·parameters·under·null·restrictions·but·evaluate·the·score·and·hessian·under·for·the·full·model·to·test·whether·an·additional·variable·is·statistically·significant.</p>
217 <div·class="line-block">169 <div·class="line-block">
218 <div·class="line"><strong>Note:</strong>·Similar·to·the·Wald·tests,·the·score·test·implemented·in·the·discrete·models·and·GLM·also·has·the·option·to·use·a·heteroscedasticity·or·correlation·robust·covariance·type.</div>170 <div·class="line"><strong>Note:</strong>·Similar·to·the·Wald·tests,·the·score·test·implemented·in·the·discrete·models·and·GLM·also·has·the·option·to·use·a·heteroscedasticity·or·correlation·robust·covariance·type.</div>
219 <div·class="line">It·currently·uses·the·same·implementation·and·defaults·for·the·robust·covariance·matrix·as·in·the·Wald·tests.·In·some·cases·the·small·sample·corrections·included·in·the·<code·class="docutils·literal·notranslate"><span·class="pre">cov_type</span></code>·for·Wald·tests·will·not·be·appropriate·for·score·tests.·In·many·cases·Wald·tests·overjects·but·score·tests·can·underreject.·Using·the·Wald·small·sample·corrections·for·score·tests·might·leads·then·to·more·conservative·p-values.</div>171 <div·class="line">It·currently·uses·the·same·implementation·and·defaults·for·the·robust·covariance·matrix·as·in·the·Wald·tests.·In·some·cases·the·small·sample·corrections·included·in·the·<code·class="docutils·literal·notranslate"><span·class="pre">cov_type</span></code>·for·Wald·tests·will·not·be·appropriate·for·score·tests.·In·many·cases·Wald·tests·overjects·but·score·tests·can·underreject.·Using·the·Wald·small·sample·corrections·for·score·tests·might·leads·then·to·more·conservative·p-values.</div>
220 <div·class="line">(The·defaults·for·small·sample·corrections·might·change·in·future.·There·is·currently·only·little·general·information·available·about·small·sample·corrections·for·heteroscedasticity·and·correlation·robust·score·tests.·Other·statistical·packages·only·implement·it·for·a·few·special·cases.)</div>172 <div·class="line">(The·defaults·for·small·sample·corrections·might·change·in·future.·There·is·currently·only·little·general·information·available·about·small·sample·corrections·for·heteroscedasticity·and·correlation·robust·score·tests.·Other·statistical·packages·only·implement·it·for·a·few·special·cases.)</div>
221 </div>173 </div>
222 <p>We·can·use·the·variable·addition·score_test·for·specification·testing.·In·the·following·example·we·test·whether·there·is·some·misspecified·nonlinearity·in·the·model·by·adding·quadratic·or·polynomial·tersm.</p>174 <p>We·can·use·the·variable·addition·score_test·for·specification·testing.·In·the·following·example·we·test·whether·there·is·some·misspecified·nonlinearity·in·the·model·by·adding·quadratic·or·polynomial·tersm.</p>
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33 emphasis·is·on·adding·features·and·not·on·finding·a·convenient·and·futureproof33 emphasis·is·on·adding·features·and·not·on·finding·a·convenient·and·futureproof
34 interface.)34 interface.)
35 *\x8**\x8**\x8**\x8**\x8*·A\x8A·s\x8si\x8im\x8mu\x8ul\x8la\x8at\x8te\x8ed\x8d·e\x8ex\x8xa\x8am\x8mp\x8pl\x8le\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*35 *\x8**\x8**\x8**\x8**\x8*·A\x8A·s\x8si\x8im\x8mu\x8ul\x8la\x8at\x8te\x8ed\x8d·e\x8ex\x8xa\x8am\x8mp\x8pl\x8le\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
36 For·the·illustration·we·simulate·data·for·the·Poisson·regression,·that·is36 For·the·illustration·we·simulate·data·for·the·Poisson·regression,·that·is
37 correctly·specified·and·has·a·relatively·large·sample.·One·regressor·is37 correctly·specified·and·has·a·relatively·large·sample.·One·regressor·is
38 categorical·with·two·levels,·The·second·regressor·is·uniformly·distributed·on38 categorical·with·two·levels,·The·second·regressor·is·uniformly·distributed·on
39 the·unit·interval.39 the·unit·interval.
40 [1]:40 [·]:
41 import·numpy·as·np41 import·numpy·as·np
42 import·pandas·as·pd42 import·pandas·as·pd
43 from·scipy·import·stats43 from·scipy·import·stats
44 import·matplotlib.pyplot·as·plt44 import·matplotlib.pyplot·as·plt
  
45 from·statsmodels.discrete.discrete_model·import·Poisson45 from·statsmodels.discrete.discrete_model·import·Poisson
46 from·statsmodels.discrete.diagnostic·import·PoissonDiagnostic46 from·statsmodels.discrete.diagnostic·import·PoissonDiagnostic
47 [2]:47 [·]:
48 np.random.seed(983154356)48 np.random.seed(983154356)
  
49 nr·=·1049 nr·=·10
50 n_groups·=·250 n_groups·=·2
51 labels·=·np.arange(n_groups)51 labels·=·np.arange(n_groups)
52 x·=·np.repeat(labels,·np.array([40,·60])·*·nr)52 x·=·np.repeat(labels,·np.array([40,·60])·*·nr)
53 nobs·=·x.shape[0]53 nobs·=·x.shape[0]
Offset 63, 30 lines modifiedOffset 63, 14 lines modified
63 linpred·=·exog·@·beta63 linpred·=·exog·@·beta
64 mean·=·np.exp(linpred)64 mean·=·np.exp(linpred)
65 y·=·np.random.poisson(mean)65 y·=·np.random.poisson(mean)
66 len(y),·y.mean(),·(y·==·0).mean()66 len(y),·y.mean(),·(y·==·0).mean()
  
67 res·=·Poisson(y,·exog).fit(disp=0)67 res·=·Poisson(y,·exog).fit(disp=0)
68 print(res.summary())68 print(res.summary())
69 ··························Poisson·Regression·Results 
70 ============================================================================== 
71 Dep.·Variable:······················y···No.·Observations:·················1000 
72 Model:························Poisson···Df·Residuals:······················997 
73 Method:···························MLE···Df·Model:····························2 
74 Date:················Sun,·10·Aug·2025···Pseudo·R-squ.:·················0.01258 
75 Time:························13:13:47···Log-Likelihood:················-1618.3 
76 converged:·······················True···LL-Null:·······················-1638.9 
77 Covariance·Type:············nonrobust···LLR·p-value:·················1.120e-09 
78 ============================================================================== 
79 ·················coef····std·err··········z······P>|z|······[0.025······0.975] 
80 ------------------------------------------------------------------------------ 
81 x1·············0.2386······0.061······3.926······0.000·······0.120·······0.358 
82 x2·············0.3229······0.055······5.873······0.000·······0.215·······0.431 
83 x3·············0.5109······0.083······6.186······0.000·······0.349·······0.673 
84 ============================================================================== 
85 [·]:69 [·]:
86 *\x8**\x8**\x8**\x8**\x8*·I\x8In\x8nf\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8e·-\x8-·W\x8Wa\x8al\x8ld\x8d_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*70 *\x8**\x8**\x8**\x8**\x8*·I\x8In\x8nf\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8e·-\x8-·W\x8Wa\x8al\x8ld\x8d_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
87 Wald·tests·and·other·inferential·statistics·like·confidence·intervals·based·on71 Wald·tests·and·other·inferential·statistics·like·confidence·intervals·based·on
88 Wald·test·have·been·a·feature·of·the·models·since·the·beginning.·Wald·inference72 Wald·test·have·been·a·feature·of·the·models·since·the·beginning.·Wald·inference
89 is·based·on·the·Hessian·or·expected·information·matrix·evaluted·at·the73 is·based·on·the·Hessian·or·expected·information·matrix·evaluted·at·the
90 estimated·parameters.74 estimated·parameters.
91 The·covariance·matrix·of·the·parameter·is·optionally·of·the·sandwich·form·which75 The·covariance·matrix·of·the·parameter·is·optionally·of·the·sandwich·form·which
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96 table,·are80 table,·are
97 ····*·t_test81 ····*·t_test
98 ····*·wald_test82 ····*·wald_test
99 ····*·t_test_pairwise83 ····*·t_test_pairwise
100 ····*·wald_test_terms84 ····*·wald_test_terms
101 f_test·is·available·as·legacy·method.·It·is·the·same·as·wald_test·with·keyword85 f_test·is·available·as·legacy·method.·It·is·the·same·as·wald_test·with·keyword
102 option·use_f=True.86 option·use_f=True.
103 [3]:87 [·]:
104 res.t_test("x1=x2")88 res.t_test("x1=x2")
105 [3]:89 [·]:
106 <class·'statsmodels.stats.contrast.ContrastResults'> 
107 ·····························Test·for·Constraints 
108 ============================================================================== 
109 ·················coef····std·err··········z······P>|z|······[0.025······0.975] 
110 ------------------------------------------------------------------------------ 
111 c0············-0.0843······0.049·····-1.717······0.086······-0.181·······0.012 
112 ============================================================================== 
113 [4]: 
114 res.wald_test("x1=x2,·x3",·scalar=True)90 res.wald_test("x1=x2,·x3",·scalar=True)
115 [4]: 
116 <class·'statsmodels.stats.contrast.ContrastResults'> 
117 <Wald·test·(chi2):·statistic=40.772322944293165,·p-value=1.400885259219231e-09, 
118 df_denom=2> 
119 *\x8**\x8**\x8**\x8**\x8*·I\x8In\x8nf\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8e·-\x8-·s\x8sc\x8co\x8or\x8re\x8e_\x8_t\x8te\x8es\x8st\x8t_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*91 *\x8**\x8**\x8**\x8**\x8*·I\x8In\x8nf\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8e·-\x8-·s\x8sc\x8co\x8or\x8re\x8e_\x8_t\x8te\x8es\x8st\x8t_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
120 new·in·statsmodels·0.14·for·most·discrete·models·and·for·GLM.92 new·in·statsmodels·0.14·for·most·discrete·models·and·for·GLM.
121 Score·or·lagrange·multiplier·(LM)·tests·are·based·on·the·model·estimated·under93 Score·or·lagrange·multiplier·(LM)·tests·are·based·on·the·model·estimated·under
122 the·null·hypothesis.·A·common·example·are·variable·addition·tests·for·which·we94 the·null·hypothesis.·A·common·example·are·variable·addition·tests·for·which·we
123 estimate·the·model·parameters·under·null·restrictions·but·evaluate·the·score95 estimate·the·model·parameters·under·null·restrictions·but·evaluate·the·score
124 and·hessian·under·for·the·full·model·to·test·whether·an·additional·variable·is96 and·hessian·under·for·the·full·model·to·test·whether·an·additional·variable·is
125 statistically·significant.97 statistically·significant.
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138 statistical·packages·only·implement·it·for·a·few·special·cases.)110 statistical·packages·only·implement·it·for·a·few·special·cases.)
139 We·can·use·the·variable·addition·score_test·for·specification·testing.·In·the111 We·can·use·the·variable·addition·score_test·for·specification·testing.·In·the
140 following·example·we·test·whether·there·is·some·misspecified·nonlinearity·in112 following·example·we·test·whether·there·is·some·misspecified·nonlinearity·in
141 the·model·by·adding·quadratic·or·polynomial·tersm.113 the·model·by·adding·quadratic·or·polynomial·tersm.
142 In·our·example·we·can·expect·that·these·specification·tests·do·not·reject·the114 In·our·example·we·can·expect·that·these·specification·tests·do·not·reject·the
143 null·hypotheses·because·the·model·is·correctly·specified·and·the·sample·size·is115 null·hypotheses·because·the·model·is·correctly·specified·and·the·sample·size·is
144 large,116 large,
145 [5]:117 [·]:
146 res.score_test(exog_extra=xc**2)118 res.score_test(exog_extra=xc**2)
147 [5]: 
148 (array([0.05300569]),·array([0.81791332]),·1) 
149 A·reset·test·is·a·test·for·the·correct·specification·of·the·link·function.·The119 A·reset·test·is·a·test·for·the·correct·specification·of·the·link·function.·The
150 standard·form·of·the·test·adds·polynomial·terms·of·the·linear·predictor·as120 standard·form·of·the·test·adds·polynomial·terms·of·the·linear·predictor·as
151 extra·regressors·and·test·for·their·significance.121 extra·regressors·and·test·for·their·significance.
152 Here·we·use·the·variable·addition·score·test·for·the·reset·test·with·powers·2122 Here·we·use·the·variable·addition·score·test·for·the·reset·test·with·powers·2
153 and·3.123 and·3.
154 [6]:124 [·]:
155 linpred·=·res.predict(which="linear")125 linpred·=·res.predict(which="linear")
156 res.score_test(exog_extra=linpred[:,None]**[2,·3])126 res.score_test(exog_extra=linpred[:,None]**[2,·3])
157 [6]: 
158 (array([1.3867703]),·array([0.49988103]),·2) 
159 *\x8**\x8**\x8**\x8**\x8*·P\x8Pr\x8re\x8ed\x8di\x8ic\x8ct\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*127 *\x8**\x8**\x8**\x8**\x8*·P\x8Pr\x8re\x8ed\x8di\x8ic\x8ct\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
160 The·model·and·results·classes·have·predict·method·which·only·returns·the128 The·model·and·results·classes·have·predict·method·which·only·returns·the
161 predicted·values.·The·get_prediction·method·adds·inferential·statistics·for·the129 predicted·values.·The·get_prediction·method·adds·inferential·statistics·for·the
162 prediction,·standard·errors,·pvalues·and·confidence·intervals.130 prediction,·standard·errors,·pvalues·and·confidence·intervals.
163 For·the·following·example,·we·create·new·sets·of·explanatory·variables·that·is131 For·the·following·example,·we·create·new·sets·of·explanatory·variables·that·is
164 split·by·the·categorical·level·and·over·a·uniform·grid·of·the·continuous132 split·by·the·categorical·level·and·over·a·uniform·grid·of·the·continuous
165 variable.133 variable.
166 [7]:134 [·]:
167 n·=·11135 n·=·11
168 exc·=·np.linspace(0,·1,·n)136 exc·=·np.linspace(0,·1,·n)
169 ex1·=·np.column_stack((np.ones(n),·np.zeros(n),·exc))137 ex1·=·np.column_stack((np.ones(n),·np.zeros(n),·exc))
170 ex2·=·np.column_stack((np.zeros(n),·np.ones(n),·exc))138 ex2·=·np.column_stack((np.zeros(n),·np.ones(n),·exc))
  
171 m1·=·res.get_prediction(ex1)139 m1·=·res.get_prediction(ex1)
172 m2·=·res.get_prediction(ex2)140 m2·=·res.get_prediction(ex2)
173 The·available·methods·and·attributes·of·the·prediction·results·class·are141 The·available·methods·and·attributes·of·the·prediction·results·class·are
174 [8]:142 [·]:
175 [i·for·i·in·dir(m1)·if·not·i.startswith("_")]143 [i·for·i·in·dir(m1)·if·not·i.startswith("_")]
176 [8]:144 [·]:
177 ['conf_int', 
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57 ······<div·class="documentwrapper">57 ······<div·class="documentwrapper">
58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Prediction-(out-of-sample)">61 ··<section·id="Prediction-(out-of-sample)">
62 <h1>Prediction·(out·of·sample)<a·class="headerlink"·href="#Prediction-(out-of-sample)"·title="Link·to·this·heading">¶</a></h1>62 <h1>Prediction·(out·of·sample)<a·class="headerlink"·href="#Prediction-(out-of-sample)"·title="Link·to·this·heading">¶</a></h1>
63 <div·class="nbinput·nblast·docutils·container">63 <div·class="nbinput·nblast·docutils·container">
64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
65 </pre></div>65 </pre></div>
66 </div>66 </div>
67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 </div>70 </div>
71 <div·class="nbinput·nblast·docutils·container">71 <div·class="nbinput·nblast·docutils·container">
72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
76 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>76 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
  
77 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>77 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
  
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82 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1234</span><span·class="p">)</span>·<span·class="c1">#·for·reproducibility</span>82 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1234</span><span·class="p">)</span>·<span·class="c1">#·for·reproducibility</span>
83 </pre></div>83 </pre></div>
84 </div>84 </div>
85 </div>85 </div>
86 <section·id="Artificial-data">86 <section·id="Artificial-data">
87 <h2>Artificial·data<a·class="headerlink"·href="#Artificial-data"·title="Link·to·this·heading">¶</a></h2>87 <h2>Artificial·data<a·class="headerlink"·href="#Artificial-data"·title="Link·to·this·heading">¶</a></h2>
88 <div·class="nbinput·nblast·docutils·container">88 <div·class="nbinput·nblast·docutils·container">
89 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:89 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
90 </pre></div>90 </pre></div>
91 </div>91 </div>
92 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">nsample</span>·<span·class="o">=</span>·<span·class="mi">50</span>92 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">nsample</span>·<span·class="o">=</span>·<span·class="mi">50</span>
93 <span·class="n">sig</span>·<span·class="o">=</span>·<span·class="mf">0.25</span>93 <span·class="n">sig</span>·<span·class="o">=</span>·<span·class="mf">0.25</span>
94 <span·class="n">x1</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">20</span><span·class="p">,</span>·<span·class="n">nsample</span><span·class="p">)</span>94 <span·class="n">x1</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">20</span><span·class="p">,</span>·<span·class="n">nsample</span><span·class="p">)</span>
95 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">column_stack</span><span·class="p">((</span><span·class="n">x1</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sin</span><span·class="p">(</span><span·class="n">x1</span><span·class="p">),</span>·<span·class="p">(</span><span·class="n">x1</span>·<span·class="o">-</span>·<span·class="mi">5</span><span·class="p">)</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">))</span>95 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">column_stack</span><span·class="p">((</span><span·class="n">x1</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">sin</span><span·class="p">(</span><span·class="n">x1</span><span·class="p">),</span>·<span·class="p">(</span><span·class="n">x1</span>·<span·class="o">-</span>·<span·class="mi">5</span><span·class="p">)</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">))</span>
96 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">X</span><span·class="p">)</span>96 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">X</span><span·class="p">)</span>
Offset 99, 209 lines modifiedOffset 99, 102 lines modified
99 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">y_true</span>·<span·class="o">+</span>·<span·class="n">sig</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">nsample</span><span·class="p">)</span>99 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">y_true</span>·<span·class="o">+</span>·<span·class="n">sig</span>·<span·class="o">*</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">normal</span><span·class="p">(</span><span·class="n">size</span><span·class="o">=</span><span·class="n">nsample</span><span·class="p">)</span>
100 </pre></div>100 </pre></div>
101 </div>101 </div>
102 </div>102 </div>
103 </section>103 </section>
104 <section·id="Estimation">104 <section·id="Estimation">
105 <h2>Estimation<a·class="headerlink"·href="#Estimation"·title="Link·to·this·heading">¶</a></h2>105 <h2>Estimation<a·class="headerlink"·href="#Estimation"·title="Link·to·this·heading">¶</a></h2>
106 <div·class="nbinput·docutils·container">106 <div·class="nbinput·nblast·docutils·container">
107 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:107 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
108 </pre></div>108 </pre></div>
109 </div>109 </div>
110 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">olsmod</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">OLS</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">X</span><span·class="p">)</span>110 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">olsmod</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">OLS</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">X</span><span·class="p">)</span>
111 <span·class="n">olsres</span>·<span·class="o">=</span>·<span·class="n">olsmod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>111 <span·class="n">olsres</span>·<span·class="o">=</span>·<span·class="n">olsmod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
112 <span·class="nb">print</span><span·class="p">(</span><span·class="n">olsres</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>112 <span·class="nb">print</span><span·class="p">(</span><span·class="n">olsres</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
113 </pre></div>113 </pre></div>
114 </div>114 </div>
115 </div>115 </div>
116 <div·class="nboutput·nblast·docutils·container"> 
117 <div·class="prompt·empty·docutils·container"> 
118 </div> 
119 <div·class="output_area·docutils·container"> 
120 <div·class="highlight"><pre> 
121 ····························OLS·Regression·Results 
122 ============================================================================== 
123 Dep.·Variable:······················y···R-squared:·······················0.984 
124 Model:····························OLS···Adj.·R-squared:··················0.983 
125 Method:·················Least·Squares···F-statistic:·····················956.6 
126 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········1.96e-41 
127 Time:························13:13:47···Log-Likelihood:·················1.2217 
128 No.·Observations:··················50···AIC:·····························5.557 
129 Df·Residuals:······················46···BIC:·····························13.20 
130 Df·Model:···························3 
131 Covariance·Type:············nonrobust 
132 ============================================================================== 
133 ·················coef····std·err··········t······P&gt;|t|······[0.025······0.975] 
134 ------------------------------------------------------------------------------ 
135 const··········4.9654······0.084·····59.175······0.000·······4.796·······5.134 
136 x1·············0.5088······0.013·····39.314······0.000·······0.483·······0.535 
137 x2·············0.5651······0.051·····11.109······0.000·······0.463·······0.668 
138 x3············-0.0206······0.001····-18.144······0.000······-0.023······-0.018 
139 ============================================================================== 
140 Omnibus:························0.840···Durbin-Watson:···················2.269 
141 Prob(Omnibus):··················0.657···Jarque-Bera·(JB):················0.577 
142 Skew:··························-0.263···Prob(JB):························0.749 
143 Kurtosis:·······················2.972···Cond.·No.·························221. 
144 ============================================================================== 
  
145 Notes: 
146 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified. 
147 </pre></div></div> 
148 </div> 
149 </section>116 </section>
150 <section·id="In-sample-prediction">117 <section·id="In-sample-prediction">
151 <h2>In-sample·prediction<a·class="headerlink"·href="#In-sample-prediction"·title="Link·to·this·heading">¶</a></h2>118 <h2>In-sample·prediction<a·class="headerlink"·href="#In-sample-prediction"·title="Link·to·this·heading">¶</a></h2>
152 <div·class="nbinput·docutils·container">119 <div·class="nbinput·nblast·docutils·container">
153 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:120 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
154 </pre></div>121 </pre></div>
155 </div>122 </div>
156 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">ypred</span>·<span·class="o">=</span>·<span·class="n">olsres</span><span·class="o">.</span><span·class="n">predict</span><span·class="p">(</span><span·class="n">X</span><span·class="p">)</span>123 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">ypred</span>·<span·class="o">=</span>·<span·class="n">olsres</span><span·class="o">.</span><span·class="n">predict</span><span·class="p">(</span><span·class="n">X</span><span·class="p">)</span>
157 <span·class="nb">print</span><span·class="p">(</span><span·class="n">ypred</span><span·class="p">)</span>124 <span·class="nb">print</span><span·class="p">(</span><span·class="n">ypred</span><span·class="p">)</span>
158 </pre></div>125 </pre></div>
159 </div>126 </div>
160 </div>127 </div>
161 <div·class="nboutput·nblast·docutils·container"> 
162 <div·class="prompt·empty·docutils·container"> 
163 </div> 
164 <div·class="output_area·docutils·container"> 
165 <div·class="highlight"><pre> 
166 [·4.44997408··4.96265684··5.43161584··5.82605136··6.12627912··6.32696437 
167 ··6.4379984···6.4828734···6.49482276··6.51136093··6.56811991··6.69299498 
168 ··6.90156162··7.1945165···7.55756297··7.96376004··8.37794864··8.76252818 
169 ··9.08363424··9.31670235··9.45050393··9.48899104··9.45064714··9.36545023 
170 ··9.26994764··9.20125134··9.19094055··9.25987342··9.41476003··9.64705998 
171 ··9.93438555·10.24417991·10.53906618·10.78298825·10.9471348··11.01467283 
172 ·10.98351335·10.86665452·10.69004615·10.4883262··10.29912985·10.15690615 
173 ·10.08725815·10.10273638·10.20077685·10.36412228·10.56365745·10.76319271 
174 ·10.92540989·11.01799353] 
175 </pre></div></div> 
176 </div> 
177 </section>128 </section>
178 <section·id="Create-a-new-sample-of-explanatory-variables-Xnew,-predict-and-plot">129 <section·id="Create-a-new-sample-of-explanatory-variables-Xnew,-predict-and-plot">
179 <h2>Create·a·new·sample·of·explanatory·variables·Xnew,·predict·and·plot<a·class="headerlink"·href="#Create-a-new-sample-of-explanatory-variables-Xnew,-predict-and-plot"·title="Link·to·this·heading">¶</a></h2>130 <h2>Create·a·new·sample·of·explanatory·variables·Xnew,·predict·and·plot<a·class="headerlink"·href="#Create-a-new-sample-of-explanatory-variables-Xnew,-predict-and-plot"·title="Link·to·this·heading">¶</a></h2>
180 <div·class="nbinput·docutils·container">131 <div·class="nbinput·nblast·docutils·container">
181 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:132 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
182 </pre></div>133 </pre></div>
183 </div>134 </div>
184 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">x1n</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mf">20.5</span><span·class="p">,</span>·<span·class="mi">25</span><span·class="p">,</span>·<span·class="mi">10</span><span·class="p">)</span>135 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">x1n</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mf">20.5</span><span·class="p">,</span>·<span·class="mi">25</span><span·class="p">,</span>·<span·class="mi">10</span><span·class="p">)</span>
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Prediction·(out·of·sample)8 ····*·Prediction·(out·of·sample)
9 *\x8**\x8**\x8**\x8**\x8**\x8*·P\x8Pr\x8re\x8ed\x8di\x8ic\x8ct\x8ti\x8io\x8on\x8n·(\x8(o\x8ou\x8ut\x8t·o\x8of\x8f·s\x8sa\x8am\x8mp\x8pl\x8le\x8e)\x8)_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·P\x8Pr\x8re\x8ed\x8di\x8ic\x8ct\x8ti\x8io\x8on\x8n·(\x8(o\x8ou\x8ut\x8t·o\x8of\x8f·s\x8sa\x8am\x8mp\x8pl\x8le\x8e)\x8)_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 %matplotlib·inline11 %matplotlib·inline
12 [2]:12 [·]:
13 import·numpy·as·np13 import·numpy·as·np
14 import·matplotlib.pyplot·as·plt14 import·matplotlib.pyplot·as·plt
  
15 import·statsmodels.api·as·sm15 import·statsmodels.api·as·sm
  
16 plt.rc("figure",·figsize=(16,·8))16 plt.rc("figure",·figsize=(16,·8))
17 plt.rc("font",·size=14)17 plt.rc("font",·size=14)
18 np.random.seed(1234)·#·for·reproducibility18 np.random.seed(1234)·#·for·reproducibility
19 *\x8**\x8**\x8**\x8**\x8*·A\x8Ar\x8rt\x8ti\x8if\x8fi\x8ic\x8ci\x8ia\x8al\x8l·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·A\x8Ar\x8rt\x8ti\x8if\x8fi\x8ic\x8ci\x8ia\x8al\x8l·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
20 [3]:20 [·]:
21 nsample·=·5021 nsample·=·50
22 sig·=·0.2522 sig·=·0.25
23 x1·=·np.linspace(0,·20,·nsample)23 x1·=·np.linspace(0,·20,·nsample)
24 X·=·np.column_stack((x1,·np.sin(x1),·(x1·-·5)·**·2))24 X·=·np.column_stack((x1,·np.sin(x1),·(x1·-·5)·**·2))
25 X·=·sm.add_constant(X)25 X·=·sm.add_constant(X)
26 beta·=·[5.0,·0.5,·0.5,·-0.02]26 beta·=·[5.0,·0.5,·0.5,·-0.02]
27 y_true·=·np.dot(X,·beta)27 y_true·=·np.dot(X,·beta)
28 y·=·y_true·+·sig·*·np.random.normal(size=nsample)28 y·=·y_true·+·sig·*·np.random.normal(size=nsample)
29 *\x8**\x8**\x8**\x8**\x8*·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*29 *\x8**\x8**\x8**\x8**\x8*·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
30 [4]:30 [·]:
31 olsmod·=·sm.OLS(y,·X)31 olsmod·=·sm.OLS(y,·X)
32 olsres·=·olsmod.fit()32 olsres·=·olsmod.fit()
33 print(olsres.summary())33 print(olsres.summary())
34 ····························OLS·Regression·Results 
35 ============================================================================== 
36 Dep.·Variable:······················y···R-squared:·······················0.984 
37 Model:····························OLS···Adj.·R-squared:··················0.983 
38 Method:·················Least·Squares···F-statistic:·····················956.6 
39 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········1.96e-41 
40 Time:························13:13:47···Log-Likelihood:·················1.2217 
41 No.·Observations:··················50···AIC:·····························5.557 
42 Df·Residuals:······················46···BIC:·····························13.20 
43 Df·Model:···························3 
44 Covariance·Type:············nonrobust 
45 ============================================================================== 
46 ·················coef····std·err··········t······P>|t|······[0.025······0.975] 
47 ------------------------------------------------------------------------------ 
48 const··········4.9654······0.084·····59.175······0.000·······4.796·······5.134 
49 x1·············0.5088······0.013·····39.314······0.000·······0.483·······0.535 
50 x2·············0.5651······0.051·····11.109······0.000·······0.463·······0.668 
51 x3············-0.0206······0.001····-18.144······0.000······-0.023······-0.018 
52 ============================================================================== 
53 Omnibus:························0.840···Durbin-Watson:···················2.269 
54 Prob(Omnibus):··················0.657···Jarque-Bera·(JB):················0.577 
55 Skew:··························-0.263···Prob(JB):························0.749 
56 Kurtosis:·······················2.972···Cond.·No.·························221. 
57 ============================================================================== 
  
58 Notes: 
59 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is 
60 correctly·specified. 
61 *\x8**\x8**\x8**\x8**\x8*·I\x8In\x8n-\x8-s\x8sa\x8am\x8mp\x8pl\x8le\x8e·p\x8pr\x8re\x8ed\x8di\x8ic\x8ct\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*34 *\x8**\x8**\x8**\x8**\x8*·I\x8In\x8n-\x8-s\x8sa\x8am\x8mp\x8pl\x8le\x8e·p\x8pr\x8re\x8ed\x8di\x8ic\x8ct\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
62 [5]:35 [·]:
63 ypred·=·olsres.predict(X)36 ypred·=·olsres.predict(X)
64 print(ypred)37 print(ypred)
65 [·4.44997408··4.96265684··5.43161584··5.82605136··6.12627912··6.32696437 
66 ··6.4379984···6.4828734···6.49482276··6.51136093··6.56811991··6.69299498 
67 ··6.90156162··7.1945165···7.55756297··7.96376004··8.37794864··8.76252818 
68 ··9.08363424··9.31670235··9.45050393··9.48899104··9.45064714··9.36545023 
69 ··9.26994764··9.20125134··9.19094055··9.25987342··9.41476003··9.64705998 
70 ··9.93438555·10.24417991·10.53906618·10.78298825·10.9471348··11.01467283 
71 ·10.98351335·10.86665452·10.69004615·10.4883262··10.29912985·10.15690615 
72 ·10.08725815·10.10273638·10.20077685·10.36412228·10.56365745·10.76319271 
73 ·10.92540989·11.01799353] 
74 *\x8**\x8**\x8**\x8**\x8*·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·n\x8ne\x8ew\x8w·s\x8sa\x8am\x8mp\x8pl\x8le\x8e·o\x8of\x8f·e\x8ex\x8xp\x8pl\x8la\x8an\x8na\x8at\x8to\x8or\x8ry\x8y·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s·X\x8Xn\x8ne\x8ew\x8w,\x8,·p\x8pr\x8re\x8ed\x8di\x8ic\x8ct\x8t·a\x8an\x8nd\x8d·p\x8pl\x8lo\x8ot\x8t_\x8?\x838 *\x8**\x8**\x8**\x8**\x8*·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·n\x8ne\x8ew\x8w·s\x8sa\x8am\x8mp\x8pl\x8le\x8e·o\x8of\x8f·e\x8ex\x8xp\x8pl\x8la\x8an\x8na\x8at\x8to\x8or\x8ry\x8y·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s·X\x8Xn\x8ne\x8ew\x8w,\x8,·p\x8pr\x8re\x8ed\x8di\x8ic\x8ct\x8t·a\x8an\x8nd\x8d·p\x8pl\x8lo\x8ot\x8t_\x8?\x8
75 *\x8**\x8**\x8**\x8**\x8*39 *\x8**\x8**\x8**\x8**\x8*
76 [6]:40 [·]:
77 x1n·=·np.linspace(20.5,·25,·10)41 x1n·=·np.linspace(20.5,·25,·10)
78 Xnew·=·np.column_stack((x1n,·np.sin(x1n),·(x1n·-·5)·**·2))42 Xnew·=·np.column_stack((x1n,·np.sin(x1n),·(x1n·-·5)·**·2))
79 Xnew·=·sm.add_constant(Xnew)43 Xnew·=·sm.add_constant(Xnew)
80 ynewpred·=·olsres.predict(Xnew)··#·predict·out·of·sample44 ynewpred·=·olsres.predict(Xnew)··#·predict·out·of·sample
81 print(ynewpred)45 print(ynewpred)
82 [11.00539682·10.84456472·10.55765996·10.1951886···9.82363439··9.50918122 
83 ··9.30150901··9.2216303···9.25674569··9.36337756] 
84 *\x8**\x8**\x8**\x8**\x8*·P\x8Pl\x8lo\x8ot\x8t·c\x8co\x8om\x8mp\x8pa\x8ar\x8ri\x8is\x8so\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*46 *\x8**\x8**\x8**\x8**\x8*·P\x8Pl\x8lo\x8ot\x8t·c\x8co\x8om\x8mp\x8pa\x8ar\x8ri\x8is\x8so\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
85 [7]:47 [·]:
86 import·matplotlib.pyplot·as·plt48 import·matplotlib.pyplot·as·plt
  
87 fig,·ax·=·plt.subplots()49 fig,·ax·=·plt.subplots()
88 ax.plot(x1,·y,·"o",·label="Data")50 ax.plot(x1,·y,·"o",·label="Data")
89 ax.plot(x1,·y_true,·"b-",·label="True")51 ax.plot(x1,·y_true,·"b-",·label="True")
90 ax.plot(np.hstack((x1,·x1n)),·np.hstack((ypred,·ynewpred)),·"r",·label="OLS52 ax.plot(np.hstack((x1,·x1n)),·np.hstack((ypred,·ynewpred)),·"r",·label="OLS
91 prediction")53 prediction")
92 ax.legend(loc="best")54 ax.legend(loc="best")
93 [7]: 
94 <matplotlib.legend.Legend·at·0xadde5de1e8ed> 
95 [../../../_images/examples_notebooks_generated_predict_12_1.png] 
96 *\x8**\x8**\x8**\x8**\x8*·P\x8Pr\x8re\x8ed\x8di\x8ic\x8ct\x8ti\x8in\x8ng\x8g·w\x8wi\x8it\x8th\x8h·F\x8Fo\x8or\x8rm\x8mu\x8ul\x8la\x8as\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*55 *\x8**\x8**\x8**\x8**\x8*·P\x8Pr\x8re\x8ed\x8di\x8ic\x8ct\x8ti\x8in\x8ng\x8g·w\x8wi\x8it\x8th\x8h·F\x8Fo\x8or\x8rm\x8mu\x8ul\x8la\x8as\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
97 Using·formulas·can·make·both·estimation·and·prediction·a·lot·easier56 Using·formulas·can·make·both·estimation·and·prediction·a·lot·easier
98 [8]:57 [·]:
99 from·statsmodels.formula.api·import·ols58 from·statsmodels.formula.api·import·ols
  
100 data·=·{"x1":·x1,·"y":·y}59 data·=·{"x1":·x1,·"y":·y}
  
101 res·=·ols("y·~·x1·+·np.sin(x1)·+·I((x1-5)**2)",·data=data).fit()60 res·=·ols("y·~·x1·+·np.sin(x1)·+·I((x1-5)**2)",·data=data).fit()
102 We·use·the·I·to·indicate·use·of·the·Identity·transform.·Ie.,·we·do·not·want·any61 We·use·the·I·to·indicate·use·of·the·Identity·transform.·Ie.,·we·do·not·want·any
103 expansion·magic·from·using·**262 expansion·magic·from·using·**2
104 [9]:63 [·]:
105 res.params64 res.params
106 [9]: 
107 Intercept···········4.965353 
108 x1··················0.508755 
109 np.sin(x1)··········0.565142 
110 I((x1·-·5)·**·2)···-0.020615 
111 dtype:·float64 
112 Now·we·only·have·to·pass·the·single·variable·and·we·get·the·transformed·right-65 Now·we·only·have·to·pass·the·single·variable·and·we·get·the·transformed·right-
113 hand·side·variables·automatically66 hand·side·variables·automatically
114 [10]:67 [·]:
115 res.predict(exog=dict(x1=x1n))68 res.predict(exog=dict(x1=x1n))
116 [10]: 
117 0····11.005397 
118 1····10.844565 
119 2····10.557660 
120 3····10.195189 
121 4·····9.823634 
122 5·····9.509181 
123 6·····9.301509 
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65 <li><p>Koenker,·Roger·and·Kevin·F.·Hallock.·“Quantile·Regression”.·Journal·of·Economic·Perspectives,·Volume·15,·Number·4,·Fall·2001,·Pages·143–156</p></li>65 <li><p>Koenker,·Roger·and·Kevin·F.·Hallock.·“Quantile·Regression”.·Journal·of·Economic·Perspectives,·Volume·15,·Number·4,·Fall·2001,·Pages·143–156</p></li>
66 </ul>66 </ul>
67 <p>We·are·interested·in·the·relationship·between·income·and·expenditures·on·food·for·a·sample·of·working·class·Belgian·households·in·1857·(the·Engel·data).</p>67 <p>We·are·interested·in·the·relationship·between·income·and·expenditures·on·food·for·a·sample·of·working·class·Belgian·households·in·1857·(the·Engel·data).</p>
68 <section·id="Setup">68 <section·id="Setup">
69 <h2>Setup<a·class="headerlink"·href="#Setup"·title="Link·to·this·heading">¶</a></h2>69 <h2>Setup<a·class="headerlink"·href="#Setup"·title="Link·to·this·heading">¶</a></h2>
70 <p>We·first·need·to·load·some·modules·and·to·retrieve·the·data.·Conveniently,·the·Engel·dataset·is·shipped·with·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>.</p>70 <p>We·first·need·to·load·some·modules·and·to·retrieve·the·data.·Conveniently,·the·Engel·dataset·is·shipped·with·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>.</p>
71 <div·class="nbinput·nblast·docutils·container">71 <div·class="nbinput·nblast·docutils·container">
72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
76 </pre></div>76 </pre></div>
77 </div>77 </div>
78 </div>78 </div>
79 <div·class="nbinput·docutils·container">79 <div·class="nbinput·nblast·docutils·container">
80 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:80 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
81 </pre></div>81 </pre></div>
82 </div>82 </div>
83 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>83 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
84 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>84 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
85 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>85 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
86 <span·class="kn">import</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="k">as</span>·<span·class="nn">smf</span>86 <span·class="kn">import</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="k">as</span>·<span·class="nn">smf</span>
87 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>87 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
  
88 <span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">engel</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>88 <span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">engel</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>
89 <span·class="n">data</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>89 <span·class="n">data</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>
90 </pre></div>90 </pre></div>
91 </div>91 </div>
92 </div>92 </div>
93 <div·class="nboutput·nblast·docutils·container"> 
94 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]: 
95 </pre></div> 
96 </div> 
97 <div·class="output_area·rendered_html·docutils·container"> 
98 <div> 
99 <style·scoped> 
100 ····.dataframe·tbody·tr·th:only-of-type·{ 
101 ········vertical-align:·middle; 
102 ····} 
  
103 ····.dataframe·tbody·tr·th·{ 
104 ········vertical-align:·top; 
105 ····} 
  
106 ····.dataframe·thead·th·{ 
107 ········text-align:·right; 
108 ····} 
109 </style> 
110 <table·border="1"·class="dataframe"> 
111 ··<thead> 
112 ····<tr·style="text-align:·right;"> 
113 ······<th></th> 
114 ······<th>income</th> 
115 ······<th>foodexp</th> 
116 ····</tr> 
117 ··</thead> 
118 ··<tbody> 
119 ····<tr> 
120 ······<th>0</th> 
121 ······<td>420.157651</td> 
122 ······<td>255.839425</td> 
123 ····</tr> 
124 ····<tr> 
125 ······<th>1</th> 
126 ······<td>541.411707</td> 
127 ······<td>310.958667</td> 
128 ····</tr> 
129 ····<tr> 
130 ······<th>2</th> 
131 ······<td>901.157457</td> 
132 ······<td>485.680014</td> 
133 ····</tr> 
134 ····<tr> 
135 ······<th>3</th> 
136 ······<td>639.080229</td> 
137 ······<td>402.997356</td> 
138 ····</tr> 
139 ····<tr> 
140 ······<th>4</th> 
141 ······<td>750.875606</td> 
142 ······<td>495.560775</td> 
143 ····</tr> 
144 ··</tbody> 
145 </table> 
146 </div></div> 
147 </div> 
148 </section>93 </section>
149 <section·id="Least-Absolute-Deviation">94 <section·id="Least-Absolute-Deviation">
150 <h2>Least·Absolute·Deviation<a·class="headerlink"·href="#Least-Absolute-Deviation"·title="Link·to·this·heading">¶</a></h2>95 <h2>Least·Absolute·Deviation<a·class="headerlink"·href="#Least-Absolute-Deviation"·title="Link·to·this·heading">¶</a></h2>
151 <p>The·LAD·model·is·a·special·case·of·quantile·regression·where·q=0.5</p>96 <p>The·LAD·model·is·a·special·case·of·quantile·regression·where·q=0.5</p>
152 <div·class="nbinput·docutils·container">97 <div·class="nbinput·nblast·docutils·container">
153 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:98 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
154 </pre></div>99 </pre></div>
155 </div>100 </div>
156 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">mod</span>·<span·class="o">=</span>·<span·class="n">smf</span><span·class="o">.</span><span·class="n">quantreg</span><span·class="p">(</span><span·class="s2">&quot;foodexp·~·income&quot;</span><span·class="p">,</span>·<span·class="n">data</span><span·class="p">)</span>101 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">mod</span>·<span·class="o">=</span>·<span·class="n">smf</span><span·class="o">.</span><span·class="n">quantreg</span><span·class="p">(</span><span·class="s2">&quot;foodexp·~·income&quot;</span><span·class="p">,</span>·<span·class="n">data</span><span·class="p">)</span>
157 <span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">mod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">q</span><span·class="o">=</span><span·class="mf">0.5</span><span·class="p">)</span>102 <span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">mod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">q</span><span·class="o">=</span><span·class="mf">0.5</span><span·class="p">)</span>
158 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>103 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
159 </pre></div>104 </pre></div>
160 </div>105 </div>
161 </div>106 </div>
162 <div·class="nboutput·nblast·docutils·container"> 
163 <div·class="prompt·empty·docutils·container"> 
164 </div> 
165 <div·class="output_area·docutils·container"> 
166 <div·class="highlight"><pre> 
167 ·························QuantReg·Regression·Results 
168 ============================================================================== 
169 Dep.·Variable:················foodexp···Pseudo·R-squared:···············0.6206 
170 Model:·······················QuantReg···Bandwidth:·······················64.51 
171 Method:·················Least·Squares···Sparsity:························209.3 
172 Date:················Sun,·10·Aug·2025···No.·Observations:··················235 
173 Time:························13:13:47···Df·Residuals:······················233 
174 ········································Df·Model:····························1 
175 ============================================================================== 
176 ·················coef····std·err··········t······P&gt;|t|······[0.025······0.975] 
177 ------------------------------------------------------------------------------ 
178 Intercept·····81.4823·····14.634······5.568······0.000······52.649·····110.315 
179 income·········0.5602······0.013·····42.516······0.000·······0.534·······0.586 
180 ============================================================================== 
  
181 The·condition·number·is·large,·2.38e+03.·This·might·indicate·that·there·are 
182 strong·multicollinearity·or·other·numerical·problems. 
183 </pre></div></div> 
184 </div> 
185 </section>107 </section>
186 <section·id="Visualizing-the-results">108 <section·id="Visualizing-the-results">
187 <h2>Visualizing·the·results<a·class="headerlink"·href="#Visualizing-the-results"·title="Link·to·this·heading">¶</a></h2>109 <h2>Visualizing·the·results<a·class="headerlink"·href="#Visualizing-the-results"·title="Link·to·this·heading">¶</a></h2>
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12 ····*·Koenker,·Roger·and·Kevin·F.·Hallock.·“Quantile·Regression”.·Journal·of12 ····*·Koenker,·Roger·and·Kevin·F.·Hallock.·“Quantile·Regression”.·Journal·of
13 ······Economic·Perspectives,·Volume·15,·Number·4,·Fall·2001,·Pages·143–15613 ······Economic·Perspectives,·Volume·15,·Number·4,·Fall·2001,·Pages·143–156
14 We·are·interested·in·the·relationship·between·income·and·expenditures·on·food14 We·are·interested·in·the·relationship·between·income·and·expenditures·on·food
15 for·a·sample·of·working·class·Belgian·households·in·1857·(the·Engel·data).15 for·a·sample·of·working·class·Belgian·households·in·1857·(the·Engel·data).
16 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8et\x8tu\x8up\x8p_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*16 *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8et\x8tu\x8up\x8p_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
17 We·first·need·to·load·some·modules·and·to·retrieve·the·data.·Conveniently,·the17 We·first·need·to·load·some·modules·and·to·retrieve·the·data.·Conveniently,·the
18 Engel·dataset·is·shipped·with·statsmodels.18 Engel·dataset·is·shipped·with·statsmodels.
19 [1]:19 [·]:
20 %matplotlib·inline20 %matplotlib·inline
21 [2]:21 [·]:
22 import·numpy·as·np22 import·numpy·as·np
23 import·pandas·as·pd23 import·pandas·as·pd
24 import·statsmodels.api·as·sm24 import·statsmodels.api·as·sm
25 import·statsmodels.formula.api·as·smf25 import·statsmodels.formula.api·as·smf
26 import·matplotlib.pyplot·as·plt26 import·matplotlib.pyplot·as·plt
  
27 data·=·sm.datasets.engel.load_pandas().data27 data·=·sm.datasets.engel.load_pandas().data
28 data.head()28 data.head()
29 [2]: 
30 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
31 |_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8i\x8i_\x8n\x8n_\x8c\x8c_\x8o\x8o_\x8m\x8m_\x8e\x8e_\x8|_\x8·_\x8·_\x8·_\x8f\x8f_\x8o\x8o_\x8o\x8o_\x8d\x8d_\x8e\x8e_\x8x\x8x_\x8p\x8p| 
32 |_\x80\x80_\x8|_\x84_\x82_\x80_\x8._\x81_\x85_\x87_\x86_\x85_\x81_\x8|_\x82_\x85_\x85_\x8._\x88_\x83_\x89_\x84_\x82_\x85| 
33 |_\x81\x81_\x8|_\x85_\x84_\x81_\x8._\x84_\x81_\x81_\x87_\x80_\x87_\x8|_\x83_\x81_\x80_\x8._\x89_\x85_\x88_\x86_\x86_\x87| 
34 |_\x82\x82_\x8|_\x89_\x80_\x81_\x8._\x81_\x85_\x87_\x84_\x85_\x87_\x8|_\x84_\x88_\x85_\x8._\x86_\x88_\x80_\x80_\x81_\x84| 
35 |_\x83\x83_\x8|_\x86_\x83_\x89_\x8._\x80_\x88_\x80_\x82_\x82_\x89_\x8|_\x84_\x80_\x82_\x8._\x89_\x89_\x87_\x83_\x85_\x86| 
36 |_\x84\x84_\x8|_\x87_\x85_\x80_\x8._\x88_\x87_\x85_\x86_\x80_\x86_\x8|_\x84_\x89_\x85_\x8._\x85_\x86_\x80_\x87_\x87_\x85| 
37 *\x8**\x8**\x8**\x8**\x8*·L\x8Le\x8ea\x8as\x8st\x8t·A\x8Ab\x8bs\x8so\x8ol\x8lu\x8ut\x8te\x8e·D\x8De\x8ev\x8vi\x8ia\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*29 *\x8**\x8**\x8**\x8**\x8*·L\x8Le\x8ea\x8as\x8st\x8t·A\x8Ab\x8bs\x8so\x8ol\x8lu\x8ut\x8te\x8e·D\x8De\x8ev\x8vi\x8ia\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
38 The·LAD·model·is·a·special·case·of·quantile·regression·where·q=0.530 The·LAD·model·is·a·special·case·of·quantile·regression·where·q=0.5
39 [3]:31 [·]:
40 mod·=·smf.quantreg("foodexp·~·income",·data)32 mod·=·smf.quantreg("foodexp·~·income",·data)
41 res·=·mod.fit(q=0.5)33 res·=·mod.fit(q=0.5)
42 print(res.summary())34 print(res.summary())
43 ·························QuantReg·Regression·Results 
44 ============================================================================== 
45 Dep.·Variable:················foodexp···Pseudo·R-squared:···············0.6206 
46 Model:·······················QuantReg···Bandwidth:·······················64.51 
47 Method:·················Least·Squares···Sparsity:························209.3 
48 Date:················Sun,·10·Aug·2025···No.·Observations:··················235 
49 Time:························13:13:47···Df·Residuals:······················233 
50 ········································Df·Model:····························1 
51 ============================================================================== 
52 ·················coef····std·err··········t······P>|t|······[0.025······0.975] 
53 ------------------------------------------------------------------------------ 
54 Intercept·····81.4823·····14.634······5.568······0.000······52.649·····110.315 
55 income·········0.5602······0.013·····42.516······0.000·······0.534·······0.586 
56 ============================================================================== 
  
57 The·condition·number·is·large,·2.38e+03.·This·might·indicate·that·there·are 
58 strong·multicollinearity·or·other·numerical·problems. 
59 *\x8**\x8**\x8**\x8**\x8*·V\x8Vi\x8is\x8su\x8ua\x8al\x8li\x8iz\x8zi\x8in\x8ng\x8g·t\x8th\x8he\x8e·r\x8re\x8es\x8su\x8ul\x8lt\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*35 *\x8**\x8**\x8**\x8**\x8*·V\x8Vi\x8is\x8su\x8ua\x8al\x8li\x8iz\x8zi\x8in\x8ng\x8g·t\x8th\x8he\x8e·r\x8re\x8es\x8su\x8ul\x8lt\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
60 We·estimate·the·quantile·regression·model·for·many·quantiles·between·.05·and36 We·estimate·the·quantile·regression·model·for·many·quantiles·between·.05·and
61 .95,·and·compare·best·fit·line·from·each·of·these·models·to·Ordinary·Least37 .95,·and·compare·best·fit·line·from·each·of·these·models·to·Ordinary·Least
62 Squares·results.38 Squares·results.
63 *\x8**\x8**\x8**\x8*·P\x8Pr\x8re\x8ep\x8pa\x8ar\x8re\x8e·d\x8da\x8at\x8ta\x8a·f\x8fo\x8or\x8r·p\x8pl\x8lo\x8ot\x8tt\x8ti\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8*39 *\x8**\x8**\x8**\x8*·P\x8Pr\x8re\x8ep\x8pa\x8ar\x8re\x8e·d\x8da\x8at\x8ta\x8a·f\x8fo\x8or\x8r·p\x8pl\x8lo\x8ot\x8tt\x8ti\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8*
64 For·convenience,·we·place·the·quantile·regression·results·in·a·Pandas40 For·convenience,·we·place·the·quantile·regression·results·in·a·Pandas
65 DataFrame,·and·the·OLS·results·in·a·dictionary.41 DataFrame,·and·the·OLS·results·in·a·dictionary.
66 [4]:42 [·]:
67 quantiles·=·np.arange(0.05,·0.96,·0.1)43 quantiles·=·np.arange(0.05,·0.96,·0.1)
  
  
68 def·fit_model(q):44 def·fit_model(q):
69 ····res·=·mod.fit(q=q)45 ····res·=·mod.fit(q=q)
70 ····return·[q,·res.params["Intercept"],·res.params["income"]]·+·res.conf_int46 ····return·[q,·res.params["Intercept"],·res.params["income"]]·+·res.conf_int
71 ().loc[47 ().loc[
Offset 85, 35 lines modifiedOffset 60, 22 lines modified
85 ols·=·dict(60 ols·=·dict(
86 ····a=ols.params["Intercept"],·b=ols.params["income"],·lb=ols_ci[0],·ub=ols_ci61 ····a=ols.params["Intercept"],·b=ols.params["income"],·lb=ols_ci[0],·ub=ols_ci
87 [1]62 [1]
88 )63 )
  
89 print(models)64 print(models)
90 print(ols)65 print(ols)
91 ······q···········a·········b········lb········ub 
92 0··0.05··124.880100··0.343361··0.268632··0.418090 
93 1··0.15··111.693660··0.423708··0.382780··0.464636 
94 2··0.25···95.483539··0.474103··0.439900··0.508306 
95 3··0.35··105.841294··0.488901··0.457759··0.520043 
96 4··0.45···81.083647··0.552428··0.525021··0.579835 
97 5··0.55···89.661370··0.565601··0.540955··0.590247 
98 6··0.65···74.033434··0.604576··0.582169··0.626982 
99 7··0.75···62.396584··0.644014··0.622411··0.665617 
100 8··0.85···52.272216··0.677603··0.657383··0.697823 
101 9··0.95···64.103964··0.709069··0.687831··0.730306 
102 {'a':·np.float64(147.47538852370585),·'b':·np.float64(0.4851784236769239), 
103 'lb':·0.4568738130184236,·'ub':·0.5134830343354242} 
104 *\x8**\x8**\x8**\x8*·F\x8Fi\x8ir\x8rs\x8st\x8t·p\x8pl\x8lo\x8ot\x8t_\x8?\x8·*\x8**\x8**\x8**\x8*66 *\x8**\x8**\x8**\x8*·F\x8Fi\x8ir\x8rs\x8st\x8t·p\x8pl\x8lo\x8ot\x8t_\x8?\x8·*\x8**\x8**\x8**\x8*
105 This·plot·compares·best·fit·lines·for·10·quantile·regression·models·to·the67 This·plot·compares·best·fit·lines·for·10·quantile·regression·models·to·the
106 least·squares·fit.·As·Koenker·and·Hallock·(2001)·point·out,·we·see·that:68 least·squares·fit.·As·Koenker·and·Hallock·(2001)·point·out,·we·see·that:
107 ···1.·Food·expenditure·increases·with·income69 ···1.·Food·expenditure·increases·with·income
108 ···2.·The·d\x8di\x8is\x8sp\x8pe\x8er\x8rs\x8si\x8io\x8on\x8n·of·food·expenditure·increases·with·income70 ···2.·The·d\x8di\x8is\x8sp\x8pe\x8er\x8rs\x8si\x8io\x8on\x8n·of·food·expenditure·increases·with·income
109 ···3.·The·least·squares·estimates·fit·low·income·observations·quite·poorly71 ···3.·The·least·squares·estimates·fit·low·income·observations·quite·poorly
110 ······(i.e.·the·OLS·line·passes·over·most·low·income·households)72 ······(i.e.·the·OLS·line·passes·over·most·low·income·households)
111 [5]:73 [·]:
112 x·=·np.arange(data.income.min(),·data.income.max(),·50)74 x·=·np.arange(data.income.min(),·data.income.max(),·50)
113 get_y·=·lambda·a,·b:·a·+·b·*·x75 get_y·=·lambda·a,·b:·a·+·b·*·x
  
114 fig,·ax·=·plt.subplots(figsize=(8,·6))76 fig,·ax·=·plt.subplots(figsize=(8,·6))
  
115 for·i·in·range(models.shape[0]):77 for·i·in·range(models.shape[0]):
116 ····y·=·get_y(models.a[i],·models.b[i])78 ····y·=·get_y(models.a[i],·models.b[i])
Offset 124, 37 lines modifiedOffset 86, 33 lines modified
124 ax.plot(x,·y,·color="red",·label="OLS")86 ax.plot(x,·y,·color="red",·label="OLS")
125 ax.scatter(data.income,·data.foodexp,·alpha=0.2)87 ax.scatter(data.income,·data.foodexp,·alpha=0.2)
126 ax.set_xlim((240,·3000))88 ax.set_xlim((240,·3000))
127 ax.set_ylim((240,·2000))89 ax.set_ylim((240,·2000))
128 legend·=·ax.legend()90 legend·=·ax.legend()
129 ax.set_xlabel("Income",·fontsize=16)91 ax.set_xlabel("Income",·fontsize=16)
130 ax.set_ylabel("Food·expenditure",·fontsize=16)92 ax.set_ylabel("Food·expenditure",·fontsize=16)
131 [5]: 
132 Text(0,·0.5,·'Food·expenditure') 
133 [../../../_images/examples_notebooks_generated_quantile_regression_10_1.png] 
134 *\x8**\x8**\x8**\x8*·S\x8Se\x8ec\x8co\x8on\x8nd\x8d·p\x8pl\x8lo\x8ot\x8t_\x8?\x8·*\x8**\x8**\x8**\x8*93 *\x8**\x8**\x8**\x8*·S\x8Se\x8ec\x8co\x8on\x8nd\x8d·p\x8pl\x8lo\x8ot\x8t_\x8?\x8·*\x8**\x8**\x8**\x8*
135 The·dotted·black·lines·form·95%·point-wise·confidence·band·around·10·quantile94 The·dotted·black·lines·form·95%·point-wise·confidence·band·around·10·quantile
136 regression·estimates·(solid·black·line).·The·red·lines·represent·OLS·regression95 regression·estimates·(solid·black·line).·The·red·lines·represent·OLS·regression
137 results·along·with·their·95%·confidence·interval.96 results·along·with·their·95%·confidence·interval.
138 In·most·cases,·the·quantile·regression·point·estimates·lie·outside·the·OLS97 In·most·cases,·the·quantile·regression·point·estimates·lie·outside·the·OLS
139 confidence·interval,·which·suggests·that·the·effect·of·income·on·food98 confidence·interval,·which·suggests·that·the·effect·of·income·on·food
140 expenditure·may·not·be·constant·across·the·distribution.99 expenditure·may·not·be·constant·across·the·distribution.
141 [6]:100 [·]:
142 n·=·models.shape[0]101 n·=·models.shape[0]
143 p1·=·plt.plot(models.q,·models.b,·color="black",·label="Quantile·Reg.")102 p1·=·plt.plot(models.q,·models.b,·color="black",·label="Quantile·Reg.")
144 p2·=·plt.plot(models.q,·models.ub,·linestyle="dotted",·color="black")103 p2·=·plt.plot(models.q,·models.ub,·linestyle="dotted",·color="black")
145 p3·=·plt.plot(models.q,·models.lb,·linestyle="dotted",·color="black")104 p3·=·plt.plot(models.q,·models.lb,·linestyle="dotted",·color="black")
146 p4·=·plt.plot(models.q,·[ols["b"]]·*·n,·color="red",·label="OLS")105 p4·=·plt.plot(models.q,·[ols["b"]]·*·n,·color="red",·label="OLS")
147 p5·=·plt.plot(models.q,·[ols["lb"]]·*·n,·linestyle="dotted",·color="red")106 p5·=·plt.plot(models.q,·[ols["lb"]]·*·n,·linestyle="dotted",·color="red")
148 p6·=·plt.plot(models.q,·[ols["ub"]]·*·n,·linestyle="dotted",·color="red")107 p6·=·plt.plot(models.q,·[ols["ub"]]·*·n,·linestyle="dotted",·color="red")
149 plt.ylabel(r"$\beta_{income}$")108 plt.ylabel(r"$\beta_{income}$")
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60 ············60 ············
61 ··<section·id="Quasi-binomial-regression">61 ··<section·id="Quasi-binomial-regression">
62 <h1>Quasi-binomial·regression<a·class="headerlink"·href="#Quasi-binomial-regression"·title="Link·to·this·heading">¶</a></h1>62 <h1>Quasi-binomial·regression<a·class="headerlink"·href="#Quasi-binomial-regression"·title="Link·to·this·heading">¶</a></h1>
63 <p>This·notebook·demonstrates·using·custom·variance·functions·and·non-binary·data·with·the·quasi-binomial·GLM·family·to·perform·a·regression·analysis·using·a·dependent·variable·that·is·a·proportion.</p>63 <p>This·notebook·demonstrates·using·custom·variance·functions·and·non-binary·data·with·the·quasi-binomial·GLM·family·to·perform·a·regression·analysis·using·a·dependent·variable·that·is·a·proportion.</p>
64 <p>The·notebook·uses·the·barley·leaf·blotch·data·that·has·been·discussed·in·several·textbooks.·See·below·for·one·reference:</p>64 <p>The·notebook·uses·the·barley·leaf·blotch·data·that·has·been·discussed·in·several·textbooks.·See·below·for·one·reference:</p>
65 <p><a·class="reference·external"·href="https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glimmix_sect016.htm">https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glimmix_sect016.htm</a></p>65 <p><a·class="reference·external"·href="https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glimmix_sect016.htm">https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glimmix_sect016.htm</a></p>
66 <div·class="nbinput·nblast·docutils·container">66 <div·class="nbinput·nblast·docutils·container">
67 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:67 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>70 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
71 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>71 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
72 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>72 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
73 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>73 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
74 <span·class="kn">from</span>·<span·class="nn">io</span>·<span·class="kn">import</span>·<span·class="n">StringIO</span>74 <span·class="kn">from</span>·<span·class="nn">io</span>·<span·class="kn">import</span>·<span·class="n">StringIO</span>
75 </pre></div>75 </pre></div>
76 </div>76 </div>
77 </div>77 </div>
78 <p>The·raw·data,·expressed·as·percentages.·We·will·divide·by·100·to·obtain·proportions.</p>78 <p>The·raw·data,·expressed·as·percentages.·We·will·divide·by·100·to·obtain·proportions.</p>
79 <div·class="nbinput·nblast·docutils·container">79 <div·class="nbinput·nblast·docutils·container">
80 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:80 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
81 </pre></div>81 </pre></div>
82 </div>82 </div>
83 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">raw</span>·<span·class="o">=</span>·<span·class="n">StringIO</span><span·class="p">(</span>83 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">raw</span>·<span·class="o">=</span>·<span·class="n">StringIO</span><span·class="p">(</span>
84 <span·class="w">····</span><span·class="sd">&quot;&quot;&quot;0.05,0.00,1.25,2.50,5.50,1.00,5.00,5.00,17.50</span>84 <span·class="w">····</span><span·class="sd">&quot;&quot;&quot;0.05,0.00,1.25,2.50,5.50,1.00,5.00,5.00,17.50</span>
85 <span·class="sd">0.00,0.05,1.25,0.50,1.00,5.00,0.10,10.00,25.00</span>85 <span·class="sd">0.00,0.05,1.25,0.50,1.00,5.00,0.10,10.00,25.00</span>
86 <span·class="sd">0.00,0.05,2.50,0.01,6.00,5.00,5.00,5.00,42.50</span>86 <span·class="sd">0.00,0.05,2.50,0.01,6.00,5.00,5.00,5.00,42.50</span>
87 <span·class="sd">0.10,0.30,16.60,3.00,1.10,5.00,5.00,5.00,50.00</span>87 <span·class="sd">0.10,0.30,16.60,3.00,1.10,5.00,5.00,5.00,50.00</span>
Offset 93, 223 lines modifiedOffset 93, 93 lines modified
93 <span·class="sd">1.50,12.70,26.25,40.00,43.50,75.00,75.00,75.00,95.00&quot;&quot;&quot;</span>93 <span·class="sd">1.50,12.70,26.25,40.00,43.50,75.00,75.00,75.00,95.00&quot;&quot;&quot;</span>
94 <span·class="p">)</span>94 <span·class="p">)</span>
95 </pre></div>95 </pre></div>
96 </div>96 </div>
97 </div>97 </div>
98 <p>The·regression·model·is·a·two-way·additive·model·with·site·and·variety·effects.·The·data·are·a·full·unreplicated·design·with·10·rows·(sites)·and·9·columns·(varieties).</p>98 <p>The·regression·model·is·a·two-way·additive·model·with·site·and·variety·effects.·The·data·are·a·full·unreplicated·design·with·10·rows·(sites)·and·9·columns·(varieties).</p>
99 <div·class="nbinput·nblast·docutils·container">99 <div·class="nbinput·nblast·docutils·container">
100 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:100 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
101 </pre></div>101 </pre></div>
102 </div>102 </div>
103 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">read_csv</span><span·class="p">(</span><span·class="n">raw</span><span·class="p">,</span>·<span·class="n">header</span><span·class="o">=</span><span·class="kc">None</span><span·class="p">)</span>103 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">read_csv</span><span·class="p">(</span><span·class="n">raw</span><span·class="p">,</span>·<span·class="n">header</span><span·class="o">=</span><span·class="kc">None</span><span·class="p">)</span>
104 <span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">df</span><span·class="o">.</span><span·class="n">melt</span><span·class="p">()</span>104 <span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">df</span><span·class="o">.</span><span·class="n">melt</span><span·class="p">()</span>
105 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;site&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="mi">1</span>·<span·class="o">+</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">floor</span><span·class="p">(</span><span·class="n">df</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">/</span>·<span·class="mi">10</span><span·class="p">)</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>105 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;site&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="mi">1</span>·<span·class="o">+</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">floor</span><span·class="p">(</span><span·class="n">df</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">/</span>·<span·class="mi">10</span><span·class="p">)</span><span·class="o">.</span><span·class="n">astype</span><span·class="p">(</span><span·class="nb">int</span><span·class="p">)</span>
106 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;variety&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="mi">1</span>·<span·class="o">+</span>·<span·class="p">(</span><span·class="n">df</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">%</span>·<span·class="mi">10</span><span·class="p">)</span>106 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;variety&quot;</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="mi">1</span>·<span·class="o">+</span>·<span·class="p">(</span><span·class="n">df</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">%</span>·<span·class="mi">10</span><span·class="p">)</span>
107 <span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">df</span><span·class="o">.</span><span·class="n">rename</span><span·class="p">(</span><span·class="n">columns</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;value&quot;</span><span·class="p">:</span>·<span·class="s2">&quot;blotch&quot;</span><span·class="p">})</span>107 <span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">df</span><span·class="o">.</span><span·class="n">rename</span><span·class="p">(</span><span·class="n">columns</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;value&quot;</span><span·class="p">:</span>·<span·class="s2">&quot;blotch&quot;</span><span·class="p">})</span>
108 <span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">df</span><span·class="o">.</span><span·class="n">drop</span><span·class="p">(</span><span·class="s2">&quot;variable&quot;</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">)</span>108 <span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">df</span><span·class="o">.</span><span·class="n">drop</span><span·class="p">(</span><span·class="s2">&quot;variable&quot;</span><span·class="p">,</span>·<span·class="n">axis</span><span·class="o">=</span><span·class="mi">1</span><span·class="p">)</span>
109 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;blotch&quot;</span><span·class="p">]</span>·<span·class="o">/=</span>·<span·class="mi">100</span>109 <span·class="n">df</span><span·class="p">[</span><span·class="s2">&quot;blotch&quot;</span><span·class="p">]</span>·<span·class="o">/=</span>·<span·class="mi">100</span>
110 </pre></div>110 </pre></div>
111 </div>111 </div>
112 </div>112 </div>
113 <p>Fit·the·quasi-binomial·regression·with·the·standard·variance·function.</p>113 <p>Fit·the·quasi-binomial·regression·with·the·standard·variance·function.</p>
114 <div·class="nbinput·docutils·container">114 <div·class="nbinput·nblast·docutils·container">
115 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:115 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
116 </pre></div>116 </pre></div>
117 </div>117 </div>
118 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">model1</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">GLM</span><span·class="o">.</span><span·class="n">from_formula</span><span·class="p">(</span>118 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">model1</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">GLM</span><span·class="o">.</span><span·class="n">from_formula</span><span·class="p">(</span>
119 ····<span·class="s2">&quot;blotch·~·0·+·C(variety)·+·C(site)&quot;</span><span·class="p">,</span>·<span·class="n">family</span><span·class="o">=</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">families</span><span·class="o">.</span><span·class="n">Binomial</span><span·class="p">(),</span>·<span·class="n">data</span><span·class="o">=</span><span·class="n">df</span>119 ····<span·class="s2">&quot;blotch·~·0·+·C(variety)·+·C(site)&quot;</span><span·class="p">,</span>·<span·class="n">family</span><span·class="o">=</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">families</span><span·class="o">.</span><span·class="n">Binomial</span><span·class="p">(),</span>·<span·class="n">data</span><span·class="o">=</span><span·class="n">df</span>
120 <span·class="p">)</span>120 <span·class="p">)</span>
121 <span·class="n">result1</span>·<span·class="o">=</span>·<span·class="n">model1</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">scale</span><span·class="o">=</span><span·class="s2">&quot;X2&quot;</span><span·class="p">)</span>121 <span·class="n">result1</span>·<span·class="o">=</span>·<span·class="n">model1</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">scale</span><span·class="o">=</span><span·class="s2">&quot;X2&quot;</span><span·class="p">)</span>
122 <span·class="nb">print</span><span·class="p">(</span><span·class="n">result1</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>122 <span·class="nb">print</span><span·class="p">(</span><span·class="n">result1</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
123 </pre></div>123 </pre></div>
124 </div>124 </div>
125 </div>125 </div>
126 <div·class="nboutput·nblast·docutils·container"> 
127 <div·class="prompt·empty·docutils·container"> 
128 </div> 
129 <div·class="output_area·docutils·container"> 
130 <div·class="highlight"><pre> 
131 ·················Generalized·Linear·Model·Regression·Results 
132 ============================================================================== 
133 Dep.·Variable:·················blotch···No.·Observations:···················90 
134 Model:····························GLM···Df·Residuals:·······················72 
135 Model·Family:················Binomial···Df·Model:···························17 
136 Link·Function:··················Logit···Scale:························0.088778 
137 Method:··························IRLS···Log-Likelihood:················-20.791 
138 Date:················Sun,·10·Aug·2025···Deviance:·······················6.1260 
139 Time:························13:13:47···Pearson·chi2:·····················6.39 
140 No.·Iterations:····················10···Pseudo·R-squ.·(CS):·············0.3198 
141 Covariance·Type:············nonrobust 
142 ================================================================================== 
143 ·····················coef····std·err··········z······P&gt;|z|······[0.025······0.975] 
144 ---------------------------------------------------------------------------------- 
145 C(variety)[1]·····-8.0546······1.422·····-5.664······0.000·····-10.842······-5.268 
146 C(variety)[2]·····-7.9046······1.412·····-5.599······0.000·····-10.672······-5.138 
147 C(variety)[3]·····-7.3652······1.384·····-5.321······0.000·····-10.078······-4.652 
148 C(variety)[4]·····-7.0065······1.372·····-5.109······0.000······-9.695······-4.318 
149 C(variety)[5]·····-6.4399······1.357·····-4.746······0.000······-9.100······-3.780 
150 C(variety)[6]·····-5.6835······1.344·····-4.230······0.000······-8.317······-3.050 
151 C(variety)[7]·····-5.4841······1.341·····-4.090······0.000······-8.112······-2.856 
152 C(variety)[8]·····-4.7126······1.331·····-3.539······0.000······-7.322······-2.103 
153 C(variety)[9]·····-4.5546······1.330·····-3.425······0.001······-7.161······-1.948 
154 C(variety)[10]····-3.8016······1.320·····-2.881······0.004······-6.388······-1.215 
155 C(site)[T.2]·······1.6391······1.443······1.136······0.256······-1.190·······4.468 
156 C(site)[T.3]·······3.3265······1.349······2.466······0.014·······0.682·······5.971 
157 C(site)[T.4]·······3.5822······1.344······2.664······0.008·······0.947·······6.217 
158 C(site)[T.5]·······3.5831······1.344······2.665······0.008·······0.948·······6.218 
159 C(site)[T.6]·······3.8933······1.340······2.905······0.004·······1.266·······6.520 
160 C(site)[T.7]·······4.7300······1.335······3.544······0.000·······2.114·······7.346 
161 C(site)[T.8]·······5.5227······1.335······4.138······0.000·······2.907·······8.139 
162 C(site)[T.9]·······6.7946······1.341······5.068······0.000·······4.167·······9.422 
163 ================================================================================== 
164 </pre></div></div> 
165 </div> 
166 <p>The·plot·below·shows·that·the·default·variance·function·is·not·capturing·the·variance·structure·very·well.·Also·note·that·the·scale·parameter·estimate·is·quite·small.</p>126 <p>The·plot·below·shows·that·the·default·variance·function·is·not·capturing·the·variance·structure·very·well.·Also·note·that·the·scale·parameter·estimate·is·quite·small.</p>
167 <div·class="nbinput·docutils·container">127 <div·class="nbinput·nblast·docutils·container">
168 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:128 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
169 </pre></div>129 </pre></div>
170 </div>130 </div>
171 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">plt</span><span·class="o">.</span><span·class="n">clf</span><span·class="p">()</span>131 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">plt</span><span·class="o">.</span><span·class="n">clf</span><span·class="p">()</span>
172 <span·class="n">plt</span><span·class="o">.</span><span·class="n">grid</span><span·class="p">(</span><span·class="kc">True</span><span·class="p">)</span>132 <span·class="n">plt</span><span·class="o">.</span><span·class="n">grid</span><span·class="p">(</span><span·class="kc">True</span><span·class="p">)</span>
173 <span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">result1</span><span·class="o">.</span><span·class="n">predict</span><span·class="p">(</span><span·class="n">linear</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">),</span>·<span·class="n">result1</span><span·class="o">.</span><span·class="n">resid_pearson</span><span·class="p">,</span>·<span·class="s2">&quot;o&quot;</span><span·class="p">)</span>133 <span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">result1</span><span·class="o">.</span><span·class="n">predict</span><span·class="p">(</span><span·class="n">linear</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">),</span>·<span·class="n">result1</span><span·class="o">.</span><span·class="n">resid_pearson</span><span·class="p">,</span>·<span·class="s2">&quot;o&quot;</span><span·class="p">)</span>
174 <span·class="n">plt</span><span·class="o">.</span><span·class="n">xlabel</span><span·class="p">(</span><span·class="s2">&quot;Linear·predictor&quot;</span><span·class="p">)</span>134 <span·class="n">plt</span><span·class="o">.</span><span·class="n">xlabel</span><span·class="p">(</span><span·class="s2">&quot;Linear·predictor&quot;</span><span·class="p">)</span>
175 <span·class="n">plt</span><span·class="o">.</span><span·class="n">ylabel</span><span·class="p">(</span><span·class="s2">&quot;Residual&quot;</span><span·class="p">)</span>135 <span·class="n">plt</span><span·class="o">.</span><span·class="n">ylabel</span><span·class="p">(</span><span·class="s2">&quot;Residual&quot;</span><span·class="p">)</span>
176 </pre></div>136 </pre></div>
177 </div>137 </div>
178 </div>138 </div>
179 <div·class="nboutput·docutils·container"> 
180 <div·class="prompt·empty·docutils·container"> 
181 </div> 
182 <div·class="output_area·stderr·docutils·container"> 
183 <div·class="highlight"><pre> 
184 /usr/lib/python3/dist-packages/statsmodels/genmod/generalized_linear_model.py:985:·FutureWarning:·linear·keyword·is·deprecated,·use·which=&#34;linear&#34; 
185 ··warnings.warn(msg,·FutureWarning) 
186 </pre></div></div> 
187 </div> 
188 <div·class="nboutput·docutils·container"> 
189 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]: 
190 </pre></div> 
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10 This·notebook·demonstrates·using·custom·variance·functions·and·non-binary·data10 This·notebook·demonstrates·using·custom·variance·functions·and·non-binary·data
11 with·the·quasi-binomial·GLM·family·to·perform·a·regression·analysis·using·a11 with·the·quasi-binomial·GLM·family·to·perform·a·regression·analysis·using·a
12 dependent·variable·that·is·a·proportion.12 dependent·variable·that·is·a·proportion.
13 The·notebook·uses·the·barley·leaf·blotch·data·that·has·been·discussed·in13 The·notebook·uses·the·barley·leaf·blotch·data·that·has·been·discussed·in
14 several·textbooks.·See·below·for·one·reference:14 several·textbooks.·See·below·for·one·reference:
15 _\x8h_\x8t_\x8t_\x8p_\x8s_\x8:_\x8/_\x8/_\x8s_\x8u_\x8p_\x8p_\x8o_\x8r_\x8t_\x8._\x8s_\x8a_\x8s_\x8._\x8c_\x8o_\x8m_\x8/_\x8d_\x8o_\x8c_\x8u_\x8m_\x8e_\x8n_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n_\x8/_\x8c_\x8d_\x8l_\x8/_\x8e_\x8n_\x8/_\x8s_\x8t_\x8a_\x8t_\x8u_\x8g_\x8/_\x86_\x83_\x80_\x83_\x83_\x8/_\x8H_\x8T_\x8M_\x8L_\x8/_\x8d_\x8e_\x8f_\x8a_\x8u_\x8l_\x8t_\x8/15 _\x8h_\x8t_\x8t_\x8p_\x8s_\x8:_\x8/_\x8/_\x8s_\x8u_\x8p_\x8p_\x8o_\x8r_\x8t_\x8._\x8s_\x8a_\x8s_\x8._\x8c_\x8o_\x8m_\x8/_\x8d_\x8o_\x8c_\x8u_\x8m_\x8e_\x8n_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n_\x8/_\x8c_\x8d_\x8l_\x8/_\x8e_\x8n_\x8/_\x8s_\x8t_\x8a_\x8t_\x8u_\x8g_\x8/_\x86_\x83_\x80_\x83_\x83_\x8/_\x8H_\x8T_\x8M_\x8L_\x8/_\x8d_\x8e_\x8f_\x8a_\x8u_\x8l_\x8t_\x8/
16 _\x8v_\x8i_\x8e_\x8w_\x8e_\x8r_\x8._\x8h_\x8t_\x8m_\x8#_\x8s_\x8t_\x8a_\x8t_\x8u_\x8g_\x8__\x8g_\x8l_\x8i_\x8m_\x8m_\x8i_\x8x_\x8__\x8s_\x8e_\x8c_\x8t_\x80_\x81_\x86_\x8._\x8h_\x8t_\x8m16 _\x8v_\x8i_\x8e_\x8w_\x8e_\x8r_\x8._\x8h_\x8t_\x8m_\x8#_\x8s_\x8t_\x8a_\x8t_\x8u_\x8g_\x8__\x8g_\x8l_\x8i_\x8m_\x8m_\x8i_\x8x_\x8__\x8s_\x8e_\x8c_\x8t_\x80_\x81_\x86_\x8._\x8h_\x8t_\x8m
17 [1]:17 [·]:
18 import·statsmodels.api·as·sm18 import·statsmodels.api·as·sm
19 import·numpy·as·np19 import·numpy·as·np
20 import·pandas·as·pd20 import·pandas·as·pd
21 import·matplotlib.pyplot·as·plt21 import·matplotlib.pyplot·as·plt
22 from·io·import·StringIO22 from·io·import·StringIO
23 The·raw·data,·expressed·as·percentages.·We·will·divide·by·100·to·obtain23 The·raw·data,·expressed·as·percentages.·We·will·divide·by·100·to·obtain
24 proportions.24 proportions.
25 [2]:25 [·]:
26 raw·=·StringIO(26 raw·=·StringIO(
27 ····"""0.05,0.00,1.25,2.50,5.50,1.00,5.00,5.00,17.5027 ····"""0.05,0.00,1.25,2.50,5.50,1.00,5.00,5.00,17.50
28 0.00,0.05,1.25,0.50,1.00,5.00,0.10,10.00,25.0028 0.00,0.05,1.25,0.50,1.00,5.00,0.10,10.00,25.00
29 0.00,0.05,2.50,0.01,6.00,5.00,5.00,5.00,42.5029 0.00,0.05,2.50,0.01,6.00,5.00,5.00,5.00,42.50
30 0.10,0.30,16.60,3.00,1.10,5.00,5.00,5.00,50.0030 0.10,0.30,16.60,3.00,1.10,5.00,5.00,5.00,50.00
31 0.25,0.75,2.50,2.50,2.50,5.00,50.00,25.00,37.5031 0.25,0.75,2.50,2.50,2.50,5.00,50.00,25.00,37.50
32 0.05,0.30,2.50,0.01,8.00,5.00,10.00,75.00,95.0032 0.05,0.30,2.50,0.01,8.00,5.00,10.00,75.00,95.00
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34 1.30,7.50,20.00,55.00,29.50,5.00,25.00,75.00,95.0034 1.30,7.50,20.00,55.00,29.50,5.00,25.00,75.00,95.00
35 1.50,1.00,37.50,5.00,20.00,50.00,50.00,75.00,95.0035 1.50,1.00,37.50,5.00,20.00,50.00,50.00,75.00,95.00
36 1.50,12.70,26.25,40.00,43.50,75.00,75.00,75.00,95.00"""36 1.50,12.70,26.25,40.00,43.50,75.00,75.00,75.00,95.00"""
37 )37 )
38 The·regression·model·is·a·two-way·additive·model·with·site·and·variety·effects.38 The·regression·model·is·a·two-way·additive·model·with·site·and·variety·effects.
39 The·data·are·a·full·unreplicated·design·with·10·rows·(sites)·and·9·columns39 The·data·are·a·full·unreplicated·design·with·10·rows·(sites)·and·9·columns
40 (varieties).40 (varieties).
41 [3]:41 [·]:
42 df·=·pd.read_csv(raw,·header=None)42 df·=·pd.read_csv(raw,·header=None)
43 df·=·df.melt()43 df·=·df.melt()
44 df["site"]·=·1·+·np.floor(df.index·/·10).astype(int)44 df["site"]·=·1·+·np.floor(df.index·/·10).astype(int)
45 df["variety"]·=·1·+·(df.index·%·10)45 df["variety"]·=·1·+·(df.index·%·10)
46 df·=·df.rename(columns={"value":·"blotch"})46 df·=·df.rename(columns={"value":·"blotch"})
47 df·=·df.drop("variable",·axis=1)47 df·=·df.drop("variable",·axis=1)
48 df["blotch"]·/=·10048 df["blotch"]·/=·100
49 Fit·the·quasi-binomial·regression·with·the·standard·variance·function.49 Fit·the·quasi-binomial·regression·with·the·standard·variance·function.
50 [4]:50 [·]:
51 model1·=·sm.GLM.from_formula(51 model1·=·sm.GLM.from_formula(
52 ····"blotch·~·0·+·C(variety)·+·C(site)",·family=sm.families.Binomial(),·data=df52 ····"blotch·~·0·+·C(variety)·+·C(site)",·family=sm.families.Binomial(),·data=df
53 )53 )
54 result1·=·model1.fit(scale="X2")54 result1·=·model1.fit(scale="X2")
55 print(result1.summary())55 print(result1.summary())
56 ·················Generalized·Linear·Model·Regression·Results 
57 ============================================================================== 
58 Dep.·Variable:·················blotch···No.·Observations:···················90 
59 Model:····························GLM···Df·Residuals:·······················72 
60 Model·Family:················Binomial···Df·Model:···························17 
61 Link·Function:··················Logit···Scale:························0.088778 
62 Method:··························IRLS···Log-Likelihood:················-20.791 
63 Date:················Sun,·10·Aug·2025···Deviance:·······················6.1260 
64 Time:························13:13:47···Pearson·chi2:·····················6.39 
65 No.·Iterations:····················10···Pseudo·R-squ.·(CS):·············0.3198 
66 Covariance·Type:············nonrobust 
67 ================================================================================== 
68 ·····················coef····std·err··········z······P>|z|······[0.025 
69 0.975] 
70 ------------------------------------------------------------------------------- 
71 --- 
72 C(variety)[1]·····-8.0546······1.422·····-5.664······0.000·····-10.842······- 
73 5.268 
74 C(variety)[2]·····-7.9046······1.412·····-5.599······0.000·····-10.672······- 
75 5.138 
76 C(variety)[3]·····-7.3652······1.384·····-5.321······0.000·····-10.078······- 
77 4.652 
78 C(variety)[4]·····-7.0065······1.372·····-5.109······0.000······-9.695······- 
79 4.318 
80 C(variety)[5]·····-6.4399······1.357·····-4.746······0.000······-9.100······- 
81 3.780 
82 C(variety)[6]·····-5.6835······1.344·····-4.230······0.000······-8.317······- 
83 3.050 
84 C(variety)[7]·····-5.4841······1.341·····-4.090······0.000······-8.112······- 
85 2.856 
86 C(variety)[8]·····-4.7126······1.331·····-3.539······0.000······-7.322······- 
87 2.103 
88 C(variety)[9]·····-4.5546······1.330·····-3.425······0.001······-7.161······- 
89 1.948 
90 C(variety)[10]····-3.8016······1.320·····-2.881······0.004······-6.388······- 
91 1.215 
92 C(site)[T.2]·······1.6391······1.443······1.136······0.256······-1.190 
93 4.468 
94 C(site)[T.3]·······3.3265······1.349······2.466······0.014·······0.682 
95 5.971 
96 C(site)[T.4]·······3.5822······1.344······2.664······0.008·······0.947 
97 6.217 
98 C(site)[T.5]·······3.5831······1.344······2.665······0.008·······0.948 
99 6.218 
100 C(site)[T.6]·······3.8933······1.340······2.905······0.004·······1.266 
101 6.520 
102 C(site)[T.7]·······4.7300······1.335······3.544······0.000·······2.114 
103 7.346 
104 C(site)[T.8]·······5.5227······1.335······4.138······0.000·······2.907 
105 8.139 
106 C(site)[T.9]·······6.7946······1.341······5.068······0.000·······4.167 
107 9.422 
108 ================================================================================== 
109 The·plot·below·shows·that·the·default·variance·function·is·not·capturing·the56 The·plot·below·shows·that·the·default·variance·function·is·not·capturing·the
110 variance·structure·very·well.·Also·note·that·the·scale·parameter·estimate·is57 variance·structure·very·well.·Also·note·that·the·scale·parameter·estimate·is
111 quite·small.58 quite·small.
112 [5]:59 [·]:
113 plt.clf()60 plt.clf()
114 plt.grid(True)61 plt.grid(True)
115 plt.plot(result1.predict(linear=True),·result1.resid_pearson,·"o")62 plt.plot(result1.predict(linear=True),·result1.resid_pearson,·"o")
116 plt.xlabel("Linear·predictor")63 plt.xlabel("Linear·predictor")
117 plt.ylabel("Residual")64 plt.ylabel("Residual")
118 /usr/lib/python3/dist-packages/statsmodels/genmod/generalized_linear_model.py: 
119 985:·FutureWarning:·linear·keyword·is·deprecated,·use·which="linear" 
120 ··warnings.warn(msg,·FutureWarning) 
121 [5]: 
122 Text(0,·0.5,·'Residual') 
123 [../../../_images/examples_notebooks_generated_quasibinomial_9_2.png] 
124 An·alternative·variance·function·is·mu^2·*·(1·-·mu)^2.65 An·alternative·variance·function·is·mu^2·*·(1·-·mu)^2.
125 [6]:66 [·]:
126 class·vf(sm.families.varfuncs.VarianceFunction):67 class·vf(sm.families.varfuncs.VarianceFunction):
127 ····def·__call__(self,·mu):68 ····def·__call__(self,·mu):
128 ········return·mu·**·2·*·(1·-·mu)·**·269 ········return·mu·**·2·*·(1·-·mu)·**·2
  
129 ····def·deriv(self,·mu):70 ····def·deriv(self,·mu):
130 ········return·2·*·mu·-·6·*·mu·**·2·+·4·*·mu·**·371 ········return·2·*·mu·-·6·*·mu·**·2·+·4·*·mu·**·3
131 Fit·the·quasi-binomial·regression·with·the·alternative·variance·function.72 Fit·the·quasi-binomial·regression·with·the·alternative·variance·function.
132 [7]:73 [·]:
133 bin·=·sm.families.Binomial()74 bin·=·sm.families.Binomial()
134 bin.variance·=·vf()75 bin.variance·=·vf()
135 model2·=·sm.GLM.from_formula("blotch·~·0·+·C(variety)·+·C(site)",·family=bin,76 model2·=·sm.GLM.from_formula("blotch·~·0·+·C(variety)·+·C(site)",·family=bin,
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61 ··<section·id="Regression-diagnostics">61 ··<section·id="Regression-diagnostics">
62 <h1>Regression·diagnostics<a·class="headerlink"·href="#Regression-diagnostics"·title="Link·to·this·heading">¶</a></h1>62 <h1>Regression·diagnostics<a·class="headerlink"·href="#Regression-diagnostics"·title="Link·to·this·heading">¶</a></h1>
63 <p>This·example·file·shows·how·to·use·a·few·of·the·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>·regression·diagnostic·tests·in·a·real-life·context.·You·can·learn·about·more·tests·and·find·out·more·information·about·the·tests·here·on·the·<a·class="reference·external"·href="https://www.statsmodels.org/stable/diagnostic.html">Regression·Diagnostics·page.</a></p>63 <p>This·example·file·shows·how·to·use·a·few·of·the·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>·regression·diagnostic·tests·in·a·real-life·context.·You·can·learn·about·more·tests·and·find·out·more·information·about·the·tests·here·on·the·<a·class="reference·external"·href="https://www.statsmodels.org/stable/diagnostic.html">Regression·Diagnostics·page.</a></p>
64 <p>Note·that·most·of·the·tests·described·here·only·return·a·tuple·of·numbers,·without·any·annotation.·A·full·description·of·outputs·is·always·included·in·the·docstring·and·in·the·online·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>·documentation.·For·presentation·purposes,·we·use·the·<code·class="docutils·literal·notranslate"><span·class="pre">zip(name,test)</span></code>·construct·to·pretty-print·short·descriptions·in·the·examples·below.</p>64 <p>Note·that·most·of·the·tests·described·here·only·return·a·tuple·of·numbers,·without·any·annotation.·A·full·description·of·outputs·is·always·included·in·the·docstring·and·in·the·online·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels</span></code>·documentation.·For·presentation·purposes,·we·use·the·<code·class="docutils·literal·notranslate"><span·class="pre">zip(name,test)</span></code>·construct·to·pretty-print·short·descriptions·in·the·examples·below.</p>
65 <section·id="Estimate-a-regression-model">65 <section·id="Estimate-a-regression-model">
66 <h2>Estimate·a·regression·model<a·class="headerlink"·href="#Estimate-a-regression-model"·title="Link·to·this·heading">¶</a></h2>66 <h2>Estimate·a·regression·model<a·class="headerlink"·href="#Estimate-a-regression-model"·title="Link·to·this·heading">¶</a></h2>
67 <div·class="nbinput·nblast·docutils·container">67 <div·class="nbinput·nblast·docutils·container">
68 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:68 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
69 </pre></div>69 </pre></div>
70 </div>70 </div>
71 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline71 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
72 </pre></div>72 </pre></div>
73 </div>73 </div>
74 </div>74 </div>
75 <div·class="nbinput·docutils·container">75 <div·class="nbinput·nblast·docutils·container">
76 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:76 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
77 </pre></div>77 </pre></div>
78 </div>78 </div>
79 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.compat</span>·<span·class="kn">import</span>·<span·class="n">lzip</span>79 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.compat</span>·<span·class="kn">import</span>·<span·class="n">lzip</span>
  
80 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>80 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
81 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>81 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
82 <span·class="kn">import</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="k">as</span>·<span·class="nn">smf</span>82 <span·class="kn">import</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="k">as</span>·<span·class="nn">smf</span>
Offset 92, 235 lines modifiedOffset 92, 119 lines modified
92 <span·class="n">results</span>·<span·class="o">=</span>·<span·class="n">smf</span><span·class="o">.</span><span·class="n">ols</span><span·class="p">(</span><span·class="s2">&quot;Lottery·~·Literacy·+·np.log(Pop1831)&quot;</span><span·class="p">,</span>·<span·class="n">data</span><span·class="o">=</span><span·class="n">dat</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>92 <span·class="n">results</span>·<span·class="o">=</span>·<span·class="n">smf</span><span·class="o">.</span><span·class="n">ols</span><span·class="p">(</span><span·class="s2">&quot;Lottery·~·Literacy·+·np.log(Pop1831)&quot;</span><span·class="p">,</span>·<span·class="n">data</span><span·class="o">=</span><span·class="n">dat</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
  
93 <span·class="c1">#·Inspect·the·results</span>93 <span·class="c1">#·Inspect·the·results</span>
94 <span·class="nb">print</span><span·class="p">(</span><span·class="n">results</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>94 <span·class="nb">print</span><span·class="p">(</span><span·class="n">results</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
95 </pre></div>95 </pre></div>
96 </div>96 </div>
97 </div>97 </div>
98 <div·class="nboutput·nblast·docutils·container"> 
99 <div·class="prompt·empty·docutils·container"> 
100 </div> 
101 <div·class="output_area·docutils·container"> 
102 <div·class="highlight"><pre> 
103 ····························OLS·Regression·Results 
104 ============================================================================== 
105 Dep.·Variable:················Lottery···R-squared:·······················0.348 
106 Model:····························OLS···Adj.·R-squared:··················0.333 
107 Method:·················Least·Squares···F-statistic:·····················22.20 
108 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········1.90e-08 
109 Time:························13:13:47···Log-Likelihood:················-379.82 
110 No.·Observations:··················86···AIC:·····························765.6 
111 Df·Residuals:······················83···BIC:·····························773.0 
112 Df·Model:···························2 
113 Covariance·Type:············nonrobust 
114 =================================================================================== 
115 ······················coef····std·err··········t······P&gt;|t|······[0.025······0.975] 
116 ----------------------------------------------------------------------------------- 
117 Intercept·········246.4341·····35.233······6.995······0.000·····176.358·····316.510 
118 Literacy···········-0.4889······0.128·····-3.832······0.000······-0.743······-0.235 
119 np.log(Pop1831)···-31.3114······5.977·····-5.239······0.000·····-43.199·····-19.424 
120 ============================================================================== 
121 Omnibus:························3.713···Durbin-Watson:···················2.019 
122 Prob(Omnibus):··················0.156···Jarque-Bera·(JB):················3.394 
123 Skew:··························-0.487···Prob(JB):························0.183 
124 Kurtosis:·······················3.003···Cond.·No.·························702. 
125 ============================================================================== 
  
126 Notes: 
127 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified. 
128 </pre></div></div> 
129 </div> 
130 </section>98 </section>
131 <section·id="Normality-of-the-residuals">99 <section·id="Normality-of-the-residuals">
132 <h2>Normality·of·the·residuals<a·class="headerlink"·href="#Normality-of-the-residuals"·title="Link·to·this·heading">¶</a></h2>100 <h2>Normality·of·the·residuals<a·class="headerlink"·href="#Normality-of-the-residuals"·title="Link·to·this·heading">¶</a></h2>
133 <p>Jarque-Bera·test:</p>101 <p>Jarque-Bera·test:</p>
134 <div·class="nbinput·docutils·container">102 <div·class="nbinput·nblast·docutils·container">
135 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:103 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
136 </pre></div>104 </pre></div>
137 </div>105 </div>
138 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">name</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;Jarque-Bera&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Chi^2·two-tail·prob.&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Skew&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Kurtosis&quot;</span><span·class="p">]</span>106 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">name</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;Jarque-Bera&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Chi^2·two-tail·prob.&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Skew&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Kurtosis&quot;</span><span·class="p">]</span>
139 <span·class="n">test</span>·<span·class="o">=</span>·<span·class="n">sms</span><span·class="o">.</span><span·class="n">jarque_bera</span><span·class="p">(</span><span·class="n">results</span><span·class="o">.</span><span·class="n">resid</span><span·class="p">)</span>107 <span·class="n">test</span>·<span·class="o">=</span>·<span·class="n">sms</span><span·class="o">.</span><span·class="n">jarque_bera</span><span·class="p">(</span><span·class="n">results</span><span·class="o">.</span><span·class="n">resid</span><span·class="p">)</span>
140 <span·class="n">lzip</span><span·class="p">(</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">test</span><span·class="p">)</span>108 <span·class="n">lzip</span><span·class="p">(</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">test</span><span·class="p">)</span>
141 </pre></div>109 </pre></div>
142 </div>110 </div>
143 </div>111 </div>
144 <div·class="nboutput·nblast·docutils·container"> 
145 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]: 
146 </pre></div> 
147 </div> 
148 <div·class="output_area·docutils·container"> 
149 <div·class="highlight"><pre> 
150 [(&#39;Jarque-Bera&#39;,·np.float64(3.393608024843183)), 
151 ·(&#39;Chi^2·two-tail·prob.&#39;,·np.float64(0.18326831231663213)), 
152 ·(&#39;Skew&#39;,·np.float64(-0.4865803431122349)), 
153 ·(&#39;Kurtosis&#39;,·np.float64(3.0034177578816337))] 
154 </pre></div></div> 
155 </div> 
156 <p>Omni·test:</p>112 <p>Omni·test:</p>
157 <div·class="nbinput·docutils·container">113 <div·class="nbinput·nblast·docutils·container">
158 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:114 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
159 </pre></div>115 </pre></div>
160 </div>116 </div>
161 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">name</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;Chi^2&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Two-tail·probability&quot;</span><span·class="p">]</span>117 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">name</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;Chi^2&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Two-tail·probability&quot;</span><span·class="p">]</span>
162 <span·class="n">test</span>·<span·class="o">=</span>·<span·class="n">sms</span><span·class="o">.</span><span·class="n">omni_normtest</span><span·class="p">(</span><span·class="n">results</span><span·class="o">.</span><span·class="n">resid</span><span·class="p">)</span>118 <span·class="n">test</span>·<span·class="o">=</span>·<span·class="n">sms</span><span·class="o">.</span><span·class="n">omni_normtest</span><span·class="p">(</span><span·class="n">results</span><span·class="o">.</span><span·class="n">resid</span><span·class="p">)</span>
163 <span·class="n">lzip</span><span·class="p">(</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">test</span><span·class="p">)</span>119 <span·class="n">lzip</span><span·class="p">(</span><span·class="n">name</span><span·class="p">,</span>·<span·class="n">test</span><span·class="p">)</span>
164 </pre></div>120 </pre></div>
165 </div>121 </div>
166 </div>122 </div>
167 <div·class="nboutput·nblast·docutils·container"> 
168 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]: 
169 </pre></div> 
170 </div> 
171 <div·class="output_area·docutils·container"> 
172 <div·class="highlight"><pre> 
173 [(&#39;Chi^2&#39;,·np.float64(3.713437811597197)), 
174 ·(&#39;Two-tail·probability&#39;,·np.float64(0.15618424580304707))] 
175 </pre></div></div> 
176 </div> 
177 </section>123 </section>
178 <section·id="Influence-tests">124 <section·id="Influence-tests">
179 <h2>Influence·tests<a·class="headerlink"·href="#Influence-tests"·title="Link·to·this·heading">¶</a></h2>125 <h2>Influence·tests<a·class="headerlink"·href="#Influence-tests"·title="Link·to·this·heading">¶</a></h2>
180 <p>Once·created,·an·object·of·class·<code·class="docutils·literal·notranslate"><span·class="pre">OLSInfluence</span></code>·holds·attributes·and·methods·that·allow·users·to·assess·the·influence·of·each·observation.·For·example,·we·can·compute·and·extract·the·first·few·rows·of·DFbetas·by:</p>126 <p>Once·created,·an·object·of·class·<code·class="docutils·literal·notranslate"><span·class="pre">OLSInfluence</span></code>·holds·attributes·and·methods·that·allow·users·to·assess·the·influence·of·each·observation.·For·example,·we·can·compute·and·extract·the·first·few·rows·of·DFbetas·by:</p>
181 <div·class="nbinput·docutils·container">127 <div·class="nbinput·nblast·docutils·container">
182 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:128 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
183 </pre></div>129 </pre></div>
184 </div>130 </div>
185 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.stats.outliers_influence</span>·<span·class="kn">import</span>·<span·class="n">OLSInfluence</span>131 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.stats.outliers_influence</span>·<span·class="kn">import</span>·<span·class="n">OLSInfluence</span>
  
186 <span·class="n">test_class</span>·<span·class="o">=</span>·<span·class="n">OLSInfluence</span><span·class="p">(</span><span·class="n">results</span><span·class="p">)</span>132 <span·class="n">test_class</span>·<span·class="o">=</span>·<span·class="n">OLSInfluence</span><span·class="p">(</span><span·class="n">results</span><span·class="p">)</span>
187 <span·class="n">test_class</span><span·class="o">.</span><span·class="n">dfbetas</span><span·class="p">[:</span><span·class="mi">5</span><span·class="p">,</span>·<span·class="p">:]</span>133 <span·class="n">test_class</span><span·class="o">.</span><span·class="n">dfbetas</span><span·class="p">[:</span><span·class="mi">5</span><span·class="p">,</span>·<span·class="p">:]</span>
188 </pre></div>134 </pre></div>
189 </div>135 </div>
190 </div>136 </div>
191 <div·class="nboutput·nblast·docutils·container"> 
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13 _\x8p_\x8a_\x8g_\x8e_\x8.13 _\x8p_\x8a_\x8g_\x8e_\x8.
14 Note·that·most·of·the·tests·described·here·only·return·a·tuple·of·numbers,14 Note·that·most·of·the·tests·described·here·only·return·a·tuple·of·numbers,
15 without·any·annotation.·A·full·description·of·outputs·is·always·included·in·the15 without·any·annotation.·A·full·description·of·outputs·is·always·included·in·the
16 docstring·and·in·the·online·statsmodels·documentation.·For·presentation16 docstring·and·in·the·online·statsmodels·documentation.·For·presentation
17 purposes,·we·use·the·zip(name,test)·construct·to·pretty-print·short17 purposes,·we·use·the·zip(name,test)·construct·to·pretty-print·short
18 descriptions·in·the·examples·below.18 descriptions·in·the·examples·below.
19 *\x8**\x8**\x8**\x8**\x8*·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8te\x8e·a\x8a·r\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·m\x8mo\x8od\x8de\x8el\x8l_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8te\x8e·a\x8a·r\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·m\x8mo\x8od\x8de\x8el\x8l_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
20 [1]:20 [·]:
21 %matplotlib·inline21 %matplotlib·inline
22 [2]:22 [·]:
23 from·statsmodels.compat·import·lzip23 from·statsmodels.compat·import·lzip
  
24 import·numpy·as·np24 import·numpy·as·np
25 import·pandas·as·pd25 import·pandas·as·pd
26 import·statsmodels.formula.api·as·smf26 import·statsmodels.formula.api·as·smf
27 import·statsmodels.stats.api·as·sms27 import·statsmodels.stats.api·as·sms
28 import·matplotlib.pyplot·as·plt28 import·matplotlib.pyplot·as·plt
Offset 33, 124 lines modifiedOffset 33, 64 lines modified
33 dat·=·statsmodels.datasets.get_rdataset("Guerry",·"HistData",·cache=True).data33 dat·=·statsmodels.datasets.get_rdataset("Guerry",·"HistData",·cache=True).data
  
34 #·Fit·regression·model·(using·the·natural·log·of·one·of·the·regressors)34 #·Fit·regression·model·(using·the·natural·log·of·one·of·the·regressors)
35 results·=·smf.ols("Lottery·~·Literacy·+·np.log(Pop1831)",·data=dat).fit()35 results·=·smf.ols("Lottery·~·Literacy·+·np.log(Pop1831)",·data=dat).fit()
  
36 #·Inspect·the·results36 #·Inspect·the·results
37 print(results.summary())37 print(results.summary())
38 ····························OLS·Regression·Results 
39 ============================================================================== 
40 Dep.·Variable:················Lottery···R-squared:·······················0.348 
41 Model:····························OLS···Adj.·R-squared:··················0.333 
42 Method:·················Least·Squares···F-statistic:·····················22.20 
43 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········1.90e-08 
44 Time:························13:13:47···Log-Likelihood:················-379.82 
45 No.·Observations:··················86···AIC:·····························765.6 
46 Df·Residuals:······················83···BIC:·····························773.0 
47 Df·Model:···························2 
48 Covariance·Type:············nonrobust 
49 =================================================================================== 
50 ······················coef····std·err··········t······P>|t|······[0.025 
51 0.975] 
52 ------------------------------------------------------------------------------- 
53 ---- 
54 Intercept·········246.4341·····35.233······6.995······0.000·····176.358 
55 316.510 
56 Literacy···········-0.4889······0.128·····-3.832······0.000······-0.743······- 
57 0.235 
58 np.log(Pop1831)···-31.3114······5.977·····-5.239······0.000·····-43.199·····- 
59 19.424 
60 ============================================================================== 
61 Omnibus:························3.713···Durbin-Watson:···················2.019 
62 Prob(Omnibus):··················0.156···Jarque-Bera·(JB):················3.394 
63 Skew:··························-0.487···Prob(JB):························0.183 
64 Kurtosis:·······················3.003···Cond.·No.·························702. 
65 ============================================================================== 
  
66 Notes: 
67 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is 
68 correctly·specified. 
69 *\x8**\x8**\x8**\x8**\x8*·N\x8No\x8or\x8rm\x8ma\x8al\x8li\x8it\x8ty\x8y·o\x8of\x8f·t\x8th\x8he\x8e·r\x8re\x8es\x8si\x8id\x8du\x8ua\x8al\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*38 *\x8**\x8**\x8**\x8**\x8*·N\x8No\x8or\x8rm\x8ma\x8al\x8li\x8it\x8ty\x8y·o\x8of\x8f·t\x8th\x8he\x8e·r\x8re\x8es\x8si\x8id\x8du\x8ua\x8al\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
70 Jarque-Bera·test:39 Jarque-Bera·test:
71 [3]:40 [·]:
72 name·=·["Jarque-Bera",·"Chi^2·two-tail·prob.",·"Skew",·"Kurtosis"]41 name·=·["Jarque-Bera",·"Chi^2·two-tail·prob.",·"Skew",·"Kurtosis"]
73 test·=·sms.jarque_bera(results.resid)42 test·=·sms.jarque_bera(results.resid)
74 lzip(name,·test)43 lzip(name,·test)
75 [3]: 
76 [('Jarque-Bera',·np.float64(3.393608024843183)), 
77 ·('Chi^2·two-tail·prob.',·np.float64(0.18326831231663213)), 
78 ·('Skew',·np.float64(-0.4865803431122349)), 
79 ·('Kurtosis',·np.float64(3.0034177578816337))] 
80 Omni·test:44 Omni·test:
81 [4]:45 [·]:
82 name·=·["Chi^2",·"Two-tail·probability"]46 name·=·["Chi^2",·"Two-tail·probability"]
83 test·=·sms.omni_normtest(results.resid)47 test·=·sms.omni_normtest(results.resid)
84 lzip(name,·test)48 lzip(name,·test)
85 [4]: 
86 [('Chi^2',·np.float64(3.713437811597197)), 
87 ·('Two-tail·probability',·np.float64(0.15618424580304707))] 
88 *\x8**\x8**\x8**\x8**\x8*·I\x8In\x8nf\x8fl\x8lu\x8ue\x8en\x8nc\x8ce\x8e·t\x8te\x8es\x8st\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*49 *\x8**\x8**\x8**\x8**\x8*·I\x8In\x8nf\x8fl\x8lu\x8ue\x8en\x8nc\x8ce\x8e·t\x8te\x8es\x8st\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
89 Once·created,·an·object·of·class·OLSInfluence·holds·attributes·and·methods·that50 Once·created,·an·object·of·class·OLSInfluence·holds·attributes·and·methods·that
90 allow·users·to·assess·the·influence·of·each·observation.·For·example,·we·can51 allow·users·to·assess·the·influence·of·each·observation.·For·example,·we·can
91 compute·and·extract·the·first·few·rows·of·DFbetas·by:52 compute·and·extract·the·first·few·rows·of·DFbetas·by:
92 [5]:53 [·]:
93 from·statsmodels.stats.outliers_influence·import·OLSInfluence54 from·statsmodels.stats.outliers_influence·import·OLSInfluence
  
94 test_class·=·OLSInfluence(results)55 test_class·=·OLSInfluence(results)
95 test_class.dfbetas[:5,·:]56 test_class.dfbetas[:5,·:]
96 [5]: 
97 array([[-0.00301154,··0.00290872,··0.00118179], 
98 ·······[-0.06425662,··0.04043093,··0.06281609], 
99 ·······[·0.01554894,·-0.03556038,·-0.00905336], 
100 ·······[·0.17899858,··0.04098207,·-0.18062352], 
101 ·······[·0.29679073,··0.21249207,·-0.3213655·]]) 
102 Explore·other·options·by·typing·dir(influence_test)57 Explore·other·options·by·typing·dir(influence_test)
103 Useful·information·on·leverage·can·also·be·plotted:58 Useful·information·on·leverage·can·also·be·plotted:
104 [6]:59 [·]:
105 from·statsmodels.graphics.regressionplots·import·plot_leverage_resid260 from·statsmodels.graphics.regressionplots·import·plot_leverage_resid2
  
106 fig,·ax·=·plt.subplots(figsize=(8,·6))61 fig,·ax·=·plt.subplots(figsize=(8,·6))
107 fig·=·plot_leverage_resid2(results,·ax=ax)62 fig·=·plot_leverage_resid2(results,·ax=ax)
108 [../../../_images/examples_notebooks_generated_regression_diagnostics_13_0.png] 
109 Other·plotting·options·can·be·found·on·the·_\x8G_\x8r_\x8a_\x8p_\x8h_\x8i_\x8c_\x8s_\x8·_\x8p_\x8a_\x8g_\x8e_\x8.63 Other·plotting·options·can·be·found·on·the·_\x8G_\x8r_\x8a_\x8p_\x8h_\x8i_\x8c_\x8s_\x8·_\x8p_\x8a_\x8g_\x8e_\x8.
110 *\x8**\x8**\x8**\x8**\x8*·M\x8Mu\x8ul\x8lt\x8ti\x8ic\x8co\x8ol\x8ll\x8li\x8in\x8ne\x8ea\x8ar\x8ri\x8it\x8ty\x8y_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*64 *\x8**\x8**\x8**\x8**\x8*·M\x8Mu\x8ul\x8lt\x8ti\x8ic\x8co\x8ol\x8ll\x8li\x8in\x8ne\x8ea\x8ar\x8ri\x8it\x8ty\x8y_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
111 Condition·number:65 Condition·number:
112 [7]:66 [·]:
113 np.linalg.cond(results.model.exog)67 np.linalg.cond(results.model.exog)
114 [7]: 
115 np.float64(702.179214549006) 
116 *\x8**\x8**\x8**\x8**\x8*·H\x8He\x8et\x8te\x8er\x8ro\x8os\x8sk\x8ke\x8ed\x8da\x8as\x8st\x8ti\x8ic\x8ci\x8it\x8ty\x8y·t\x8te\x8es\x8st\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*68 *\x8**\x8**\x8**\x8**\x8*·H\x8He\x8et\x8te\x8er\x8ro\x8os\x8sk\x8ke\x8ed\x8da\x8as\x8st\x8ti\x8ic\x8ci\x8it\x8ty\x8y·t\x8te\x8es\x8st\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
117 Breush-Pagan·test:69 Breush-Pagan·test:
118 [8]:70 [·]:
119 name·=·["Lagrange·multiplier·statistic",·"p-value",·"f-value",·"f·p-value"]71 name·=·["Lagrange·multiplier·statistic",·"p-value",·"f-value",·"f·p-value"]
120 test·=·sms.het_breuschpagan(results.resid,·results.model.exog)72 test·=·sms.het_breuschpagan(results.resid,·results.model.exog)
121 lzip(name,·test)73 lzip(name,·test)
122 [8]: 
123 [('Lagrange·multiplier·statistic',·np.float64(4.893213374094005)), 
124 ·('p-value',·np.float64(0.08658690502352002)), 
125 ·('f-value',·np.float64(2.503715946256461)), 
126 ·('f·p-value',·np.float64(0.08794028782672814))] 
127 Goldfeld-Quandt·test74 Goldfeld-Quandt·test
128 [9]:75 [·]:
129 name·=·["F·statistic",·"p-value"]76 name·=·["F·statistic",·"p-value"]
130 test·=·sms.het_goldfeldquandt(results.resid,·results.model.exog)77 test·=·sms.het_goldfeldquandt(results.resid,·results.model.exog)
131 lzip(name,·test)78 lzip(name,·test)
132 [9]: 
133 [('F·statistic',·np.float64(1.1002422436378139)), 
134 ·('p-value',·np.float64(0.38202950686925286))] 
135 *\x8**\x8**\x8**\x8**\x8*·L\x8Li\x8in\x8ne\x8ea\x8ar\x8ri\x8it\x8ty\x8y_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*79 *\x8**\x8**\x8**\x8**\x8*·L\x8Li\x8in\x8ne\x8ea\x8ar\x8ri\x8it\x8ty\x8y_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
136 Harvey-Collier·multiplier·test·for·Null·hypothesis·that·the·linear80 Harvey-Collier·multiplier·test·for·Null·hypothesis·that·the·linear
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59 ······<div·class="documentwrapper">59 ······<div·class="documentwrapper">
60 ········<div·class="bodywrapper">60 ········<div·class="bodywrapper">
61 ··········<div·class="body"·role="main">61 ··········<div·class="body"·role="main">
62 ············62 ············
63 ··<section·id="Regression-Plots">63 ··<section·id="Regression-Plots">
64 <h1>Regression·Plots<a·class="headerlink"·href="#Regression-Plots"·title="Link·to·this·heading">¶</a></h1>64 <h1>Regression·Plots<a·class="headerlink"·href="#Regression-Plots"·title="Link·to·this·heading">¶</a></h1>
65 <div·class="nbinput·nblast·docutils·container">65 <div·class="nbinput·nblast·docutils·container">
66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
67 </pre></div>67 </pre></div>
68 </div>68 </div>
69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
70 </pre></div>70 </pre></div>
71 </div>71 </div>
72 </div>72 </div>
73 <div·class="nbinput·nblast·docutils·container">73 <div·class="nbinput·nblast·docutils·container">
74 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:74 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
75 </pre></div>75 </pre></div>
76 </div>76 </div>
77 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.compat</span>·<span·class="kn">import</span>·<span·class="n">lzip</span>77 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.compat</span>·<span·class="kn">import</span>·<span·class="n">lzip</span>
78 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>78 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
79 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>79 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
80 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>80 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
81 <span·class="kn">from</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="kn">import</span>·<span·class="n">ols</span>81 <span·class="kn">from</span>·<span·class="nn">statsmodels.formula.api</span>·<span·class="kn">import</span>·<span·class="n">ols</span>
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87 </div>87 </div>
88 <section·id="Duncan's-Prestige-Dataset">88 <section·id="Duncan's-Prestige-Dataset">
89 <h2>Duncan’s·Prestige·Dataset<a·class="headerlink"·href="#Duncan's-Prestige-Dataset"·title="Link·to·this·heading">¶</a></h2>89 <h2>Duncan’s·Prestige·Dataset<a·class="headerlink"·href="#Duncan's-Prestige-Dataset"·title="Link·to·this·heading">¶</a></h2>
90 <section·id="Load-the-Data">90 <section·id="Load-the-Data">
91 <h3>Load·the·Data<a·class="headerlink"·href="#Load-the-Data"·title="Link·to·this·heading">¶</a></h3>91 <h3>Load·the·Data<a·class="headerlink"·href="#Load-the-Data"·title="Link·to·this·heading">¶</a></h3>
92 <p>We·can·use·a·utility·function·to·load·any·R·dataset·available·from·the·great·Rdatasets·package.</p>92 <p>We·can·use·a·utility·function·to·load·any·R·dataset·available·from·the·great·Rdatasets·package.</p>
93 <div·class="nbinput·nblast·docutils·container">93 <div·class="nbinput·nblast·docutils·container">
94 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:94 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
95 </pre></div>95 </pre></div>
96 </div>96 </div>
97 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">prestige</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">get_rdataset</span><span·class="p">(</span><span·class="s2">&quot;Duncan&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;carData&quot;</span><span·class="p">,</span>·<span·class="n">cache</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span><span·class="o">.</span><span·class="n">data</span>97 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">prestige</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">get_rdataset</span><span·class="p">(</span><span·class="s2">&quot;Duncan&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;carData&quot;</span><span·class="p">,</span>·<span·class="n">cache</span><span·class="o">=</span><span·class="kc">True</span><span·class="p">)</span><span·class="o">.</span><span·class="n">data</span>
98 </pre></div>98 </pre></div>
99 </div>99 </div>
100 </div>100 </div>
101 <div·class="nbinput·docutils·container">101 <div·class="nbinput·nblast·docutils·container">
102 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:102 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
103 </pre></div>103 </pre></div>
104 </div>104 </div>
105 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">prestige</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>105 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">prestige</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>
106 </pre></div>106 </pre></div>
107 </div>107 </div>
108 </div>108 </div>
109 <div·class="nboutput·nblast·docutils·container"> 
110 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]: 
111 </pre></div> 
112 </div> 
113 <div·class="output_area·rendered_html·docutils·container"> 
114 <div> 
115 <style·scoped> 
116 ····.dataframe·tbody·tr·th:only-of-type·{ 
117 ········vertical-align:·middle; 
118 ····} 
  
119 ····.dataframe·tbody·tr·th·{ 
120 ········vertical-align:·top; 
121 ····} 
  
122 ····.dataframe·thead·th·{ 
123 ········text-align:·right; 
124 ····} 
125 </style> 
126 <table·border="1"·class="dataframe"> 
127 ··<thead> 
128 ····<tr·style="text-align:·right;"> 
129 ······<th></th> 
130 ······<th>type</th> 
131 ······<th>income</th> 
132 ······<th>education</th> 
133 ······<th>prestige</th> 
134 ····</tr> 
135 ··</thead> 
136 ··<tbody> 
137 ····<tr> 
138 ······<th>accountant</th> 
139 ······<td>prof</td> 
140 ······<td>62</td> 
141 ······<td>86</td> 
142 ······<td>82</td> 
143 ····</tr> 
144 ····<tr> 
145 ······<th>pilot</th> 
146 ······<td>prof</td> 
147 ······<td>72</td> 
148 ······<td>76</td> 
149 ······<td>83</td> 
150 ····</tr> 
151 ····<tr> 
152 ······<th>architect</th> 
153 ······<td>prof</td> 
154 ······<td>75</td> 
155 ······<td>92</td> 
156 ······<td>90</td> 
157 ····</tr> 
158 ····<tr> 
159 ······<th>author</th> 
160 ······<td>prof</td> 
161 ······<td>55</td> 
162 ······<td>90</td> 
163 ······<td>76</td> 
164 ····</tr> 
165 ····<tr> 
166 ······<th>chemist</th> 
167 ······<td>prof</td> 
168 ······<td>64</td> 
169 ······<td>86</td> 
170 ······<td>90</td> 
171 ····</tr> 
172 ··</tbody> 
173 </table> 
174 </div></div> 
175 </div> 
176 <div·class="nbinput·nblast·docutils·container">109 <div·class="nbinput·nblast·docutils·container">
177 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:110 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
178 </pre></div>111 </pre></div>
179 </div>112 </div>
180 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">prestige_model</span>·<span·class="o">=</span>·<span·class="n">ols</span><span·class="p">(</span><span·class="s2">&quot;prestige·~·income·+·education&quot;</span><span·class="p">,</span>·<span·class="n">data</span><span·class="o">=</span><span·class="n">prestige</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>113 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">prestige_model</span>·<span·class="o">=</span>·<span·class="n">ols</span><span·class="p">(</span><span·class="s2">&quot;prestige·~·income·+·education&quot;</span><span·class="p">,</span>·<span·class="n">data</span><span·class="o">=</span><span·class="n">prestige</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
181 </pre></div>114 </pre></div>
182 </div>115 </div>
183 </div>116 </div>
184 <div·class="nbinput·docutils·container">117 <div·class="nbinput·nblast·docutils·container">
185 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:118 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
186 </pre></div>119 </pre></div>
187 </div>120 </div>
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Regression·Plots8 ····*·Regression·Plots
9 *\x8**\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·P\x8Pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 %matplotlib·inline11 %matplotlib·inline
12 [2]:12 [·]:
13 from·statsmodels.compat·import·lzip13 from·statsmodels.compat·import·lzip
14 import·numpy·as·np14 import·numpy·as·np
15 import·matplotlib.pyplot·as·plt15 import·matplotlib.pyplot·as·plt
16 import·statsmodels.api·as·sm16 import·statsmodels.api·as·sm
17 from·statsmodels.formula.api·import·ols17 from·statsmodels.formula.api·import·ols
  
18 plt.rc("figure",·figsize=(16,·8))18 plt.rc("figure",·figsize=(16,·8))
19 plt.rc("font",·size=14)19 plt.rc("font",·size=14)
20 *\x8**\x8**\x8**\x8**\x8*·D\x8Du\x8un\x8nc\x8ca\x8an\x8n?\x8’s\x8s·P\x8Pr\x8re\x8es\x8st\x8ti\x8ig\x8ge\x8e·D\x8Da\x8at\x8ta\x8as\x8se\x8et\x8t_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8**\x8*·D\x8Du\x8un\x8nc\x8ca\x8an\x8n?\x8’s\x8s·P\x8Pr\x8re\x8es\x8st\x8ti\x8ig\x8ge\x8e·D\x8Da\x8at\x8ta\x8as\x8se\x8et\x8t_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
21 *\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8d·t\x8th\x8he\x8e·D\x8Da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*21 *\x8**\x8**\x8**\x8*·L\x8Lo\x8oa\x8ad\x8d·t\x8th\x8he\x8e·D\x8Da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8*
22 We·can·use·a·utility·function·to·load·any·R·dataset·available·from·the·great22 We·can·use·a·utility·function·to·load·any·R·dataset·available·from·the·great
23 Rdatasets·package.23 Rdatasets·package.
24 [3]:24 [·]:
25 prestige·=·sm.datasets.get_rdataset("Duncan",·"carData",·cache=True).data25 prestige·=·sm.datasets.get_rdataset("Duncan",·"carData",·cache=True).data
26 [4]:26 [·]:
27 prestige.head()27 prestige.head()
28 [4]:28 [·]:
29 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
30 |_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8t\x8t_\x8y\x8y_\x8p\x8p_\x8e\x8e_\x8|_\x8i\x8i_\x8n\x8n_\x8c\x8c_\x8o\x8o_\x8m\x8m_\x8e\x8e_\x8|_\x8e\x8e_\x8d\x8d_\x8u\x8u_\x8c\x8c_\x8a\x8a_\x8t\x8t_\x8i\x8i_\x8o\x8o_\x8n\x8n_\x8|_\x8p\x8p_\x8r\x8r_\x8e\x8e_\x8s\x8s_\x8t\x8t_\x8i\x8i_\x8g\x8g_\x8e\x8e| 
31 |_\x8a\x8a_\x8c\x8c_\x8c\x8c_\x8o\x8o_\x8u\x8u_\x8n\x8n_\x8t\x8t_\x8a\x8a_\x8n\x8n_\x8t\x8t_\x8|_\x8p_\x8r_\x8o_\x8f_\x8|_\x86_\x82_\x8·_\x8·_\x8·_\x8·_\x8|_\x88_\x86_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x88_\x82_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
32 |_\x8p\x8p_\x8i\x8i_\x8l\x8l_\x8o\x8o_\x8t\x8t_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8p_\x8r_\x8o_\x8f_\x8|_\x87_\x82_\x8·_\x8·_\x8·_\x8·_\x8|_\x87_\x86_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x88_\x83_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
33 |_\x8a\x8a_\x8r\x8r_\x8c\x8c_\x8h\x8h_\x8i\x8i_\x8t\x8t_\x8e\x8e_\x8c\x8c_\x8t\x8t_\x8·_\x8|_\x8p_\x8r_\x8o_\x8f_\x8|_\x87_\x85_\x8·_\x8·_\x8·_\x8·_\x8|_\x89_\x82_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x89_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
34 |_\x8a\x8a_\x8u\x8u_\x8t\x8t_\x8h\x8h_\x8o\x8o_\x8r\x8r_\x8·_\x8·_\x8·_\x8·_\x8|_\x8p_\x8r_\x8o_\x8f_\x8|_\x85_\x85_\x8·_\x8·_\x8·_\x8·_\x8|_\x89_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x87_\x86_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
35 |_\x8c\x8c_\x8h\x8h_\x8e\x8e_\x8m\x8m_\x8i\x8i_\x8s\x8s_\x8t\x8t_\x8·_\x8·_\x8·_\x8|_\x8p_\x8r_\x8o_\x8f_\x8|_\x86_\x84_\x8·_\x8·_\x8·_\x8·_\x8|_\x88_\x86_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x89_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·| 
36 [5]: 
37 prestige_model·=·ols("prestige·~·income·+·education",·data=prestige).fit()29 prestige_model·=·ols("prestige·~·income·+·education",·data=prestige).fit()
38 [6]:30 [·]:
39 print(prestige_model.summary())31 print(prestige_model.summary())
40 ····························OLS·Regression·Results 
41 ============================================================================== 
42 Dep.·Variable:···············prestige···R-squared:·······················0.828 
43 Model:····························OLS···Adj.·R-squared:··················0.820 
44 Method:·················Least·Squares···F-statistic:·····················101.2 
45 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········8.65e-17 
46 Time:························13:13:47···Log-Likelihood:················-178.98 
47 No.·Observations:··················45···AIC:·····························364.0 
48 Df·Residuals:······················42···BIC:·····························369.4 
49 Df·Model:···························2 
50 Covariance·Type:············nonrobust 
51 ============================================================================== 
52 ·················coef····std·err··········t······P>|t|······[0.025······0.975] 
53 ------------------------------------------------------------------------------ 
54 Intercept·····-6.0647······4.272·····-1.420······0.163·····-14.686·······2.556 
55 income·········0.5987······0.120······5.003······0.000·······0.357·······0.840 
56 education······0.5458······0.098······5.555······0.000·······0.348·······0.744 
57 ============================================================================== 
58 Omnibus:························1.279···Durbin-Watson:···················1.458 
59 Prob(Omnibus):··················0.528···Jarque-Bera·(JB):················0.520 
60 Skew:···························0.155···Prob(JB):························0.771 
61 Kurtosis:·······················3.426···Cond.·No.·························163. 
62 ============================================================================== 
  
63 Notes: 
64 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is 
65 correctly·specified. 
66 *\x8**\x8**\x8**\x8*·I\x8In\x8nf\x8fl\x8lu\x8ue\x8en\x8nc\x8ce\x8e·p\x8pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*32 *\x8**\x8**\x8**\x8*·I\x8In\x8nf\x8fl\x8lu\x8ue\x8en\x8nc\x8ce\x8e·p\x8pl\x8lo\x8ot\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*
67 Influence·plots·show·the·(externally)·studentized·residuals·vs.·the·leverage·of33 Influence·plots·show·the·(externally)·studentized·residuals·vs.·the·leverage·of
68 each·observation·as·measured·by·the·hat·matrix.34 each·observation·as·measured·by·the·hat·matrix.
69 Externally·studentized·residuals·are·residuals·that·are·scaled·by·their35 Externally·studentized·residuals·are·residuals·that·are·scaled·by·their
70 standard·deviation·where36 standard·deviation·where
71 \[var(\hat{\epsilon}_i)=\hat{\sigma}^2_i(1-h_{ii})\]37 \[var(\hat{\epsilon}_i)=\hat{\sigma}^2_i(1-h_{ii})\]
72 with38 with
73 \[\hat{\sigma}^2_i=\frac{1}{n·-·p·-·1·\;\;}\sum_{j}^{n}\;\;\;\forall·\;\;\;·j39 \[\hat{\sigma}^2_i=\frac{1}{n·-·p·-·1·\;\;}\sum_{j}^{n}\;\;\;\forall·\;\;\;·j
74 \neq·i\]40 \neq·i\]
75 \(n\)·is·the·number·of·observations·and·\(p\)·is·the·number·of·regressors.·\(h_41 \(n\)·is·the·number·of·observations·and·\(p\)·is·the·number·of·regressors.·\(h_
76 {ii}\)·is·the·\(i\)-th·diagonal·element·of·the·hat·matrix42 {ii}\)·is·the·\(i\)-th·diagonal·element·of·the·hat·matrix
77 \[H=X(X^{\;\prime}X)^{-1}X^{\;\prime}\]43 \[H=X(X^{\;\prime}X)^{-1}X^{\;\prime}\]
78 The·influence·of·each·point·can·be·visualized·by·the·criterion·keyword44 The·influence·of·each·point·can·be·visualized·by·the·criterion·keyword
79 argument.·Options·are·Cook’s·distance·and·DFFITS,·two·measures·of·influence.45 argument.·Options·are·Cook’s·distance·and·DFFITS,·two·measures·of·influence.
80 [7]:46 [·]:
81 fig·=·sm.graphics.influence_plot(prestige_model,·criterion="cooks")47 fig·=·sm.graphics.influence_plot(prestige_model,·criterion="cooks")
82 fig.tight_layout(pad=1.0)48 fig.tight_layout(pad=1.0)
83 [../../../_images/examples_notebooks_generated_regression_plots_12_0.png] 
84 As·you·can·see·there·are·a·few·worrisome·observations.·Both·contractor·and49 As·you·can·see·there·are·a·few·worrisome·observations.·Both·contractor·and
85 reporter·have·low·leverage·but·a·large·residual.·RR.engineer·has·small·residual50 reporter·have·low·leverage·but·a·large·residual.·RR.engineer·has·small·residual
86 and·large·leverage.·Conductor·and·minister·have·both·high·leverage·and·large51 and·large·leverage.·Conductor·and·minister·have·both·high·leverage·and·large
87 residuals,·and,·therefore,·large·influence.52 residuals,·and,·therefore,·large·influence.
88 *\x8**\x8**\x8**\x8*·P\x8Pa\x8ar\x8rt\x8ti\x8ia\x8al\x8l·R\x8Re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·P\x8Pl\x8lo\x8ot\x8ts\x8s·(\x8(D\x8Du\x8un\x8nc\x8ca\x8an\x8n)\x8)_\x8?\x8·*\x8**\x8**\x8**\x8*53 *\x8**\x8**\x8**\x8*·P\x8Pa\x8ar\x8rt\x8ti\x8ia\x8al\x8l·R\x8Re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8io\x8on\x8n·P\x8Pl\x8lo\x8ot\x8ts\x8s·(\x8(D\x8Du\x8un\x8nc\x8ca\x8an\x8n)\x8)_\x8?\x8·*\x8**\x8**\x8**\x8*
89 Since·we·are·doing·multivariate·regressions,·we·cannot·just·look·at·individual54 Since·we·are·doing·multivariate·regressions,·we·cannot·just·look·at·individual
90 bivariate·plots·to·discern·relationships.·Instead,·we·want·to·look·at·the55 bivariate·plots·to·discern·relationships.·Instead,·we·want·to·look·at·the
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102 The·notable·points·of·this·plot·are·that·the·fitted·line·has·slope·\(\beta_k\)66 The·notable·points·of·this·plot·are·that·the·fitted·line·has·slope·\(\beta_k\)
103 and·intercept·zero.·The·residuals·of·this·plot·are·the·same·as·those·of·the67 and·intercept·zero.·The·residuals·of·this·plot·are·the·same·as·those·of·the
104 least·squares·fit·of·the·original·model·with·full·\(X\).·You·can·discern·the68 least·squares·fit·of·the·original·model·with·full·\(X\).·You·can·discern·the
105 effects·of·the·individual·data·values·on·the·estimation·of·a·coefficient69 effects·of·the·individual·data·values·on·the·estimation·of·a·coefficient
106 easily.·If·obs_labels·is·True,·then·these·points·are·annotated·with·their70 easily.·If·obs_labels·is·True,·then·these·points·are·annotated·with·their
107 observation·label.·You·can·also·see·the·violation·of·underlying·assumptions71 observation·label.·You·can·also·see·the·violation·of·underlying·assumptions
108 such·as·homoskedasticity·and·linearity.72 such·as·homoskedasticity·and·linearity.
109 [8]:73 [·]:
110 fig·=·sm.graphics.plot_partregress(74 fig·=·sm.graphics.plot_partregress(
111 ····"prestige",·"income",·["income",·"education"],·data=prestige75 ····"prestige",·"income",·["income",·"education"],·data=prestige
112 )76 )
113 fig.tight_layout(pad=1.0)77 fig.tight_layout(pad=1.0)
114 [../../../_images/examples_notebooks_generated_regression_plots_16_0.png] 
115 [9]:78 [·]:
116 fig·=·sm.graphics.plot_partregress("prestige",·"income",·["education"],79 fig·=·sm.graphics.plot_partregress("prestige",·"income",·["education"],
117 data=prestige)80 data=prestige)
118 fig.tight_layout(pad=1.0)81 fig.tight_layout(pad=1.0)
119 [../../../_images/examples_notebooks_generated_regression_plots_17_0.png] 
120 As·you·can·see·the·partial·regression·plot·confirms·the·influence·of·conductor,82 As·you·can·see·the·partial·regression·plot·confirms·the·influence·of·conductor,
121 minister,·and·RR.engineer·on·the·partial·relationship·between·income·and83 minister,·and·RR.engineer·on·the·partial·relationship·between·income·and
122 prestige.·The·cases·greatly·decrease·the·effect·of·income·on·prestige.·Dropping84 prestige.·The·cases·greatly·decrease·the·effect·of·income·on·prestige.·Dropping
123 these·cases·confirms·this.85 these·cases·confirms·this.
124 [10]:86 [·]:
125 subset·=·~prestige.index.isin(["conductor",·"RR.engineer",·"minister"])87 subset·=·~prestige.index.isin(["conductor",·"RR.engineer",·"minister"])
126 prestige_model2·=·ols(88 prestige_model2·=·ols(
127 ····"prestige·~·income·+·education",·data=prestige,·subset=subset89 ····"prestige·~·income·+·education",·data=prestige,·subset=subset
128 ).fit()90 ).fit()
129 print(prestige_model2.summary())91 print(prestige_model2.summary())
130 ····························OLS·Regression·Results 
131 ============================================================================== 
132 Dep.·Variable:···············prestige···R-squared:·······················0.876 
133 Model:····························OLS···Adj.·R-squared:··················0.870 
134 Method:·················Least·Squares···F-statistic:·····················138.1 
135 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········2.02e-18 
136 Time:························13:13:47···Log-Likelihood:················-160.59 
137 No.·Observations:··················42···AIC:·····························327.2 
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57 ······<div·class="documentwrapper">57 ······<div·class="documentwrapper">
58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Robust-Linear-Models">61 ··<section·id="Robust-Linear-Models">
62 <h1>Robust·Linear·Models<a·class="headerlink"·href="#Robust-Linear-Models"·title="Link·to·this·heading">¶</a></h1>62 <h1>Robust·Linear·Models<a·class="headerlink"·href="#Robust-Linear-Models"·title="Link·to·this·heading">¶</a></h1>
63 <div·class="nbinput·nblast·docutils·container">63 <div·class="nbinput·nblast·docutils·container">
64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
65 </pre></div>65 </pre></div>
66 </div>66 </div>
67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 </div>70 </div>
71 <div·class="nbinput·nblast·docutils·container">71 <div·class="nbinput·nblast·docutils·container">
72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
76 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>76 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
77 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>77 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
78 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1234</span><span·class="p">)</span>·<span·class="c1">#·for·reproducibility</span>78 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">1234</span><span·class="p">)</span>·<span·class="c1">#·for·reproducibility</span>
79 </pre></div>79 </pre></div>
80 </div>80 </div>
81 </div>81 </div>
82 <section·id="Estimation">82 <section·id="Estimation">
83 <h2>Estimation<a·class="headerlink"·href="#Estimation"·title="Link·to·this·heading">¶</a></h2>83 <h2>Estimation<a·class="headerlink"·href="#Estimation"·title="Link·to·this·heading">¶</a></h2>
84 <p>Load·data:</p>84 <p>Load·data:</p>
85 <div·class="nbinput·nblast·docutils·container">85 <div·class="nbinput·nblast·docutils·container">
86 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:86 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
87 </pre></div>87 </pre></div>
88 </div>88 </div>
89 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">stackloss</span><span·class="o">.</span><span·class="n">load</span><span·class="p">()</span>89 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">data</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">stackloss</span><span·class="o">.</span><span·class="n">load</span><span·class="p">()</span>
90 <span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">)</span>90 <span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">)</span>
91 </pre></div>91 </pre></div>
92 </div>92 </div>
93 </div>93 </div>
94 <p>Huber’s·T·norm·with·the·(default)·median·absolute·deviation·scaling</p>94 <p>Huber’s·T·norm·with·the·(default)·median·absolute·deviation·scaling</p>
95 <div·class="nbinput·docutils·container">95 <div·class="nbinput·nblast·docutils·container">
96 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:96 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
97 </pre></div>97 </pre></div>
98 </div>98 </div>
99 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">huber_t</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">RLM</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">endog</span><span·class="p">,</span>·<span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">,</span>·<span·class="n">M</span><span·class="o">=</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">robust</span><span·class="o">.</span><span·class="n">norms</span><span·class="o">.</span><span·class="n">HuberT</span><span·class="p">())</span>99 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">huber_t</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">RLM</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">endog</span><span·class="p">,</span>·<span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">,</span>·<span·class="n">M</span><span·class="o">=</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">robust</span><span·class="o">.</span><span·class="n">norms</span><span·class="o">.</span><span·class="n">HuberT</span><span·class="p">())</span>
100 <span·class="n">hub_results</span>·<span·class="o">=</span>·<span·class="n">huber_t</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>100 <span·class="n">hub_results</span>·<span·class="o">=</span>·<span·class="n">huber_t</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
101 <span·class="nb">print</span><span·class="p">(</span><span·class="n">hub_results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>101 <span·class="nb">print</span><span·class="p">(</span><span·class="n">hub_results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>
102 <span·class="nb">print</span><span·class="p">(</span><span·class="n">hub_results</span><span·class="o">.</span><span·class="n">bse</span><span·class="p">)</span>102 <span·class="nb">print</span><span·class="p">(</span><span·class="n">hub_results</span><span·class="o">.</span><span·class="n">bse</span><span·class="p">)</span>
103 <span·class="nb">print</span><span·class="p">(</span>103 <span·class="nb">print</span><span·class="p">(</span>
104 ····<span·class="n">hub_results</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">(</span>104 ····<span·class="n">hub_results</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">(</span>
105 ········<span·class="n">yname</span><span·class="o">=</span><span·class="s2">&quot;y&quot;</span><span·class="p">,</span>·<span·class="n">xname</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;var_</span><span·class="si">%d</span><span·class="s2">&quot;</span>·<span·class="o">%</span>·<span·class="n">i</span>·<span·class="k">for</span>·<span·class="n">i</span>·<span·class="ow">in</span>·<span·class="nb">range</span><span·class="p">(</span><span·class="nb">len</span><span·class="p">(</span><span·class="n">hub_results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">))]</span>105 ········<span·class="n">yname</span><span·class="o">=</span><span·class="s2">&quot;y&quot;</span><span·class="p">,</span>·<span·class="n">xname</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;var_</span><span·class="si">%d</span><span·class="s2">&quot;</span>·<span·class="o">%</span>·<span·class="n">i</span>·<span·class="k">for</span>·<span·class="n">i</span>·<span·class="ow">in</span>·<span·class="nb">range</span><span·class="p">(</span><span·class="nb">len</span><span·class="p">(</span><span·class="n">hub_results</span><span·class="o">.</span><span·class="n">params</span><span·class="p">))]</span>
106 ····<span·class="p">)</span>106 ····<span·class="p">)</span>
107 <span·class="p">)</span>107 <span·class="p">)</span>
108 </pre></div>108 </pre></div>
109 </div>109 </div>
110 </div>110 </div>
111 <div·class="nboutput·nblast·docutils·container"> 
112 <div·class="prompt·empty·docutils·container"> 
113 </div> 
114 <div·class="output_area·docutils·container"> 
115 <div·class="highlight"><pre> 
116 const·······-41.026498 
117 AIRFLOW·······0.829384 
118 WATERTEMP·····0.926066 
119 ACIDCONC·····-0.127847 
120 dtype:·float64 
121 const········9.791899 
122 AIRFLOW······0.111005 
123 WATERTEMP····0.302930 
124 ACIDCONC·····0.128650 
125 dtype:·float64 
126 ····················Robust·linear·Model·Regression·Results 
127 ============================================================================== 
128 Dep.·Variable:······················y···No.·Observations:···················21 
129 Model:····························RLM···Df·Residuals:·······················17 
130 Method:··························IRLS···Df·Model:····························3 
131 Norm:··························HuberT 
132 Scale·Est.:·······················mad 
133 Cov·Type:··························H1 
134 Date:················Sun,·10·Aug·2025 
135 Time:························13:13:47 
136 No.·Iterations:····················19 
137 ============================================================================== 
138 ·················coef····std·err··········z······P&gt;|z|······[0.025······0.975] 
139 ------------------------------------------------------------------------------ 
140 var_0········-41.0265······9.792·····-4.190······0.000·····-60.218·····-21.835 
141 var_1··········0.8294······0.111······7.472······0.000·······0.612·······1.047 
142 var_2··········0.9261······0.303······3.057······0.002·······0.332·······1.520 
143 var_3·········-0.1278······0.129·····-0.994······0.320······-0.380·······0.124 
144 ============================================================================== 
  
145 If·the·model·instance·has·been·used·for·another·fit·with·different·fit·parameters,·then·the·fit·options·might·not·be·the·correct·ones·anymore·. 
146 </pre></div></div> 
147 </div> 
148 <p>Huber’s·T·norm·with·‘H2’·covariance·matrix</p>111 <p>Huber’s·T·norm·with·‘H2’·covariance·matrix</p>
149 <div·class="nbinput·docutils·container">112 <div·class="nbinput·nblast·docutils·container">
150 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:113 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
151 </pre></div>114 </pre></div>
152 </div>115 </div>
153 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">hub_results2</span>·<span·class="o">=</span>·<span·class="n">huber_t</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">cov</span><span·class="o">=</span><span·class="s2">&quot;H2&quot;</span><span·class="p">)</span>116 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">hub_results2</span>·<span·class="o">=</span>·<span·class="n">huber_t</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">cov</span><span·class="o">=</span><span·class="s2">&quot;H2&quot;</span><span·class="p">)</span>
154 <span·class="nb">print</span><span·class="p">(</span><span·class="n">hub_results2</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>117 <span·class="nb">print</span><span·class="p">(</span><span·class="n">hub_results2</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>
155 <span·class="nb">print</span><span·class="p">(</span><span·class="n">hub_results2</span><span·class="o">.</span><span·class="n">bse</span><span·class="p">)</span>118 <span·class="nb">print</span><span·class="p">(</span><span·class="n">hub_results2</span><span·class="o">.</span><span·class="n">bse</span><span·class="p">)</span>
156 </pre></div>119 </pre></div>
157 </div>120 </div>
158 </div>121 </div>
159 <div·class="nboutput·nblast·docutils·container"> 
160 <div·class="prompt·empty·docutils·container"> 
161 </div> 
162 <div·class="output_area·docutils·container"> 
163 <div·class="highlight"><pre> 
164 const·······-41.026498 
165 AIRFLOW·······0.829384 
166 WATERTEMP·····0.926066 
167 ACIDCONC·····-0.127847 
168 dtype:·float64 
169 const········9.089504 
170 AIRFLOW······0.119460 
171 WATERTEMP····0.322355 
172 ACIDCONC·····0.117963 
173 dtype:·float64 
174 </pre></div></div> 
175 </div> 
176 <p>Andrew’s·Wave·norm·with·Huber’s·Proposal·2·scaling·and·‘H3’·covariance·matrix</p>122 <p>Andrew’s·Wave·norm·with·Huber’s·Proposal·2·scaling·and·‘H3’·covariance·matrix</p>
177 <div·class="nbinput·docutils·container">123 <div·class="nbinput·nblast·docutils·container">
178 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:124 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
179 </pre></div>125 </pre></div>
180 </div>126 </div>
181 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">andrew_mod</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">RLM</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">endog</span><span·class="p">,</span>·<span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">,</span>·<span·class="n">M</span><span·class="o">=</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">robust</span><span·class="o">.</span><span·class="n">norms</span><span·class="o">.</span><span·class="n">AndrewWave</span><span·class="p">())</span>127 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">andrew_mod</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">RLM</span><span·class="p">(</span><span·class="n">data</span><span·class="o">.</span><span·class="n">endog</span><span·class="p">,</span>·<span·class="n">data</span><span·class="o">.</span><span·class="n">exog</span><span·class="p">,</span>·<span·class="n">M</span><span·class="o">=</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">robust</span><span·class="o">.</span><span·class="n">norms</span><span·class="o">.</span><span·class="n">AndrewWave</span><span·class="p">())</span>
182 <span·class="n">andrew_results</span>·<span·class="o">=</span>·<span·class="n">andrew_mod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">scale_est</span><span·class="o">=</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">robust</span><span·class="o">.</span><span·class="n">scale</span><span·class="o">.</span><span·class="n">HuberScale</span><span·class="p">(),</span>·<span·class="n">cov</span><span·class="o">=</span><span·class="s2">&quot;H3&quot;</span><span·class="p">)</span>128 <span·class="n">andrew_results</span>·<span·class="o">=</span>·<span·class="n">andrew_mod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">scale_est</span><span·class="o">=</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">robust</span><span·class="o">.</span><span·class="n">scale</span><span·class="o">.</span><span·class="n">HuberScale</span><span·class="p">(),</span>·<span·class="n">cov</span><span·class="o">=</span><span·class="s2">&quot;H3&quot;</span><span·class="p">)</span>
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Robust·Linear·Models8 ····*·Robust·Linear·Models
9 *\x8**\x8**\x8**\x8**\x8**\x8*·R\x8Ro\x8ob\x8bu\x8us\x8st\x8t·L\x8Li\x8in\x8ne\x8ea\x8ar\x8r·M\x8Mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·R\x8Ro\x8ob\x8bu\x8us\x8st\x8t·L\x8Li\x8in\x8ne\x8ea\x8ar\x8r·M\x8Mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 %matplotlib·inline11 %matplotlib·inline
12 [2]:12 [·]:
13 import·matplotlib.pyplot·as·plt13 import·matplotlib.pyplot·as·plt
14 import·numpy·as·np14 import·numpy·as·np
15 import·statsmodels.api·as·sm15 import·statsmodels.api·as·sm
16 np.random.seed(1234)·#·for·reproducibility16 np.random.seed(1234)·#·for·reproducibility
17 *\x8**\x8**\x8**\x8**\x8*·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*17 *\x8**\x8**\x8**\x8**\x8*·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
18 Load·data:18 Load·data:
19 [3]:19 [·]:
20 data·=·sm.datasets.stackloss.load()20 data·=·sm.datasets.stackloss.load()
21 data.exog·=·sm.add_constant(data.exog)21 data.exog·=·sm.add_constant(data.exog)
22 Huber’s·T·norm·with·the·(default)·median·absolute·deviation·scaling22 Huber’s·T·norm·with·the·(default)·median·absolute·deviation·scaling
23 [4]:23 [·]:
24 huber_t·=·sm.RLM(data.endog,·data.exog,·M=sm.robust.norms.HuberT())24 huber_t·=·sm.RLM(data.endog,·data.exog,·M=sm.robust.norms.HuberT())
25 hub_results·=·huber_t.fit()25 hub_results·=·huber_t.fit()
26 print(hub_results.params)26 print(hub_results.params)
27 print(hub_results.bse)27 print(hub_results.bse)
28 print(28 print(
29 ····hub_results.summary(29 ····hub_results.summary(
30 ········yname="y",·xname=["var_%d"·%·i·for·i·in·range(len(hub_results.params))]30 ········yname="y",·xname=["var_%d"·%·i·for·i·in·range(len(hub_results.params))]
31 ····)31 ····)
32 )32 )
33 const·······-41.026498 
34 AIRFLOW·······0.829384 
35 WATERTEMP·····0.926066 
36 ACIDCONC·····-0.127847 
37 dtype:·float64 
38 const········9.791899 
39 AIRFLOW······0.111005 
40 WATERTEMP····0.302930 
41 ACIDCONC·····0.128650 
42 dtype:·float64 
43 ····················Robust·linear·Model·Regression·Results 
44 ============================================================================== 
45 Dep.·Variable:······················y···No.·Observations:···················21 
46 Model:····························RLM···Df·Residuals:·······················17 
47 Method:··························IRLS···Df·Model:····························3 
48 Norm:··························HuberT 
49 Scale·Est.:·······················mad 
50 Cov·Type:··························H1 
51 Date:················Sun,·10·Aug·2025 
52 Time:························13:13:47 
53 No.·Iterations:····················19 
54 ============================================================================== 
55 ·················coef····std·err··········z······P>|z|······[0.025······0.975] 
56 ------------------------------------------------------------------------------ 
57 var_0········-41.0265······9.792·····-4.190······0.000·····-60.218·····-21.835 
58 var_1··········0.8294······0.111······7.472······0.000·······0.612·······1.047 
59 var_2··········0.9261······0.303······3.057······0.002·······0.332·······1.520 
60 var_3·········-0.1278······0.129·····-0.994······0.320······-0.380·······0.124 
61 ============================================================================== 
  
62 If·the·model·instance·has·been·used·for·another·fit·with·different·fit 
63 parameters,·then·the·fit·options·might·not·be·the·correct·ones·anymore·. 
64 Huber’s·T·norm·with·‘H2’·covariance·matrix33 Huber’s·T·norm·with·‘H2’·covariance·matrix
65 [5]:34 [·]:
66 hub_results2·=·huber_t.fit(cov="H2")35 hub_results2·=·huber_t.fit(cov="H2")
67 print(hub_results2.params)36 print(hub_results2.params)
68 print(hub_results2.bse)37 print(hub_results2.bse)
69 const·······-41.026498 
70 AIRFLOW·······0.829384 
71 WATERTEMP·····0.926066 
72 ACIDCONC·····-0.127847 
73 dtype:·float64 
74 const········9.089504 
75 AIRFLOW······0.119460 
76 WATERTEMP····0.322355 
77 ACIDCONC·····0.117963 
78 dtype:·float64 
79 Andrew’s·Wave·norm·with·Huber’s·Proposal·2·scaling·and·‘H3’·covariance·matrix38 Andrew’s·Wave·norm·with·Huber’s·Proposal·2·scaling·and·‘H3’·covariance·matrix
80 [6]:39 [·]:
81 andrew_mod·=·sm.RLM(data.endog,·data.exog,·M=sm.robust.norms.AndrewWave())40 andrew_mod·=·sm.RLM(data.endog,·data.exog,·M=sm.robust.norms.AndrewWave())
82 andrew_results·=·andrew_mod.fit(scale_est=sm.robust.scale.HuberScale(),41 andrew_results·=·andrew_mod.fit(scale_est=sm.robust.scale.HuberScale(),
83 cov="H3")42 cov="H3")
84 print("Parameters:·",·andrew_results.params)43 print("Parameters:·",·andrew_results.params)
85 Parameters:··const·······-40.881796 
86 AIRFLOW·······0.792761 
87 WATERTEMP·····1.048576 
88 ACIDCONC·····-0.133609 
89 dtype:·float64 
90 See·help(sm.RLM.fit)·for·more·options·and·module·sm.robust.scale·for·scale44 See·help(sm.RLM.fit)·for·more·options·and·module·sm.robust.scale·for·scale
91 options45 options
92 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8om\x8mp\x8pa\x8ar\x8ri\x8in\x8ng\x8g·O\x8OL\x8LS\x8S·a\x8an\x8nd\x8d·R\x8RL\x8LM\x8M_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*46 *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8om\x8mp\x8pa\x8ar\x8ri\x8in\x8ng\x8g·O\x8OL\x8LS\x8S·a\x8an\x8nd\x8d·R\x8RL\x8LM\x8M_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
93 Artificial·data·with·outliers:47 Artificial·data·with·outliers:
94 [7]:48 [·]:
95 nsample·=·5049 nsample·=·50
96 x1·=·np.linspace(0,·20,·nsample)50 x1·=·np.linspace(0,·20,·nsample)
97 X·=·np.column_stack((x1,·(x1·-·5)·**·2))51 X·=·np.column_stack((x1,·(x1·-·5)·**·2))
98 X·=·sm.add_constant(X)52 X·=·sm.add_constant(X)
99 sig·=·0.3··#·smaller·error·variance·makes·OLS<->RLM·contrast·bigger53 sig·=·0.3··#·smaller·error·variance·makes·OLS<->RLM·contrast·bigger
100 beta·=·[5,·0.5,·-0.0]54 beta·=·[5,·0.5,·-0.0]
101 y_true2·=·np.dot(X,·beta)55 y_true2·=·np.dot(X,·beta)
102 y2·=·y_true2·+·sig·*·1.0·*·np.random.normal(size=nsample)56 y2·=·y_true2·+·sig·*·1.0·*·np.random.normal(size=nsample)
103 y2[[39,·41,·43,·45,·48]]·-=·5··#·add·some·outliers·(10%·of·nsample)57 y2[[39,·41,·43,·45,·48]]·-=·5··#·add·some·outliers·(10%·of·nsample)
104 *\x8**\x8**\x8**\x8*·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e·1\x81:\x8:·q\x8qu\x8ua\x8ad\x8dr\x8ra\x8at\x8ti\x8ic\x8c·f\x8fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8n·w\x8wi\x8it\x8th\x8h·l\x8li\x8in\x8ne\x8ea\x8ar\x8r·t\x8tr\x8ru\x8ut\x8th\x8h_\x8?\x8·*\x8**\x8**\x8**\x8*58 *\x8**\x8**\x8**\x8*·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e·1\x81:\x8:·q\x8qu\x8ua\x8ad\x8dr\x8ra\x8at\x8ti\x8ic\x8c·f\x8fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8n·w\x8wi\x8it\x8th\x8h·l\x8li\x8in\x8ne\x8ea\x8ar\x8r·t\x8tr\x8ru\x8ut\x8th\x8h_\x8?\x8·*\x8**\x8**\x8**\x8*
105 Note·that·the·quadratic·term·in·OLS·regression·will·capture·outlier·effects.59 Note·that·the·quadratic·term·in·OLS·regression·will·capture·outlier·effects.
106 [8]:60 [·]:
107 res·=·sm.OLS(y2,·X).fit()61 res·=·sm.OLS(y2,·X).fit()
108 print(res.params)62 print(res.params)
109 print(res.bse)63 print(res.bse)
110 print(res.predict())64 print(res.predict())
111 [·5.05665597··0.5275415··-0.0135642·] 
112 [0.46154403·0.07125617·0.00630507] 
113 [·4.717551····4.98597838··5.24988624··5.50927459··5.76414342··6.01449273 
114 ··6.26032253··6.50163281··6.73842358··6.97069482··7.19844655··7.42167877 
115 ··7.64039147··7.85458465··8.06425831··8.26941246··8.4700471···8.66616221 
116 ··8.85775781··9.04483389··9.22739046··9.40542751··9.57894504··9.74794306 
117 ··9.91242156·10.07238055·10.22782001·10.37873997·10.5251404··10.66702132 
118 ·10.80438272·10.93722461·11.06554698·11.18934983·11.30863316·11.42339698 
119 ·11.53364129·11.63936607·11.74057135·11.8372571··11.92942334·12.01707006 
120 ·12.10019726·12.17880495·12.25289312·12.32246178·12.38751092·12.44804054 
121 ·12.50405064·12.55554123] 
122 Estimate·RLM:65 Estimate·RLM:
123 [9]:66 [·]:
124 resrlm·=·sm.RLM(y2,·X).fit()67 resrlm·=·sm.RLM(y2,·X).fit()
125 print(resrlm.params)68 print(resrlm.params)
126 print(resrlm.bse)69 print(resrlm.bse)
127 [·5.01422175e+00··5.08736800e-01·-2.21950568e-03] 
128 [0.12351938·0.01906972·0.00168738] 
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59 ······<div·class="documentwrapper">59 ······<div·class="documentwrapper">
60 ········<div·class="bodywrapper">60 ········<div·class="bodywrapper">
61 ··········<div·class="body"·role="main">61 ··········<div·class="body"·role="main">
62 ············62 ············
63 ··<section·id="M-Estimators-for-Robust-Linear-Modeling">63 ··<section·id="M-Estimators-for-Robust-Linear-Modeling">
64 <h1>M-Estimators·for·Robust·Linear·Modeling<a·class="headerlink"·href="#M-Estimators-for-Robust-Linear-Modeling"·title="Link·to·this·heading">¶</a></h1>64 <h1>M-Estimators·for·Robust·Linear·Modeling<a·class="headerlink"·href="#M-Estimators-for-Robust-Linear-Modeling"·title="Link·to·this·heading">¶</a></h1>
65 <div·class="nbinput·nblast·docutils·container">65 <div·class="nbinput·nblast·docutils·container">
66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:66 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
67 </pre></div>67 </pre></div>
68 </div>68 </div>
69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline69 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
70 </pre></div>70 </pre></div>
71 </div>71 </div>
72 </div>72 </div>
73 <div·class="nbinput·nblast·docutils·container">73 <div·class="nbinput·nblast·docutils·container">
74 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:74 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
75 </pre></div>75 </pre></div>
76 </div>76 </div>
77 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.compat</span>·<span·class="kn">import</span>·<span·class="n">lmap</span>77 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.compat</span>·<span·class="kn">import</span>·<span·class="n">lmap</span>
78 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>78 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
79 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>79 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>
80 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>80 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
  
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94 <li><p><span·class="math·notranslate·nohighlight">\(s\)</span>·is·an·estimate·of·scale.</p></li>94 <li><p><span·class="math·notranslate·nohighlight">\(s\)</span>·is·an·estimate·of·scale.</p></li>
95 <li><p>The·robust·estimates·<span·class="math·notranslate·nohighlight">\(\hat{\beta}\)</span>·are·computed·by·the·iteratively·re-weighted·least·squares·algorithm</p></li>95 <li><p>The·robust·estimates·<span·class="math·notranslate·nohighlight">\(\hat{\beta}\)</span>·are·computed·by·the·iteratively·re-weighted·least·squares·algorithm</p></li>
96 </ul>96 </ul>
97 <ul·class="simple">97 <ul·class="simple">
98 <li><p>We·have·several·choices·available·for·the·weighting·functions·to·be·used</p></li>98 <li><p>We·have·several·choices·available·for·the·weighting·functions·to·be·used</p></li>
99 </ul>99 </ul>
100 <div·class="nbinput·nblast·docutils·container">100 <div·class="nbinput·nblast·docutils·container">
101 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:101 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
102 </pre></div>102 </pre></div>
103 </div>103 </div>
104 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">norms</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">robust</span><span·class="o">.</span><span·class="n">norms</span>104 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">norms</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">robust</span><span·class="o">.</span><span·class="n">norms</span>
105 </pre></div>105 </pre></div>
106 </div>106 </div>
107 </div>107 </div>
108 <div·class="nbinput·nblast·docutils·container">108 <div·class="nbinput·nblast·docutils·container">
109 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:109 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
110 </pre></div>110 </pre></div>
111 </div>111 </div>
112 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">plot_weights</span><span·class="p">(</span><span·class="n">support</span><span·class="p">,</span>·<span·class="n">weights_func</span><span·class="p">,</span>·<span·class="n">xlabels</span><span·class="p">,</span>·<span·class="n">xticks</span><span·class="p">):</span>112 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">plot_weights</span><span·class="p">(</span><span·class="n">support</span><span·class="p">,</span>·<span·class="n">weights_func</span><span·class="p">,</span>·<span·class="n">xlabels</span><span·class="p">,</span>·<span·class="n">xticks</span><span·class="p">):</span>
113 ····<span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>113 ····<span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>
114 ····<span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">111</span><span·class="p">)</span>114 ····<span·class="n">ax</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">111</span><span·class="p">)</span>
115 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">support</span><span·class="p">,</span>·<span·class="n">weights_func</span><span·class="p">(</span><span·class="n">support</span><span·class="p">))</span>115 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">support</span><span·class="p">,</span>·<span·class="n">weights_func</span><span·class="p">(</span><span·class="n">support</span><span·class="p">))</span>
116 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">set_xticks</span><span·class="p">(</span><span·class="n">xticks</span><span·class="p">)</span>116 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">set_xticks</span><span·class="p">(</span><span·class="n">xticks</span><span·class="p">)</span>
Offset 118, 1296 lines modifiedOffset 118, 498 lines modified
118 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">set_ylim</span><span·class="p">(</span><span·class="o">-</span><span·class="mf">0.1</span><span·class="p">,</span>·<span·class="mf">1.1</span><span·class="p">)</span>118 ····<span·class="n">ax</span><span·class="o">.</span><span·class="n">set_ylim</span><span·class="p">(</span><span·class="o">-</span><span·class="mf">0.1</span><span·class="p">,</span>·<span·class="mf">1.1</span><span·class="p">)</span>
119 ····<span·class="k">return</span>·<span·class="n">ax</span>119 ····<span·class="k">return</span>·<span·class="n">ax</span>
120 </pre></div>120 </pre></div>
121 </div>121 </div>
122 </div>122 </div>
123 <section·id="Andrew's-Wave">123 <section·id="Andrew's-Wave">
124 <h2>Andrew’s·Wave<a·class="headerlink"·href="#Andrew's-Wave"·title="Link·to·this·heading">¶</a></h2>124 <h2>Andrew’s·Wave<a·class="headerlink"·href="#Andrew's-Wave"·title="Link·to·this·heading">¶</a></h2>
125 <div·class="nbinput·docutils·container">125 <div·class="nbinput·nblast·docutils·container">
126 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:126 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
127 </pre></div>127 </pre></div>
128 </div>128 </div>
129 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">help</span><span·class="p">(</span><span·class="n">norms</span><span·class="o">.</span><span·class="n">AndrewWave</span><span·class="o">.</span><span·class="n">weights</span><span·class="p">)</span>129 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">help</span><span·class="p">(</span><span·class="n">norms</span><span·class="o">.</span><span·class="n">AndrewWave</span><span·class="o">.</span><span·class="n">weights</span><span·class="p">)</span>
130 </pre></div>130 </pre></div>
131 </div>131 </div>
132 </div>132 </div>
133 <div·class="nboutput·nblast·docutils·container">133 <div·class="nbinput·nblast·docutils·container">
134 <div·class="prompt·empty·docutils·container"> 
135 </div> 
136 <div·class="output_area·docutils·container"> 
137 <div·class="highlight"><pre> 
138 Help·on·function·weights·in·module·statsmodels.robust.norms: 
  
139 weights(self,·z) 
140 ····Andrew&#39;s·wave·weighting·function·for·the·IRLS·algorithm 
  
141 ····The·psi·function·scaled·by·z 
  
142 ····Parameters 
143 ····---------- 
144 ····z·:·array_like 
145 ········1d·array 
  
146 ····Returns 
147 ····------- 
148 ····weights·:·ndarray 
149 ········weights(z)·=·sin(z/a)·/·(z/a)·····for·\|z\|·&lt;=·a*pi 
  
150 ········weights(z)·=·0····················for·\|z\|·&gt;·a*pi 
  
151 </pre></div></div> 
152 </div> 
153 <div·class="nbinput·docutils·container"> 
154 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:134 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
155 </pre></div>135 </pre></div>
156 </div>136 </div>
157 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">a</span>·<span·class="o">=</span>·<span·class="mf">1.339</span>137 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">a</span>·<span·class="o">=</span>·<span·class="mf">1.339</span>
158 <span·class="n">support</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="o">-</span><span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span>·<span·class="o">*</span>·<span·class="n">a</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span>·<span·class="o">*</span>·<span·class="n">a</span><span·class="p">,</span>·<span·class="mi">100</span><span·class="p">)</span>138 <span·class="n">support</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="o">-</span><span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span>·<span·class="o">*</span>·<span·class="n">a</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span>·<span·class="o">*</span>·<span·class="n">a</span><span·class="p">,</span>·<span·class="mi">100</span><span·class="p">)</span>
159 <span·class="n">andrew</span>·<span·class="o">=</span>·<span·class="n">norms</span><span·class="o">.</span><span·class="n">AndrewWave</span><span·class="p">(</span><span·class="n">a</span><span·class="o">=</span><span·class="n">a</span><span·class="p">)</span>139 <span·class="n">andrew</span>·<span·class="o">=</span>·<span·class="n">norms</span><span·class="o">.</span><span·class="n">AndrewWave</span><span·class="p">(</span><span·class="n">a</span><span·class="o">=</span><span·class="n">a</span><span·class="p">)</span>
160 <span·class="n">plot_weights</span><span·class="p">(</span>140 <span·class="n">plot_weights</span><span·class="p">(</span>
161 ····<span·class="n">support</span><span·class="p">,</span>·<span·class="n">andrew</span><span·class="o">.</span><span·class="n">weights</span><span·class="p">,</span>·<span·class="p">[</span><span·class="s2">&quot;$-\pi*a$&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;0&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;$\pi*a$&quot;</span><span·class="p">],</span>·<span·class="p">[</span><span·class="o">-</span><span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span>·<span·class="o">*</span>·<span·class="n">a</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span>·<span·class="o">*</span>·<span·class="n">a</span><span·class="p">]</span>141 ····<span·class="n">support</span><span·class="p">,</span>·<span·class="n">andrew</span><span·class="o">.</span><span·class="n">weights</span><span·class="p">,</span>·<span·class="p">[</span><span·class="s2">&quot;$-\pi*a$&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;0&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;$\pi*a$&quot;</span><span·class="p">],</span>·<span·class="p">[</span><span·class="o">-</span><span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span>·<span·class="o">*</span>·<span·class="n">a</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">pi</span>·<span·class="o">*</span>·<span·class="n">a</span><span·class="p">]</span>
162 <span·class="p">)</span>142 <span·class="p">)</span>
163 </pre></div>143 </pre></div>
164 </div>144 </div>
165 </div>145 </div>
166 <div·class="nboutput·docutils·container"> 
167 <div·class="prompt·empty·docutils·container"> 
168 </div> 
169 <div·class="output_area·stderr·docutils·container"> 
170 <div·class="highlight"><pre> 
171 &lt;&gt;:5:·SyntaxWarning:·invalid·escape·sequence·&#39;\p&#39; 
172 &lt;&gt;:5:·SyntaxWarning:·invalid·escape·sequence·&#39;\p&#39; 
173 &lt;&gt;:5:·SyntaxWarning:·invalid·escape·sequence·&#39;\p&#39; 
174 &lt;&gt;:5:·SyntaxWarning:·invalid·escape·sequence·&#39;\p&#39; 
175 /tmp/ipykernel_nnnnnnn/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·&#39;\p&#39; 
176 ··support,·andrew.weights,·[&#34;$-\pi*a$&#34;,·&#34;0&#34;,·&#34;$\pi*a$&#34;],·[-np.pi·*·a,·0,·np.pi·*·a] 
177 /tmp/ipykernel_nnnnnnn/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence·&#39;\p&#39; 
178 ··support,·andrew.weights,·[&#34;$-\pi*a$&#34;,·&#34;0&#34;,·&#34;$\pi*a$&#34;],·[-np.pi·*·a,·0,·np.pi·*·a] 
179 </pre></div></div> 
180 </div> 
181 <div·class="nboutput·docutils·container"> 
182 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]: 
183 </pre></div> 
184 </div> 
185 <div·class="output_area·docutils·container"> 
186 <div·class="highlight"><pre> 
187 &lt;Axes:·&gt; 
188 </pre></div></div> 
189 </div> 
190 <div·class="nboutput·nblast·docutils·container"> 
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·M-Estimators·for·Robust·Linear·Modeling8 ····*·M-Estimators·for·Robust·Linear·Modeling
9 *\x8**\x8**\x8**\x8**\x8**\x8*·M\x8M-\x8-E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8to\x8or\x8rs\x8s·f\x8fo\x8or\x8r·R\x8Ro\x8ob\x8bu\x8us\x8st\x8t·L\x8Li\x8in\x8ne\x8ea\x8ar\x8r·M\x8Mo\x8od\x8de\x8el\x8li\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·M\x8M-\x8-E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8to\x8or\x8rs\x8s·f\x8fo\x8or\x8r·R\x8Ro\x8ob\x8bu\x8us\x8st\x8t·L\x8Li\x8in\x8ne\x8ea\x8ar\x8r·M\x8Mo\x8od\x8de\x8el\x8li\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 %matplotlib·inline11 %matplotlib·inline
12 [2]:12 [·]:
13 from·statsmodels.compat·import·lmap13 from·statsmodels.compat·import·lmap
14 import·numpy·as·np14 import·numpy·as·np
15 from·scipy·import·stats15 from·scipy·import·stats
16 import·matplotlib.pyplot·as·plt16 import·matplotlib.pyplot·as·plt
  
17 import·statsmodels.api·as·sm17 import·statsmodels.api·as·sm
18 ····*·An·M-estimator·minimizes·the·function18 ····*·An·M-estimator·minimizes·the·function
19 \[Q(e_i,·\rho)·=·\sum_i~\rho·\left·(\frac{e_i}{s}\right·)\]19 \[Q(e_i,·\rho)·=·\sum_i~\rho·\left·(\frac{e_i}{s}\right·)\]
20 where·\(\rho\)·is·a·symmetric·function·of·the·residuals20 where·\(\rho\)·is·a·symmetric·function·of·the·residuals
21 ····*·The·effect·of·\(\rho\)·is·to·reduce·the·influence·of·outliers21 ····*·The·effect·of·\(\rho\)·is·to·reduce·the·influence·of·outliers
22 ····*·\(s\)·is·an·estimate·of·scale.22 ····*·\(s\)·is·an·estimate·of·scale.
23 ····*·The·robust·estimates·\(\hat{\beta}\)·are·computed·by·the·iteratively·re-23 ····*·The·robust·estimates·\(\hat{\beta}\)·are·computed·by·the·iteratively·re-
24 ······weighted·least·squares·algorithm24 ······weighted·least·squares·algorithm
25 ····*·We·have·several·choices·available·for·the·weighting·functions·to·be·used25 ····*·We·have·several·choices·available·for·the·weighting·functions·to·be·used
26 [3]:26 [·]:
27 norms·=·sm.robust.norms27 norms·=·sm.robust.norms
28 [4]:28 [·]:
29 def·plot_weights(support,·weights_func,·xlabels,·xticks):29 def·plot_weights(support,·weights_func,·xlabels,·xticks):
30 ····fig·=·plt.figure(figsize=(12,·8))30 ····fig·=·plt.figure(figsize=(12,·8))
31 ····ax·=·fig.add_subplot(111)31 ····ax·=·fig.add_subplot(111)
32 ····ax.plot(support,·weights_func(support))32 ····ax.plot(support,·weights_func(support))
33 ····ax.set_xticks(xticks)33 ····ax.set_xticks(xticks)
34 ····ax.set_xticklabels(xlabels,·fontsize=16)34 ····ax.set_xticklabels(xlabels,·fontsize=16)
35 ····ax.set_ylim(-0.1,·1.1)35 ····ax.set_ylim(-0.1,·1.1)
36 ····return·ax36 ····return·ax
37 *\x8**\x8**\x8**\x8**\x8*·A\x8An\x8nd\x8dr\x8re\x8ew\x8w?\x8’s\x8s·W\x8Wa\x8av\x8ve\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*37 *\x8**\x8**\x8**\x8**\x8*·A\x8An\x8nd\x8dr\x8re\x8ew\x8w?\x8’s\x8s·W\x8Wa\x8av\x8ve\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
38 [5]:38 [·]:
39 help(norms.AndrewWave.weights)39 help(norms.AndrewWave.weights)
40 Help·on·function·weights·in·module·statsmodels.robust.norms: 
  
41 weights(self,·z) 
42 ····Andrew's·wave·weighting·function·for·the·IRLS·algorithm 
  
43 ····The·psi·function·scaled·by·z 
  
44 ····Parameters 
45 ····---------- 
46 ····z·:·array_like 
47 ········1d·array 
  
48 ····Returns 
49 ····------- 
50 ····weights·:·ndarray 
51 ········weights(z)·=·sin(z/a)·/·(z/a)·····for·\|z\|·<=·a*pi 
  
52 ········weights(z)·=·0····················for·\|z\|·>·a*pi 
53 [6]:40 [·]:
54 a·=·1.33941 a·=·1.339
55 support·=·np.linspace(-np.pi·*·a,·np.pi·*·a,·100)42 support·=·np.linspace(-np.pi·*·a,·np.pi·*·a,·100)
56 andrew·=·norms.AndrewWave(a=a)43 andrew·=·norms.AndrewWave(a=a)
57 plot_weights(44 plot_weights(
58 ····support,·andrew.weights,·["$-\pi*a$",·"0",·"$\pi*a$"],·[-np.pi·*·a,·0,45 ····support,·andrew.weights,·["$-\pi*a$",·"0",·"$\pi*a$"],·[-np.pi·*·a,·0,
59 np.pi·*·a]46 np.pi·*·a]
60 )47 )
61 <>:5:·SyntaxWarning:·invalid·escape·sequence·'\p' 
62 <>:5:·SyntaxWarning:·invalid·escape·sequence·'\p' 
63 <>:5:·SyntaxWarning:·invalid·escape·sequence·'\p' 
64 <>:5:·SyntaxWarning:·invalid·escape·sequence·'\p' 
65 /tmp/ipykernel_nnnnnnn/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence 
66 '\p' 
67 ··support,·andrew.weights,·["$-\pi*a$",·"0",·"$\pi*a$"],·[-np.pi·*·a,·0,·np.pi 
68 *·a] 
69 /tmp/ipykernel_nnnnnnn/3509132601.py:5:·SyntaxWarning:·invalid·escape·sequence 
70 '\p' 
71 ··support,·andrew.weights,·["$-\pi*a$",·"0",·"$\pi*a$"],·[-np.pi·*·a,·0,·np.pi 
72 *·a] 
73 [6]: 
74 <Axes:·> 
75 [../../../_images/examples_notebooks_generated_robust_models_1_9_2.png] 
76 *\x8**\x8**\x8**\x8**\x8*·H\x8Ha\x8am\x8mp\x8pe\x8el\x8l?\x8’s\x8s·1\x817\x87A\x8A_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*48 *\x8**\x8**\x8**\x8**\x8*·H\x8Ha\x8am\x8mp\x8pe\x8el\x8l?\x8’s\x8s·1\x817\x87A\x8A_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
77 [7]:49 [·]:
78 help(norms.Hampel.weights)50 help(norms.Hampel.weights)
79 Help·on·function·weights·in·module·statsmodels.robust.norms: 
  
80 weights(self,·z) 
81 ····Hampel·weighting·function·for·the·IRLS·algorithm 
  
82 ····The·psi·function·scaled·by·z 
  
83 ····Parameters 
84 ····---------- 
85 ····z·:·array_like 
86 ········1d·array 
  
87 ····Returns 
88 ····------- 
89 ····weights·:·ndarray 
90 ········weights(z)·=·1································for·\|z\|·<=·a 
  
91 ········weights(z)·=·a/\|z\|··························for·a·<·\|z\|·<=·b 
  
92 ········weights(z)·=·a*(c·-·\|z\|)/(\|z\|*(c-b))······for·b·<·\|z\|·<=·c 
  
93 ········weights(z)·=·0································for·\|z\|·>·c 
94 [8]:51 [·]:
95 c·=·852 c·=·8
96 support·=·np.linspace(-3·*·c,·3·*·c,·1000)53 support·=·np.linspace(-3·*·c,·3·*·c,·1000)
97 hampel·=·norms.Hampel(a=2.0,·b=4.0,·c=c)54 hampel·=·norms.Hampel(a=2.0,·b=4.0,·c=c)
98 plot_weights(support,·hampel.weights,·["3*c",·"0",·"3*c"],·[-3·*·c,·0,·3·*·c])55 plot_weights(support,·hampel.weights,·["3*c",·"0",·"3*c"],·[-3·*·c,·0,·3·*·c])
99 [8]: 
100 <Axes:·> 
101 [../../../_images/examples_notebooks_generated_robust_models_1_12_1.png] 
102 *\x8**\x8**\x8**\x8**\x8*·H\x8Hu\x8ub\x8be\x8er\x8r?\x8’s\x8s·t\x8t_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*56 *\x8**\x8**\x8**\x8**\x8*·H\x8Hu\x8ub\x8be\x8er\x8r?\x8’s\x8s·t\x8t_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
103 [9]:57 [·]:
104 help(norms.HuberT.weights)58 help(norms.HuberT.weights)
 59 [·]:
105 Help·on·function·weights·in·module·statsmodels.robust.norms: 
  
106 weights(self,·z) 
107 ····Huber's·t·weighting·function·for·the·IRLS·algorithm 
  
108 ····The·psi·function·scaled·by·z 
  
109 ····Parameters 
110 ····---------- 
111 ····z·:·array_like 
112 ········1d·array 
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58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Autoregressive-Moving-Average-(ARMA):-Sunspots-data">61 ··<section·id="Autoregressive-Moving-Average-(ARMA):-Sunspots-data">
62 <h1>Autoregressive·Moving·Average·(ARMA):·Sunspots·data<a·class="headerlink"·href="#Autoregressive-Moving-Average-(ARMA):-Sunspots-data"·title="Link·to·this·heading">¶</a></h1>62 <h1>Autoregressive·Moving·Average·(ARMA):·Sunspots·data<a·class="headerlink"·href="#Autoregressive-Moving-Average-(ARMA):-Sunspots-data"·title="Link·to·this·heading">¶</a></h1>
63 <p>This·notebook·replicates·the·existing·ARMA·notebook·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.tsa.statespace.SARIMAX</span></code>·class·rather·than·the·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.tsa.ARMA</span></code>·class.</p>63 <p>This·notebook·replicates·the·existing·ARMA·notebook·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.tsa.statespace.SARIMAX</span></code>·class·rather·than·the·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.tsa.ARMA</span></code>·class.</p>
64 <div·class="nbinput·nblast·docutils·container">64 <div·class="nbinput·nblast·docutils·container">
65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
66 </pre></div>66 </pre></div>
67 </div>67 </div>
68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
69 </pre></div>69 </pre></div>
70 </div>70 </div>
71 </div>71 </div>
72 <div·class="nbinput·nblast·docutils·container">72 <div·class="nbinput·nblast·docutils·container">
73 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:73 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
74 </pre></div>74 </pre></div>
75 </div>75 </div>
76 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>76 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
77 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>77 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>
78 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>78 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
79 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>79 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
  
80 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>80 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
81 </pre></div>81 </pre></div>
82 </div>82 </div>
83 </div>83 </div>
84 <div·class="nbinput·nblast·docutils·container">84 <div·class="nbinput·nblast·docutils·container">
85 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:85 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
86 </pre></div>86 </pre></div>
87 </div>87 </div>
88 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.graphics.api</span>·<span·class="kn">import</span>·<span·class="n">qqplot</span>88 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.graphics.api</span>·<span·class="kn">import</span>·<span·class="n">qqplot</span>
89 </pre></div>89 </pre></div>
90 </div>90 </div>
91 </div>91 </div>
92 <section·id="Sunspots-Data">92 <section·id="Sunspots-Data">
93 <h2>Sunspots·Data<a·class="headerlink"·href="#Sunspots-Data"·title="Link·to·this·heading">¶</a></h2>93 <h2>Sunspots·Data<a·class="headerlink"·href="#Sunspots-Data"·title="Link·to·this·heading">¶</a></h2>
94 <div·class="nbinput·docutils·container">94 <div·class="nbinput·nblast·docutils·container">
95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
96 </pre></div>96 </pre></div>
97 </div>97 </div>
98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">sunspots</span><span·class="o">.</span><span·class="n">NOTE</span><span·class="p">)</span>98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">sunspots</span><span·class="o">.</span><span·class="n">NOTE</span><span·class="p">)</span>
99 </pre></div>99 </pre></div>
100 </div>100 </div>
101 </div>101 </div>
102 <div·class="nboutput·nblast·docutils·container"> 
103 <div·class="prompt·empty·docutils·container"> 
104 </div> 
105 <div·class="output_area·docutils·container"> 
106 <div·class="highlight"><pre> 
107 :: 
  
108 ····Number·of·Observations·-·309·(Annual·1700·-·2008) 
109 ····Number·of·Variables·-·1 
110 ····Variable·name·definitions:: 
  
111 ········SUNACTIVITY·-·Number·of·sunspots·for·each·year 
  
112 ····The·data·file·contains·a·&#39;YEAR&#39;·variable·that·is·not·returned·by·load. 
  
113 </pre></div></div> 
114 </div> 
115 <div·class="nbinput·nblast·docutils·container">102 <div·class="nbinput·nblast·docutils·container">
116 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:103 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
117 </pre></div>104 </pre></div>
118 </div>105 </div>
119 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">sunspots</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>106 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">sunspots</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>
120 </pre></div>107 </pre></div>
121 </div>108 </div>
122 </div>109 </div>
123 <div·class="nbinput·nblast·docutils·container">110 <div·class="nbinput·nblast·docutils·container">
124 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:111 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
125 </pre></div>112 </pre></div>
126 </div>113 </div>
127 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">Index</span><span·class="p">(</span><span·class="n">pd</span><span·class="o">.</span><span·class="n">date_range</span><span·class="p">(</span><span·class="s2">&quot;1700&quot;</span><span·class="p">,</span>·<span·class="n">end</span><span·class="o">=</span><span·class="s2">&quot;2009&quot;</span><span·class="p">,</span>·<span·class="n">freq</span><span·class="o">=</span><span·class="s2">&quot;YE-DEC&quot;</span><span·class="p">))</span>114 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">Index</span><span·class="p">(</span><span·class="n">pd</span><span·class="o">.</span><span·class="n">date_range</span><span·class="p">(</span><span·class="s2">&quot;1700&quot;</span><span·class="p">,</span>·<span·class="n">end</span><span·class="o">=</span><span·class="s2">&quot;2009&quot;</span><span·class="p">,</span>·<span·class="n">freq</span><span·class="o">=</span><span·class="s2">&quot;YE-DEC&quot;</span><span·class="p">))</span>
128 <span·class="k">del</span>·<span·class="n">dta</span><span·class="p">[</span><span·class="s2">&quot;YEAR&quot;</span><span·class="p">]</span>115 <span·class="k">del</span>·<span·class="n">dta</span><span·class="p">[</span><span·class="s2">&quot;YEAR&quot;</span><span·class="p">]</span>
129 </pre></div>116 </pre></div>
130 </div>117 </div>
131 </div>118 </div>
132 <div·class="nbinput·docutils·container">119 <div·class="nbinput·nblast·docutils·container">
133 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:120 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
134 </pre></div>121 </pre></div>
135 </div>122 </div>
136 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span><span·class="mi">4</span><span·class="p">));</span>123 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span><span·class="mi">4</span><span·class="p">));</span>
137 </pre></div>124 </pre></div>
138 </div>125 </div>
139 </div>126 </div>
140 <div·class="nboutput·nblast·docutils·container">127 <div·class="nbinput·nblast·docutils·container">
141 <div·class="prompt·empty·docutils·container"> 
142 </div> 
143 <div·class="output_area·docutils·container"> 
144 <img·alt="../../../_images/examples_notebooks_generated_statespace_arma_0_9_0.png"·src="../../../_images/examples_notebooks_generated_statespace_arma_0_9_0.png"·/> 
145 </div> 
146 </div> 
147 <div·class="nbinput·docutils·container"> 
148 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[8]:128 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
149 </pre></div>129 </pre></div>
150 </div>130 </div>
151 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span><span·class="mi">8</span><span·class="p">))</span>131 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span><span·class="mi">8</span><span·class="p">))</span>
152 <span·class="n">ax1</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">211</span><span·class="p">)</span>132 <span·class="n">ax1</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">211</span><span·class="p">)</span>
153 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">plot_acf</span><span·class="p">(</span><span·class="n">dta</span><span·class="o">.</span><span·class="n">values</span><span·class="o">.</span><span·class="n">squeeze</span><span·class="p">(),</span>·<span·class="n">lags</span><span·class="o">=</span><span·class="mi">40</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax1</span><span·class="p">)</span>133 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">plot_acf</span><span·class="p">(</span><span·class="n">dta</span><span·class="o">.</span><span·class="n">values</span><span·class="o">.</span><span·class="n">squeeze</span><span·class="p">(),</span>·<span·class="n">lags</span><span·class="o">=</span><span·class="mi">40</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax1</span><span·class="p">)</span>
154 <span·class="n">ax2</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">212</span><span·class="p">)</span>134 <span·class="n">ax2</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">212</span><span·class="p">)</span>
155 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">plot_pacf</span><span·class="p">(</span><span·class="n">dta</span><span·class="p">,</span>·<span·class="n">lags</span><span·class="o">=</span><span·class="mi">40</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax2</span><span·class="p">)</span>135 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">plot_pacf</span><span·class="p">(</span><span·class="n">dta</span><span·class="p">,</span>·<span·class="n">lags</span><span·class="o">=</span><span·class="mi">40</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax2</span><span·class="p">)</span>
156 </pre></div>136 </pre></div>
157 </div>137 </div>
158 </div>138 </div>
159 <div·class="nboutput·nblast·docutils·container">139 <div·class="nbinput·nblast·docutils·container">
160 <div·class="prompt·empty·docutils·container"> 
161 </div> 
162 <div·class="output_area·docutils·container"> 
163 <img·alt="../../../_images/examples_notebooks_generated_statespace_arma_0_10_0.png"·src="../../../_images/examples_notebooks_generated_statespace_arma_0_10_0.png"·/> 
164 </div> 
165 </div> 
166 <div·class="nbinput·docutils·container"> 
167 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[9]:140 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
168 </pre></div>141 </pre></div>
169 </div>142 </div>
170 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">arma_mod20</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">statespace</span><span·class="o">.</span><span·class="n">SARIMAX</span><span·class="p">(</span><span·class="n">dta</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">2</span><span·class="p">,</span><span·class="mi">0</span><span·class="p">,</span><span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s1">&#39;c&#39;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">disp</span><span·class="o">=</span><span·class="kc">False</span><span·class="p">)</span>143 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">arma_mod20</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">statespace</span><span·class="o">.</span><span·class="n">SARIMAX</span><span·class="p">(</span><span·class="n">dta</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">2</span><span·class="p">,</span><span·class="mi">0</span><span·class="p">,</span><span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s1">&#39;c&#39;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">(</span><span·class="n">disp</span><span·class="o">=</span><span·class="kc">False</span><span·class="p">)</span>
171 <span·class="nb">print</span><span·class="p">(</span><span·class="n">arma_mod20</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>144 <span·class="nb">print</span><span·class="p">(</span><span·class="n">arma_mod20</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>
172 </pre></div>145 </pre></div>
173 </div>146 </div>
174 </div>147 </div>
175 <div·class="nboutput·nblast·docutils·container"> 
176 <div·class="prompt·empty·docutils·container"> 
177 </div> 
178 <div·class="output_area·docutils·container"> 
179 <div·class="highlight"><pre> 
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6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Autoregressive·Moving·Average·(ARMA):·Sunspots·data8 ····*·Autoregressive·Moving·Average·(ARMA):·Sunspots·data
9 *\x8**\x8**\x8**\x8**\x8**\x8*·A\x8Au\x8ut\x8to\x8or\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8iv\x8ve\x8e·M\x8Mo\x8ov\x8vi\x8in\x8ng\x8g·A\x8Av\x8ve\x8er\x8ra\x8ag\x8ge\x8e·(\x8(A\x8AR\x8RM\x8MA\x8A)\x8):\x8:·S\x8Su\x8un\x8ns\x8sp\x8po\x8ot\x8ts\x8s·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·A\x8Au\x8ut\x8to\x8or\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8iv\x8ve\x8e·M\x8Mo\x8ov\x8vi\x8in\x8ng\x8g·A\x8Av\x8ve\x8er\x8ra\x8ag\x8ge\x8e·(\x8(A\x8AR\x8RM\x8MA\x8A)\x8):\x8:·S\x8Su\x8un\x8ns\x8sp\x8po\x8ot\x8ts\x8s·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 This·notebook·replicates·the·existing·ARMA·notebook·using·the10 This·notebook·replicates·the·existing·ARMA·notebook·using·the
11 statsmodels.tsa.statespace.SARIMAX·class·rather·than·the·statsmodels.tsa.ARMA11 statsmodels.tsa.statespace.SARIMAX·class·rather·than·the·statsmodels.tsa.ARMA
12 class.12 class.
13 [1]:13 [·]:
14 %matplotlib·inline14 %matplotlib·inline
15 [2]:15 [·]:
16 import·numpy·as·np16 import·numpy·as·np
17 from·scipy·import·stats17 from·scipy·import·stats
18 import·pandas·as·pd18 import·pandas·as·pd
19 import·matplotlib.pyplot·as·plt19 import·matplotlib.pyplot·as·plt
  
20 import·statsmodels.api·as·sm20 import·statsmodels.api·as·sm
21 [3]:21 [·]:
22 from·statsmodels.graphics.api·import·qqplot22 from·statsmodels.graphics.api·import·qqplot
23 *\x8**\x8**\x8**\x8**\x8*·S\x8Su\x8un\x8ns\x8sp\x8po\x8ot\x8ts\x8s·D\x8Da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*23 *\x8**\x8**\x8**\x8**\x8*·S\x8Su\x8un\x8ns\x8sp\x8po\x8ot\x8ts\x8s·D\x8Da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
24 [4]:24 [·]:
25 print(sm.datasets.sunspots.NOTE)25 print(sm.datasets.sunspots.NOTE)
26 :: 
  
27 ····Number·of·Observations·-·309·(Annual·1700·-·2008) 
28 ····Number·of·Variables·-·1 
29 ····Variable·name·definitions:: 
  
30 ········SUNACTIVITY·-·Number·of·sunspots·for·each·year 
  
31 ····The·data·file·contains·a·'YEAR'·variable·that·is·not·returned·by·load. 
32 [5]:26 [·]:
33 dta·=·sm.datasets.sunspots.load_pandas().data27 dta·=·sm.datasets.sunspots.load_pandas().data
34 [6]:28 [·]:
35 dta.index·=·pd.Index(pd.date_range("1700",·end="2009",·freq="YE-DEC"))29 dta.index·=·pd.Index(pd.date_range("1700",·end="2009",·freq="YE-DEC"))
36 del·dta["YEAR"]30 del·dta["YEAR"]
37 [7]:31 [·]:
38 dta.plot(figsize=(12,4));32 dta.plot(figsize=(12,4));
39 [../../../_images/examples_notebooks_generated_statespace_arma_0_9_0.png] 
40 [8]:33 [·]:
41 fig·=·plt.figure(figsize=(12,8))34 fig·=·plt.figure(figsize=(12,8))
42 ax1·=·fig.add_subplot(211)35 ax1·=·fig.add_subplot(211)
43 fig·=·sm.graphics.tsa.plot_acf(dta.values.squeeze(),·lags=40,·ax=ax1)36 fig·=·sm.graphics.tsa.plot_acf(dta.values.squeeze(),·lags=40,·ax=ax1)
44 ax2·=·fig.add_subplot(212)37 ax2·=·fig.add_subplot(212)
45 fig·=·sm.graphics.tsa.plot_pacf(dta,·lags=40,·ax=ax2)38 fig·=·sm.graphics.tsa.plot_pacf(dta,·lags=40,·ax=ax2)
46 [../../../_images/examples_notebooks_generated_statespace_arma_0_10_0.png] 
47 [9]:39 [·]:
48 arma_mod20·=·sm.tsa.statespace.SARIMAX(dta,·order=(2,0,0),·trend='c').fit40 arma_mod20·=·sm.tsa.statespace.SARIMAX(dta,·order=(2,0,0),·trend='c').fit
49 (disp=False)41 (disp=False)
50 print(arma_mod20.params)42 print(arma_mod20.params)
 43 [·]:
51 intercept·····14.793947 
52 ar.L1··········1.390659 
53 ar.L2·········-0.688568 
54 sigma2·······274.761105 
55 dtype:·float64 
56 [10]: 
57 arma_mod30·=·sm.tsa.statespace.SARIMAX(dta,·order=(3,0,0),·trend='c').fit44 arma_mod30·=·sm.tsa.statespace.SARIMAX(dta,·order=(3,0,0),·trend='c').fit
58 (disp=False)45 (disp=False)
59 [11]:46 [·]:
60 print(arma_mod20.aic,·arma_mod20.bic,·arma_mod20.hqic)47 print(arma_mod20.aic,·arma_mod20.bic,·arma_mod20.hqic)
 48 [·]:
61 2622.636338141593·2637.569703249184·2628.606725986839 
62 [12]: 
63 print(arma_mod30.params)49 print(arma_mod30.params)
 50 [·]:
64 intercept·····16.762205 
65 ar.L1··········1.300810 
66 ar.L2·········-0.508122 
67 ar.L3·········-0.129612 
68 sigma2·······270.102651 
69 dtype:·float64 
70 [13]: 
71 print(arma_mod30.aic,·arma_mod30.bic,·arma_mod30.hqic)51 print(arma_mod30.aic,·arma_mod30.bic,·arma_mod30.hqic)
72 2619.403629663393·2638.070336047882·2626.8666144699505 
73 ····*·Does·our·model·obey·the·theory?52 ····*·Does·our·model·obey·the·theory?
74 [14]:53 [·]:
75 sm.stats.durbin_watson(arma_mod30.resid)54 sm.stats.durbin_watson(arma_mod30.resid)
 55 [·]:
76 [14]: 
77 np.float64(1.9564844839276543) 
78 [15]: 
79 fig·=·plt.figure(figsize=(12,4))56 fig·=·plt.figure(figsize=(12,4))
80 ax·=·fig.add_subplot(111)57 ax·=·fig.add_subplot(111)
81 ax·=·plt.plot(arma_mod30.resid)58 ax·=·plt.plot(arma_mod30.resid)
 59 [·]:
82 [../../../_images/examples_notebooks_generated_statespace_arma_0_18_0.png] 
83 [16]: 
84 resid·=·arma_mod30.resid60 resid·=·arma_mod30.resid
85 [17]:61 [·]:
86 stats.normaltest(resid)62 stats.normaltest(resid)
 63 [·]:
87 [17]: 
88 NormaltestResult(statistic=np.float64(49.8470061602401),·pvalue=np.float64 
89 (1.4992019644216866e-11)) 
90 [18]: 
91 fig·=·plt.figure(figsize=(12,4))64 fig·=·plt.figure(figsize=(12,4))
92 ax·=·fig.add_subplot(111)65 ax·=·fig.add_subplot(111)
93 fig·=·qqplot(resid,·line='q',·ax=ax,·fit=True)66 fig·=·qqplot(resid,·line='q',·ax=ax,·fit=True)
 67 [·]:
94 [../../../_images/examples_notebooks_generated_statespace_arma_0_21_0.png] 
95 [19]: 
96 fig·=·plt.figure(figsize=(12,8))68 fig·=·plt.figure(figsize=(12,8))
97 ax1·=·fig.add_subplot(211)69 ax1·=·fig.add_subplot(211)
98 fig·=·sm.graphics.tsa.plot_acf(resid,·lags=40,·ax=ax1)70 fig·=·sm.graphics.tsa.plot_acf(resid,·lags=40,·ax=ax1)
99 ax2·=·fig.add_subplot(212)71 ax2·=·fig.add_subplot(212)
100 fig·=·sm.graphics.tsa.plot_pacf(resid,·lags=40,·ax=ax2)72 fig·=·sm.graphics.tsa.plot_pacf(resid,·lags=40,·ax=ax2)
 73 [·]:
101 [../../../_images/examples_notebooks_generated_statespace_arma_0_22_0.png] 
102 [20]: 
103 r,q,p·=·sm.tsa.acf(resid,·fft=True,·qstat=True)74 r,q,p·=·sm.tsa.acf(resid,·fft=True,·qstat=True)
104 data·=·np.c_[r[1:],·q,·p]75 data·=·np.c_[r[1:],·q,·p]
105 index·=·pd.Index(range(1,q.shape[0]+1),·name="lag")76 index·=·pd.Index(range(1,q.shape[0]+1),·name="lag")
106 table·=·pd.DataFrame(data,·columns=["AC",·"Q",·"Prob(>Q)"],·index=index)77 table·=·pd.DataFrame(data,·columns=["AC",·"Q",·"Prob(>Q)"],·index=index)
107 print(table)78 print(table)
108 ···········AC··········Q······Prob(>Q) 
109 lag 
110 1····0.009176···0.026273··8.712350e-01 
111 2····0.041820···0.573727··7.506142e-01 
112 3···-0.001342···0.574292··9.022915e-01 
113 4····0.136064···6.407488··1.707135e-01 
114 5····0.092433···9.108334··1.048203e-01 
115 6····0.091919··11.788018··6.686842e-02 
116 7····0.068735··13.291375··6.531941e-02 
117 8···-0.015021··13.363411··9.994248e-02 
118 9····0.187599··24.636916··3.400197e-03 
119 10···0.213724··39.317881··2.233182e-05 
120 11···0.201092··52.358270··2.347759e-07 
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67 <ul·class="simple">67 <ul·class="simple">
68 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">sm.tsa.SARIMAX</span></code></p></li>68 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">sm.tsa.SARIMAX</span></code></p></li>
69 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">sm.tsa.UnobservedComponents</span></code></p></li>69 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">sm.tsa.UnobservedComponents</span></code></p></li>
70 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">sm.tsa.VARMAX</span></code></p></li>70 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">sm.tsa.VARMAX</span></code></p></li>
71 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">sm.tsa.DynamicFactor</span></code></p></li>71 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">sm.tsa.DynamicFactor</span></code></p></li>
72 </ul>72 </ul>
73 <div·class="nbinput·nblast·docutils·container">73 <div·class="nbinput·nblast·docutils·container">
74 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:74 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
75 </pre></div>75 </pre></div>
76 </div>76 </div>
77 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline77 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
  
78 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>78 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
79 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>79 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
80 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>80 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
Offset 85, 244 lines modifiedOffset 85, 130 lines modified
85 <span·class="n">macrodata</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">period_range</span><span·class="p">(</span><span·class="s1">&#39;1959Q1&#39;</span><span·class="p">,</span>·<span·class="s1">&#39;2009Q3&#39;</span><span·class="p">,</span>·<span·class="n">freq</span><span·class="o">=</span><span·class="s1">&#39;Q&#39;</span><span·class="p">)</span>85 <span·class="n">macrodata</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">period_range</span><span·class="p">(</span><span·class="s1">&#39;1959Q1&#39;</span><span·class="p">,</span>·<span·class="s1">&#39;2009Q3&#39;</span><span·class="p">,</span>·<span·class="n">freq</span><span·class="o">=</span><span·class="s1">&#39;Q&#39;</span><span·class="p">)</span>
86 </pre></div>86 </pre></div>
87 </div>87 </div>
88 </div>88 </div>
89 <section·id="Basic-example">89 <section·id="Basic-example">
90 <h2>Basic·example<a·class="headerlink"·href="#Basic-example"·title="Link·to·this·heading">¶</a></h2>90 <h2>Basic·example<a·class="headerlink"·href="#Basic-example"·title="Link·to·this·heading">¶</a></h2>
91 <p>A·simple·example·is·to·use·an·AR(1)·model·to·forecast·inflation.·Before·forecasting,·let’s·take·a·look·at·the·series:</p>91 <p>A·simple·example·is·to·use·an·AR(1)·model·to·forecast·inflation.·Before·forecasting,·let’s·take·a·look·at·the·series:</p>
92 <div·class="nbinput·docutils·container">92 <div·class="nbinput·nblast·docutils·container">
93 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:93 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
94 </pre></div>94 </pre></div>
95 </div>95 </div>
96 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">endog</span>·<span·class="o">=</span>·<span·class="n">macrodata</span><span·class="p">[</span><span·class="s1">&#39;infl&#39;</span><span·class="p">]</span>96 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">endog</span>·<span·class="o">=</span>·<span·class="n">macrodata</span><span·class="p">[</span><span·class="s1">&#39;infl&#39;</span><span·class="p">]</span>
97 <span·class="n">endog</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">15</span><span·class="p">,</span>·<span·class="mi">5</span><span·class="p">))</span>97 <span·class="n">endog</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">15</span><span·class="p">,</span>·<span·class="mi">5</span><span·class="p">))</span>
98 </pre></div>98 </pre></div>
99 </div>99 </div>
100 </div>100 </div>
101 <div·class="nboutput·docutils·container"> 
102 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]: 
103 </pre></div> 
104 </div> 
105 <div·class="output_area·docutils·container"> 
106 <div·class="highlight"><pre> 
107 &lt;Axes:·&gt; 
108 </pre></div></div> 
109 </div> 
110 <div·class="nboutput·nblast·docutils·container"> 
111 <div·class="prompt·empty·docutils·container"> 
112 </div> 
113 <div·class="output_area·docutils·container"> 
114 <img·alt="../../../_images/examples_notebooks_generated_statespace_forecasting_3_1.png"·src="../../../_images/examples_notebooks_generated_statespace_forecasting_3_1.png"·/> 
115 </div> 
116 </div> 
117 <section·id="Constructing-and-estimating-the-model">101 <section·id="Constructing-and-estimating-the-model">
118 <h3>Constructing·and·estimating·the·model<a·class="headerlink"·href="#Constructing-and-estimating-the-model"·title="Link·to·this·heading">¶</a></h3>102 <h3>Constructing·and·estimating·the·model<a·class="headerlink"·href="#Constructing-and-estimating-the-model"·title="Link·to·this·heading">¶</a></h3>
119 <p>The·next·step·is·to·formulate·the·econometric·model·that·we·want·to·use·for·forecasting.·In·this·case,·we·will·use·an·AR(1)·model·via·the·<code·class="docutils·literal·notranslate"><span·class="pre">SARIMAX</span></code>·class·in·statsmodels.</p>103 <p>The·next·step·is·to·formulate·the·econometric·model·that·we·want·to·use·for·forecasting.·In·this·case,·we·will·use·an·AR(1)·model·via·the·<code·class="docutils·literal·notranslate"><span·class="pre">SARIMAX</span></code>·class·in·statsmodels.</p>
120 <p>After·constructing·the·model,·we·need·to·estimate·its·parameters.·This·is·done·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">fit</span></code>·method.·The·<code·class="docutils·literal·notranslate"><span·class="pre">summary</span></code>·method·produces·several·convenient·tables·showing·the·results.</p>104 <p>After·constructing·the·model,·we·need·to·estimate·its·parameters.·This·is·done·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">fit</span></code>·method.·The·<code·class="docutils·literal·notranslate"><span·class="pre">summary</span></code>·method·produces·several·convenient·tables·showing·the·results.</p>
121 <div·class="nbinput·docutils·container">105 <div·class="nbinput·nblast·docutils·container">
122 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:106 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
123 </pre></div>107 </pre></div>
124 </div>108 </div>
125 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Construct·the·model</span>109 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Construct·the·model</span>
126 <span·class="n">mod</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">SARIMAX</span><span·class="p">(</span><span·class="n">endog</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s1">&#39;c&#39;</span><span·class="p">)</span>110 <span·class="n">mod</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">SARIMAX</span><span·class="p">(</span><span·class="n">endog</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s1">&#39;c&#39;</span><span·class="p">)</span>
127 <span·class="c1">#·Estimate·the·parameters</span>111 <span·class="c1">#·Estimate·the·parameters</span>
128 <span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">mod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>112 <span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">mod</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
  
129 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>113 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
130 </pre></div>114 </pre></div>
131 </div>115 </div>
132 </div>116 </div>
133 <div·class="nboutput·nblast·docutils·container"> 
134 <div·class="prompt·empty·docutils·container"> 
135 </div> 
136 <div·class="output_area·docutils·container"> 
137 <div·class="highlight"><pre> 
138 ·······························SARIMAX·Results 
139 ============================================================================== 
140 Dep.·Variable:···················infl···No.·Observations:··················203 
141 Model:···············SARIMAX(1,·0,·0)···Log·Likelihood················-472.714 
142 Date:················Sun,·10·Aug·2025···AIC····························951.427 
143 Time:························13:13:47···BIC····························961.367 
144 Sample:····················03-31-1959···HQIC···························955.449 
145 ·························-·09-30-2009 
146 Covariance·Type:··················opg 
147 ============================================================================== 
148 ·················coef····std·err··········z······P&gt;|z|······[0.025······0.975] 
149 ------------------------------------------------------------------------------ 
150 intercept······1.3962······0.254······5.488······0.000·······0.898·······1.895 
151 ar.L1··········0.6441······0.039·····16.482······0.000·······0.568·······0.721 
152 sigma2·········6.1519······0.397·····15.487······0.000·······5.373·······6.930 
153 =================================================================================== 
154 Ljung-Box·(L1)·(Q):···················8.43···Jarque-Bera·(JB):················68.45 
155 Prob(Q):······························0.00···Prob(JB):·························0.00 
156 Heteroskedasticity·(H):···············1.47···Skew:····························-0.22 
157 Prob(H)·(two-sided):··················0.12···Kurtosis:·························5.81 
158 =================================================================================== 
  
159 Warnings: 
160 [1]·Covariance·matrix·calculated·using·the·outer·product·of·gradients·(complex-step). 
161 </pre></div></div> 
162 </div> 
163 </section>117 </section>
164 <section·id="Forecasting">118 <section·id="Forecasting">
165 <h3>Forecasting<a·class="headerlink"·href="#Forecasting"·title="Link·to·this·heading">¶</a></h3>119 <h3>Forecasting<a·class="headerlink"·href="#Forecasting"·title="Link·to·this·heading">¶</a></h3>
166 <p>Out-of-sample·forecasts·are·produced·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">forecast</span></code>·or·<code·class="docutils·literal·notranslate"><span·class="pre">get_forecast</span></code>·methods·from·the·results·object.</p>120 <p>Out-of-sample·forecasts·are·produced·using·the·<code·class="docutils·literal·notranslate"><span·class="pre">forecast</span></code>·or·<code·class="docutils·literal·notranslate"><span·class="pre">get_forecast</span></code>·methods·from·the·results·object.</p>
167 <p>The·<code·class="docutils·literal·notranslate"><span·class="pre">forecast</span></code>·method·gives·only·point·forecasts.</p>121 <p>The·<code·class="docutils·literal·notranslate"><span·class="pre">forecast</span></code>·method·gives·only·point·forecasts.</p>
168 <div·class="nbinput·docutils·container">122 <div·class="nbinput·nblast·docutils·container">
169 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:123 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
170 </pre></div>124 </pre></div>
171 </div>125 </div>
172 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·The·default·is·to·get·a·one-step-ahead·forecast:</span>126 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·The·default·is·to·get·a·one-step-ahead·forecast:</span>
173 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">forecast</span><span·class="p">())</span>127 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">forecast</span><span·class="p">())</span>
174 </pre></div>128 </pre></div>
175 </div>129 </div>
176 </div>130 </div>
177 <div·class="nboutput·nblast·docutils·container"> 
178 <div·class="prompt·empty·docutils·container"> 
179 </div> 
180 <div·class="output_area·docutils·container"> 
181 <div·class="highlight"><pre> 
182 2009Q4····3.68921 
183 Freq:·Q-DEC,·dtype:·float64 
184 </pre></div></div> 
185 </div> 
186 <p>The·<code·class="docutils·literal·notranslate"><span·class="pre">get_forecast</span></code>·method·is·more·general,·and·also·allows·constructing·confidence·intervals.</p>131 <p>The·<code·class="docutils·literal·notranslate"><span·class="pre">get_forecast</span></code>·method·is·more·general,·and·also·allows·constructing·confidence·intervals.</p>
187 <div·class="nbinput·docutils·container">132 <div·class="nbinput·nblast·docutils·container">
188 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:133 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
189 </pre></div>134 </pre></div>
190 </div>135 </div>
191 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Here·we·construct·a·more·complete·results·object.</span>136 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·Here·we·construct·a·more·complete·results·object.</span>
192 <span·class="n">fcast_res1</span>·<span·class="o">=</span>·<span·class="n">res</span><span·class="o">.</span><span·class="n">get_forecast</span><span·class="p">()</span>137 <span·class="n">fcast_res1</span>·<span·class="o">=</span>·<span·class="n">res</span><span·class="o">.</span><span·class="n">get_forecast</span><span·class="p">()</span>
  
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9 *\x8**\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ti\x8in\x8ng\x8g·i\x8in\x8n·s\x8st\x8ta\x8at\x8ts\x8sm\x8mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ti\x8in\x8ng\x8g·i\x8in\x8n·s\x8st\x8ta\x8at\x8ts\x8sm\x8mo\x8od\x8de\x8el\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 This·notebook·describes·forecasting·using·time·series·models·in·statsmodels.10 This·notebook·describes·forecasting·using·time·series·models·in·statsmodels.
11 N\x8No\x8ot\x8te\x8e:·this·notebook·applies·only·to·the·state·space·model·classes,·which·are:11 N\x8No\x8ot\x8te\x8e:·this·notebook·applies·only·to·the·state·space·model·classes,·which·are:
12 ····*·sm.tsa.SARIMAX12 ····*·sm.tsa.SARIMAX
13 ····*·sm.tsa.UnobservedComponents13 ····*·sm.tsa.UnobservedComponents
14 ····*·sm.tsa.VARMAX14 ····*·sm.tsa.VARMAX
15 ····*·sm.tsa.DynamicFactor15 ····*·sm.tsa.DynamicFactor
16 [1]:16 [·]:
17 %matplotlib·inline17 %matplotlib·inline
  
18 import·numpy·as·np18 import·numpy·as·np
19 import·pandas·as·pd19 import·pandas·as·pd
20 import·statsmodels.api·as·sm20 import·statsmodels.api·as·sm
21 import·matplotlib.pyplot·as·plt21 import·matplotlib.pyplot·as·plt
  
22 macrodata·=·sm.datasets.macrodata.load_pandas().data22 macrodata·=·sm.datasets.macrodata.load_pandas().data
23 macrodata.index·=·pd.period_range('1959Q1',·'2009Q3',·freq='Q')23 macrodata.index·=·pd.period_range('1959Q1',·'2009Q3',·freq='Q')
24 *\x8**\x8**\x8**\x8**\x8*·B\x8Ba\x8as\x8si\x8ic\x8c·e\x8ex\x8xa\x8am\x8mp\x8pl\x8le\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*24 *\x8**\x8**\x8**\x8**\x8*·B\x8Ba\x8as\x8si\x8ic\x8c·e\x8ex\x8xa\x8am\x8mp\x8pl\x8le\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
25 A·simple·example·is·to·use·an·AR(1)·model·to·forecast·inflation.·Before25 A·simple·example·is·to·use·an·AR(1)·model·to·forecast·inflation.·Before
26 forecasting,·let’s·take·a·look·at·the·series:26 forecasting,·let’s·take·a·look·at·the·series:
27 [2]:27 [·]:
28 endog·=·macrodata['infl']28 endog·=·macrodata['infl']
29 endog.plot(figsize=(15,·5))29 endog.plot(figsize=(15,·5))
30 [2]: 
31 <Axes:·> 
32 [../../../_images/examples_notebooks_generated_statespace_forecasting_3_1.png] 
33 *\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8ns\x8st\x8tr\x8ru\x8uc\x8ct\x8ti\x8in\x8ng\x8g·a\x8an\x8nd\x8d·e\x8es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8in\x8ng\x8g·t\x8th\x8he\x8e·m\x8mo\x8od\x8de\x8el\x8l_\x8?\x8·*\x8**\x8**\x8**\x8*30 *\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8ns\x8st\x8tr\x8ru\x8uc\x8ct\x8ti\x8in\x8ng\x8g·a\x8an\x8nd\x8d·e\x8es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8in\x8ng\x8g·t\x8th\x8he\x8e·m\x8mo\x8od\x8de\x8el\x8l_\x8?\x8·*\x8**\x8**\x8**\x8*
34 The·next·step·is·to·formulate·the·econometric·model·that·we·want·to·use·for31 The·next·step·is·to·formulate·the·econometric·model·that·we·want·to·use·for
35 forecasting.·In·this·case,·we·will·use·an·AR(1)·model·via·the·SARIMAX·class·in32 forecasting.·In·this·case,·we·will·use·an·AR(1)·model·via·the·SARIMAX·class·in
36 statsmodels.33 statsmodels.
37 After·constructing·the·model,·we·need·to·estimate·its·parameters.·This·is·done34 After·constructing·the·model,·we·need·to·estimate·its·parameters.·This·is·done
38 using·the·fit·method.·The·summary·method·produces·several·convenient·tables35 using·the·fit·method.·The·summary·method·produces·several·convenient·tables
39 showing·the·results.36 showing·the·results.
40 [3]:37 [·]:
41 #·Construct·the·model38 #·Construct·the·model
42 mod·=·sm.tsa.SARIMAX(endog,·order=(1,·0,·0),·trend='c')39 mod·=·sm.tsa.SARIMAX(endog,·order=(1,·0,·0),·trend='c')
43 #·Estimate·the·parameters40 #·Estimate·the·parameters
44 res·=·mod.fit()41 res·=·mod.fit()
  
45 print(res.summary())42 print(res.summary())
46 ·······························SARIMAX·Results 
47 ============================================================================== 
48 Dep.·Variable:···················infl···No.·Observations:··················203 
49 Model:···············SARIMAX(1,·0,·0)···Log·Likelihood················-472.714 
50 Date:················Sun,·10·Aug·2025···AIC····························951.427 
51 Time:························13:13:47···BIC····························961.367 
52 Sample:····················03-31-1959···HQIC···························955.449 
53 ·························-·09-30-2009 
54 Covariance·Type:··················opg 
55 ============================================================================== 
56 ·················coef····std·err··········z······P>|z|······[0.025······0.975] 
57 ------------------------------------------------------------------------------ 
58 intercept······1.3962······0.254······5.488······0.000·······0.898·······1.895 
59 ar.L1··········0.6441······0.039·····16.482······0.000·······0.568·······0.721 
60 sigma2·········6.1519······0.397·····15.487······0.000·······5.373·······6.930 
61 =================================================================================== 
62 Ljung-Box·(L1)·(Q):···················8.43···Jarque-Bera·(JB): 
63 68.45 
64 Prob(Q):······························0.00···Prob(JB): 
65 0.00 
66 Heteroskedasticity·(H):···············1.47···Skew:····························- 
67 0.22 
68 Prob(H)·(two-sided):··················0.12···Kurtosis: 
69 5.81 
70 =================================================================================== 
  
71 Warnings: 
72 [1]·Covariance·matrix·calculated·using·the·outer·product·of·gradients·(complex- 
73 step). 
74 *\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ti\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8*43 *\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ti\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8*
75 Out-of-sample·forecasts·are·produced·using·the·forecast·or·get_forecast·methods44 Out-of-sample·forecasts·are·produced·using·the·forecast·or·get_forecast·methods
76 from·the·results·object.45 from·the·results·object.
77 The·forecast·method·gives·only·point·forecasts.46 The·forecast·method·gives·only·point·forecasts.
78 [4]:47 [·]:
79 #·The·default·is·to·get·a·one-step-ahead·forecast:48 #·The·default·is·to·get·a·one-step-ahead·forecast:
80 print(res.forecast())49 print(res.forecast())
81 2009Q4····3.68921 
82 Freq:·Q-DEC,·dtype:·float64 
83 The·get_forecast·method·is·more·general,·and·also·allows·constructing50 The·get_forecast·method·is·more·general,·and·also·allows·constructing
84 confidence·intervals.51 confidence·intervals.
85 [5]:52 [·]:
86 #·Here·we·construct·a·more·complete·results·object.53 #·Here·we·construct·a·more·complete·results·object.
87 fcast_res1·=·res.get_forecast()54 fcast_res1·=·res.get_forecast()
  
88 #·Most·results·are·collected·in·the·`summary_frame`·attribute.55 #·Most·results·are·collected·in·the·`summary_frame`·attribute.
89 #·Here·we·specify·that·we·want·a·confidence·level·of·90%56 #·Here·we·specify·that·we·want·a·confidence·level·of·90%
90 print(fcast_res1.summary_frame(alpha=0.10))57 print(fcast_res1.summary_frame(alpha=0.10))
91 infl·······mean···mean_se··mean_ci_lower··mean_ci_upper 
92 2009Q4··3.68921··2.480302······-0.390523·······7.768943 
93 The·default·confidence·level·is·95%,·but·this·can·be·controlled·by·setting·the58 The·default·confidence·level·is·95%,·but·this·can·be·controlled·by·setting·the
94 alpha·parameter,·where·the·confidence·level·is·defined·as·\((1·-·\alpha)·\times59 alpha·parameter,·where·the·confidence·level·is·defined·as·\((1·-·\alpha)·\times
95 100\%\).·In·the·example·above,·we·specified·a·confidence·level·of·90%,·using60 100\%\).·In·the·example·above,·we·specified·a·confidence·level·of·90%,·using
96 alpha=0.10.61 alpha=0.10.
97 *\x8**\x8**\x8**\x8*·S\x8Sp\x8pe\x8ec\x8ci\x8if\x8fy\x8yi\x8in\x8ng\x8g·t\x8th\x8he\x8e·n\x8nu\x8um\x8mb\x8be\x8er\x8r·o\x8of\x8f·f\x8fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*62 *\x8**\x8**\x8**\x8*·S\x8Sp\x8pe\x8ec\x8ci\x8if\x8fy\x8yi\x8in\x8ng\x8g·t\x8th\x8he\x8e·n\x8nu\x8um\x8mb\x8be\x8er\x8r·o\x8of\x8f·f\x8fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*
98 Both·of·the·functions·forecast·and·get_forecast·accept·a·single·argument63 Both·of·the·functions·forecast·and·get_forecast·accept·a·single·argument
99 indicating·how·many·forecasting·steps·are·desired.·One·option·for·this·argument64 indicating·how·many·forecasting·steps·are·desired.·One·option·for·this·argument
100 is·always·to·provide·an·integer·describing·the·number·of·steps·ahead·you·want.65 is·always·to·provide·an·integer·describing·the·number·of·steps·ahead·you·want.
101 [6]:66 [·]:
102 print(res.forecast(steps=2))67 print(res.forecast(steps=2))
103 2009Q4····3.689210 
104 2010Q1····3.772434 
105 Freq:·Q-DEC,·Name:·predicted_mean,·dtype:·float64 
106 [7]:68 [·]:
107 fcast_res2·=·res.get_forecast(steps=2)69 fcast_res2·=·res.get_forecast(steps=2)
108 #·Note:·since·we·did·not·specify·the·alpha·parameter,·the70 #·Note:·since·we·did·not·specify·the·alpha·parameter,·the
109 #·confidence·level·is·at·the·default,·95%71 #·confidence·level·is·at·the·default,·95%
110 print(fcast_res2.summary_frame())72 print(fcast_res2.summary_frame())
111 infl········mean···mean_se··mean_ci_lower··mean_ci_upper 
112 2009Q4··3.689210··2.480302······-1.172092·······8.550512 
113 2010Q1··3.772434··2.950274······-2.009996·······9.554865 
114 However,·i\x8if\x8f·y\x8yo\x8ou\x8ur\x8r·d\x8da\x8at\x8ta\x8a·i\x8in\x8nc\x8cl\x8lu\x8ud\x8de\x8ed\x8d·a\x8a·P\x8Pa\x8an\x8nd\x8da\x8as\x8s·i\x8in\x8nd\x8de\x8ex\x8x·w\x8wi\x8it\x8th\x8h·a\x8a·d\x8de\x8ef\x8fi\x8in\x8ne\x8ed\x8d·f\x8fr\x8re\x8eq\x8qu\x8ue\x8en\x8nc\x8cy\x8y·(see·the73 However,·i\x8if\x8f·y\x8yo\x8ou\x8ur\x8r·d\x8da\x8at\x8ta\x8a·i\x8in\x8nc\x8cl\x8lu\x8ud\x8de\x8ed\x8d·a\x8a·P\x8Pa\x8an\x8nd\x8da\x8as\x8s·i\x8in\x8nd\x8de\x8ex\x8x·w\x8wi\x8it\x8th\x8h·a\x8a·d\x8de\x8ef\x8fi\x8in\x8ne\x8ed\x8d·f\x8fr\x8re\x8eq\x8qu\x8ue\x8en\x8nc\x8cy\x8y·(see·the
115 section·at·the·end·on·Indexes·for·more·information),·then·you·can·alternatively74 section·at·the·end·on·Indexes·for·more·information),·then·you·can·alternatively
116 specify·the·date·through·which·you·want·forecasts·to·be·produced:75 specify·the·date·through·which·you·want·forecasts·to·be·produced:
117 [8]:76 [·]:
118 print(res.forecast('2010Q2'))77 print(res.forecast('2010Q2'))
119 2009Q4····3.689210 
120 2010Q1····3.772434 
121 2010Q2····3.826039 
122 Freq:·Q-DEC,·Name:·predicted_mean,·dtype:·float64 
123 [9]:78 [·]:
124 fcast_res3·=·res.get_forecast('2010Q2')79 fcast_res3·=·res.get_forecast('2010Q2')
125 print(fcast_res3.summary_frame())80 print(fcast_res3.summary_frame())
126 infl········mean···mean_se··mean_ci_lower··mean_ci_upper 
127 2009Q4··3.689210··2.480302······-1.172092·······8.550512 
128 2010Q1··3.772434··2.950274······-2.009996·······9.554865 
129 2010Q2··3.826039··3.124571······-2.298008·······9.950087 
130 *\x8**\x8**\x8**\x8*·P\x8Pl\x8lo\x8ot\x8tt\x8ti\x8in\x8ng\x8g·t\x8th\x8he\x8e·d\x8da\x8at\x8ta\x8a,\x8,·f\x8fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ts\x8s,\x8,·a\x8an\x8nd\x8d·c\x8co\x8on\x8nf\x8fi\x8id\x8de\x8en\x8nc\x8ce\x8e·i\x8in\x8nt\x8te\x8er\x8rv\x8va\x8al\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*81 *\x8**\x8**\x8**\x8*·P\x8Pl\x8lo\x8ot\x8tt\x8ti\x8in\x8ng\x8g·t\x8th\x8he\x8e·d\x8da\x8at\x8ta\x8a,\x8,·f\x8fo\x8or\x8re\x8ec\x8ca\x8as\x8st\x8ts\x8s,\x8,·a\x8an\x8nd\x8d·c\x8co\x8on\x8nf\x8fi\x8id\x8de\x8en\x8nc\x8ce\x8e·i\x8in\x8nt\x8te\x8er\x8rv\x8va\x8al\x8ls\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*
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83 \[\begin{split}\begin{align}83 \[\begin{split}\begin{align}
84 Y_t·&amp;·=·\phi·+·\rho·Y_{t-1}·+·\eta_t·\\84 Y_t·&amp;·=·\phi·+·\rho·Y_{t-1}·+·\eta_t·\\
85 \eta_t·&amp;·\sim·WN(0,\sigma^2)·\\85 \eta_t·&amp;·\sim·WN(0,\sigma^2)·\\
86 \end{align}\end{split}\]</div>86 \end{align}\end{split}\]</div>
87 <p>This·is·the·same·representation·that·is·used·when·the·model·is·estimated·using·OLS·(<code·class="docutils·literal·notranslate"><span·class="pre">AutoReg</span></code>).·In·large·samples,·<span·class="math·notranslate·nohighlight">\(\hat{\phi}\stackrel{p}{\rightarrow}·E[Y](1-\rho)\)</span>.</p>87 <p>This·is·the·same·representation·that·is·used·when·the·model·is·estimated·using·OLS·(<code·class="docutils·literal·notranslate"><span·class="pre">AutoReg</span></code>).·In·large·samples,·<span·class="math·notranslate·nohighlight">\(\hat{\phi}\stackrel{p}{\rightarrow}·E[Y](1-\rho)\)</span>.</p>
88 <p>In·the·next·cell,·we·simulate·a·large·sample·and·verify·that·these·relationship·hold·in·practice.</p>88 <p>In·the·next·cell,·we·simulate·a·large·sample·and·verify·that·these·relationship·hold·in·practice.</p>
89 <div·class="nbinput·nblast·docutils·container">89 <div·class="nbinput·nblast·docutils·container">
90 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:90 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
91 </pre></div>91 </pre></div>
92 </div>92 </div>
93 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline93 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
94 </pre></div>94 </pre></div>
95 </div>95 </div>
96 </div>96 </div>
97 <div·class="nbinput·nblast·docutils·container">97 <div·class="nbinput·nblast·docutils·container">
98 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:98 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
99 </pre></div>99 </pre></div>
100 </div>100 </div>
101 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>101 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
102 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>102 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
  
103 <span·class="n">rng</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">default_rng</span><span·class="p">(</span><span·class="mi">20210819</span><span·class="p">)</span>103 <span·class="n">rng</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">default_rng</span><span·class="p">(</span><span·class="mi">20210819</span><span·class="p">)</span>
104 <span·class="n">eta</span>·<span·class="o">=</span>·<span·class="n">rng</span><span·class="o">.</span><span·class="n">standard_normal</span><span·class="p">(</span><span·class="mi">5200</span><span·class="p">)</span>104 <span·class="n">eta</span>·<span·class="o">=</span>·<span·class="n">rng</span><span·class="o">.</span><span·class="n">standard_normal</span><span·class="p">(</span><span·class="mi">5200</span><span·class="p">)</span>
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110 ····<span·class="n">epsilon</span><span·class="p">[</span><span·class="n">i</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">rho</span>·<span·class="o">*</span>·<span·class="n">epsilon</span><span·class="p">[</span><span·class="n">i</span>·<span·class="o">-</span>·<span·class="mi">1</span><span·class="p">]</span>·<span·class="o">+</span>·<span·class="n">eta</span><span·class="p">[</span><span·class="n">i</span><span·class="p">]</span>110 ····<span·class="n">epsilon</span><span·class="p">[</span><span·class="n">i</span><span·class="p">]</span>·<span·class="o">=</span>·<span·class="n">rho</span>·<span·class="o">*</span>·<span·class="n">epsilon</span><span·class="p">[</span><span·class="n">i</span>·<span·class="o">-</span>·<span·class="mi">1</span><span·class="p">]</span>·<span·class="o">+</span>·<span·class="n">eta</span><span·class="p">[</span><span·class="n">i</span><span·class="p">]</span>
111 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">beta</span>·<span·class="o">+</span>·<span·class="n">epsilon</span>111 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">beta</span>·<span·class="o">+</span>·<span·class="n">epsilon</span>
112 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">y</span><span·class="p">[</span><span·class="mi">200</span><span·class="p">:]</span>112 <span·class="n">y</span>·<span·class="o">=</span>·<span·class="n">y</span><span·class="p">[</span><span·class="mi">200</span><span·class="p">:]</span>
113 </pre></div>113 </pre></div>
114 </div>114 </div>
115 </div>115 </div>
116 <div·class="nbinput·nblast·docutils·container">116 <div·class="nbinput·nblast·docutils·container">
117 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:117 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
118 </pre></div>118 </pre></div>
119 </div>119 </div>
120 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.api</span>·<span·class="kn">import</span>·<span·class="n">SARIMAX</span><span·class="p">,</span>·<span·class="n">AutoReg</span>120 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.api</span>·<span·class="kn">import</span>·<span·class="n">SARIMAX</span><span·class="p">,</span>·<span·class="n">AutoReg</span>
121 <span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.arima.model</span>·<span·class="kn">import</span>·<span·class="n">ARIMA</span>121 <span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.arima.model</span>·<span·class="kn">import</span>·<span·class="n">ARIMA</span>
122 </pre></div>122 </pre></div>
123 </div>123 </div>
124 </div>124 </div>
125 <p>The·three·models·are·specified·and·estimated·in·the·next·cell.·An·AR(0)·is·included·as·a·reference.·The·AR(0)·is·identical·using·all·three·estimators.</p>125 <p>The·three·models·are·specified·and·estimated·in·the·next·cell.·An·AR(0)·is·included·as·a·reference.·The·AR(0)·is·identical·using·all·three·estimators.</p>
126 <div·class="nbinput·nblast·docutils·container">126 <div·class="nbinput·nblast·docutils·container">
127 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:127 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
128 </pre></div>128 </pre></div>
129 </div>129 </div>
130 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">ar0_res</span>·<span·class="o">=</span>·<span·class="n">SARIMAX</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s2">&quot;c&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>130 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">ar0_res</span>·<span·class="o">=</span>·<span·class="n">SARIMAX</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s2">&quot;c&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
131 <span·class="n">sarimax_res</span>·<span·class="o">=</span>·<span·class="n">SARIMAX</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s2">&quot;c&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>131 <span·class="n">sarimax_res</span>·<span·class="o">=</span>·<span·class="n">SARIMAX</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s2">&quot;c&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
132 <span·class="n">arima_res</span>·<span·class="o">=</span>·<span·class="n">ARIMA</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s2">&quot;c&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>132 <span·class="n">arima_res</span>·<span·class="o">=</span>·<span·class="n">ARIMA</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">order</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">),</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s2">&quot;c&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
133 <span·class="n">autoreg_res</span>·<span·class="o">=</span>·<span·class="n">AutoReg</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="mi">1</span><span·class="p">,</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s2">&quot;c&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>133 <span·class="n">autoreg_res</span>·<span·class="o">=</span>·<span·class="n">AutoReg</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="mi">1</span><span·class="p">,</span>·<span·class="n">trend</span><span·class="o">=</span><span·class="s2">&quot;c&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
134 </pre></div>134 </pre></div>
135 </div>135 </div>
136 </div>136 </div>
137 <p>The·table·below·contains·the·estimated·parameter·in·the·model,·the·estimated·AR(1)·coefficient,·and·the·long-run·mean·which·is·either·equal·to·the·estimated·parameters·(AR(0)·or·<code·class="docutils·literal·notranslate"><span·class="pre">ARIMA</span></code>),·or·depends·on·the·ratio·of·the·intercept·to·1·minus·the·AR(1)·parameter.</p>137 <p>The·table·below·contains·the·estimated·parameter·in·the·model,·the·estimated·AR(1)·coefficient,·and·the·long-run·mean·which·is·either·equal·to·the·estimated·parameters·(AR(0)·or·<code·class="docutils·literal·notranslate"><span·class="pre">ARIMA</span></code>),·or·depends·on·the·ratio·of·the·intercept·to·1·minus·the·AR(1)·parameter.</p>
138 <div·class="nbinput·docutils·container">138 <div·class="nbinput·nblast·docutils·container">
139 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:139 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
140 </pre></div>140 </pre></div>
141 </div>141 </div>
142 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">intercept</span>·<span·class="o">=</span>·<span·class="p">[</span>142 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">intercept</span>·<span·class="o">=</span>·<span·class="p">[</span>
143 ····<span·class="n">ar0_res</span><span·class="o">.</span><span·class="n">params</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">],</span>143 ····<span·class="n">ar0_res</span><span·class="o">.</span><span·class="n">params</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">],</span>
144 ····<span·class="n">sarimax_res</span><span·class="o">.</span><span·class="n">params</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">],</span>144 ····<span·class="n">sarimax_res</span><span·class="o">.</span><span·class="n">params</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">],</span>
145 ····<span·class="n">arima_res</span><span·class="o">.</span><span·class="n">params</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">],</span>145 ····<span·class="n">arima_res</span><span·class="o">.</span><span·class="n">params</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">],</span>
146 ····<span·class="n">autoreg_res</span><span·class="o">.</span><span·class="n">params</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">],</span>146 ····<span·class="n">autoreg_res</span><span·class="o">.</span><span·class="n">params</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">],</span>
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157 ····<span·class="p">[</span><span·class="n">intercept</span><span·class="p">,</span>·<span·class="n">rho_hat</span><span·class="p">,</span>·<span·class="n">long_run</span><span·class="p">],</span>157 ····<span·class="p">[</span><span·class="n">intercept</span><span·class="p">,</span>·<span·class="n">rho_hat</span><span·class="p">,</span>·<span·class="n">long_run</span><span·class="p">],</span>
158 ····<span·class="n">columns</span><span·class="o">=</span><span·class="n">cols</span><span·class="p">,</span>158 ····<span·class="n">columns</span><span·class="o">=</span><span·class="n">cols</span><span·class="p">,</span>
159 ····<span·class="n">index</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;delta-or-phi&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;rho&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;long-run·mean&quot;</span><span·class="p">],</span>159 ····<span·class="n">index</span><span·class="o">=</span><span·class="p">[</span><span·class="s2">&quot;delta-or-phi&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;rho&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;long-run·mean&quot;</span><span·class="p">],</span>
160 <span·class="p">)</span>160 <span·class="p">)</span>
161 </pre></div>161 </pre></div>
162 </div>162 </div>
163 </div>163 </div>
164 <div·class="nboutput·nblast·docutils·container"> 
165 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]: 
166 </pre></div> 
167 </div> 
168 <div·class="output_area·rendered_html·docutils·container"> 
169 <div> 
170 <style·scoped> 
171 ····.dataframe·tbody·tr·th:only-of-type·{ 
172 ········vertical-align:·middle; 
173 ····} 
  
174 ····.dataframe·tbody·tr·th·{ 
175 ········vertical-align:·top; 
176 ····} 
  
177 ····.dataframe·thead·th·{ 
178 ········text-align:·right; 
179 ····} 
180 </style> 
181 <table·border="1"·class="dataframe"> 
182 ··<thead> 
183 ····<tr·style="text-align:·right;"> 
184 ······<th></th> 
185 ······<th>AR(0)</th> 
186 ······<th>SARIMAX</th> 
187 ······<th>ARIMA</th> 
188 ······<th>AutoReg</th> 
189 ····</tr> 
190 ··</thead> 
191 ··<tbody> 
192 ····<tr> 
193 ······<th>delta-or-phi</th> 
194 ······<td>9.7745</td> 
195 ······<td>1.985714</td> 
196 ······<td>9.774498</td> 
197 ······<td>1.985790</td> 
198 ····</tr> 
199 ····<tr> 
200 ······<th>rho</th> 
201 ······<td>0.0000</td> 
202 ······<td>0.796846</td> 
203 ······<td>0.796875</td> 
204 ······<td>0.796882</td> 
205 ····</tr> 
206 ····<tr> 
207 ······<th>long-run·mean</th> 
208 ······<td>9.7745</td> 
209 ······<td>9.774424</td> 
210 ······<td>9.774498</td> 
211 ······<td>9.776537</td> 
212 ····</tr> 
213 ··</tbody> 
214 </table> 
215 </div></div> 
216 </div> 
217 <section·id="Differences-between-trend-and-exog-in-SARIMAX">164 <section·id="Differences-between-trend-and-exog-in-SARIMAX">
218 <h3>Differences·between·trend·and·exog·in·<code·class="docutils·literal·notranslate"><span·class="pre">SARIMAX</span></code><a·class="headerlink"·href="#Differences-between-trend-and-exog-in-SARIMAX"·title="Link·to·this·heading">¶</a></h3>165 <h3>Differences·between·trend·and·exog·in·<code·class="docutils·literal·notranslate"><span·class="pre">SARIMAX</span></code><a·class="headerlink"·href="#Differences-between-trend-and-exog-in-SARIMAX"·title="Link·to·this·heading">¶</a></h3>
219 <p>When·<code·class="docutils·literal·notranslate"><span·class="pre">SARIMAX</span></code>·includes·<code·class="docutils·literal·notranslate"><span·class="pre">exog</span></code>·variables,·then·the·<code·class="docutils·literal·notranslate"><span·class="pre">exog</span></code>·are·treated·as·OLS·regressors,·so·that·the·model·estimated·is</p>166 <p>When·<code·class="docutils·literal·notranslate"><span·class="pre">SARIMAX</span></code>·includes·<code·class="docutils·literal·notranslate"><span·class="pre">exog</span></code>·variables,·then·the·<code·class="docutils·literal·notranslate"><span·class="pre">exog</span></code>·are·treated·as·OLS·regressors,·so·that·the·model·estimated·is</p>
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25 \[\begin{split}\begin{align}·Y_t·&·=·\phi·+·\rho·Y_{t-1}·+·\eta_t·\\·\eta_t·&25 \[\begin{split}\begin{align}·Y_t·&·=·\phi·+·\rho·Y_{t-1}·+·\eta_t·\\·\eta_t·&
26 \sim·WN(0,\sigma^2)·\\·\end{align}\end{split}\]26 \sim·WN(0,\sigma^2)·\\·\end{align}\end{split}\]
27 This·is·the·same·representation·that·is·used·when·the·model·is·estimated·using27 This·is·the·same·representation·that·is·used·when·the·model·is·estimated·using
28 OLS·(AutoReg).·In·large·samples,·\(\hat{\phi}\stackrel{p}{\rightarrow}·E[Y](1-28 OLS·(AutoReg).·In·large·samples,·\(\hat{\phi}\stackrel{p}{\rightarrow}·E[Y](1-
29 \rho)\).29 \rho)\).
30 In·the·next·cell,·we·simulate·a·large·sample·and·verify·that·these·relationship30 In·the·next·cell,·we·simulate·a·large·sample·and·verify·that·these·relationship
31 hold·in·practice.31 hold·in·practice.
32 [1]:32 [·]:
33 %matplotlib·inline33 %matplotlib·inline
34 [2]:34 [·]:
35 import·numpy·as·np35 import·numpy·as·np
36 import·pandas·as·pd36 import·pandas·as·pd
  
37 rng·=·np.random.default_rng(20210819)37 rng·=·np.random.default_rng(20210819)
38 eta·=·rng.standard_normal(5200)38 eta·=·rng.standard_normal(5200)
39 rho·=·0.839 rho·=·0.8
40 beta·=·1040 beta·=·10
41 epsilon·=·eta.copy()41 epsilon·=·eta.copy()
42 for·i·in·range(1,·eta.shape[0]):42 for·i·in·range(1,·eta.shape[0]):
43 ····epsilon[i]·=·rho·*·epsilon[i·-·1]·+·eta[i]43 ····epsilon[i]·=·rho·*·epsilon[i·-·1]·+·eta[i]
44 y·=·beta·+·epsilon44 y·=·beta·+·epsilon
45 y·=·y[200:]45 y·=·y[200:]
46 [3]:46 [·]:
47 from·statsmodels.tsa.api·import·SARIMAX,·AutoReg47 from·statsmodels.tsa.api·import·SARIMAX,·AutoReg
48 from·statsmodels.tsa.arima.model·import·ARIMA48 from·statsmodels.tsa.arima.model·import·ARIMA
49 The·three·models·are·specified·and·estimated·in·the·next·cell.·An·AR(0)·is49 The·three·models·are·specified·and·estimated·in·the·next·cell.·An·AR(0)·is
50 included·as·a·reference.·The·AR(0)·is·identical·using·all·three·estimators.50 included·as·a·reference.·The·AR(0)·is·identical·using·all·three·estimators.
51 [4]:51 [·]:
52 ar0_res·=·SARIMAX(y,·order=(0,·0,·0),·trend="c").fit()52 ar0_res·=·SARIMAX(y,·order=(0,·0,·0),·trend="c").fit()
53 sarimax_res·=·SARIMAX(y,·order=(1,·0,·0),·trend="c").fit()53 sarimax_res·=·SARIMAX(y,·order=(1,·0,·0),·trend="c").fit()
54 arima_res·=·ARIMA(y,·order=(1,·0,·0),·trend="c").fit()54 arima_res·=·ARIMA(y,·order=(1,·0,·0),·trend="c").fit()
55 autoreg_res·=·AutoReg(y,·1,·trend="c").fit()55 autoreg_res·=·AutoReg(y,·1,·trend="c").fit()
56 The·table·below·contains·the·estimated·parameter·in·the·model,·the·estimated·AR56 The·table·below·contains·the·estimated·parameter·in·the·model,·the·estimated·AR
57 (1)·coefficient,·and·the·long-run·mean·which·is·either·equal·to·the·estimated57 (1)·coefficient,·and·the·long-run·mean·which·is·either·equal·to·the·estimated
58 parameters·(AR(0)·or·ARIMA),·or·depends·on·the·ratio·of·the·intercept·to·158 parameters·(AR(0)·or·ARIMA),·or·depends·on·the·ratio·of·the·intercept·to·1
59 minus·the·AR(1)·parameter.59 minus·the·AR(1)·parameter.
60 [5]:60 [·]:
61 intercept·=·[61 intercept·=·[
62 ····ar0_res.params[0],62 ····ar0_res.params[0],
63 ····sarimax_res.params[0],63 ····sarimax_res.params[0],
64 ····arima_res.params[0],64 ····arima_res.params[0],
65 ····autoreg_res.params[0],65 ····autoreg_res.params[0],
66 ]66 ]
67 rho_hat·=·[0]·+·[r.params[1]·for·r·in·(sarimax_res,·arima_res,·autoreg_res)]67 rho_hat·=·[0]·+·[r.params[1]·for·r·in·(sarimax_res,·arima_res,·autoreg_res)]
Offset 74, 126 lines modifiedOffset 74, 71 lines modified
74 ]74 ]
75 cols·=·["AR(0)",·"SARIMAX",·"ARIMA",·"AutoReg"]75 cols·=·["AR(0)",·"SARIMAX",·"ARIMA",·"AutoReg"]
76 pd.DataFrame(76 pd.DataFrame(
77 ····[intercept,·rho_hat,·long_run],77 ····[intercept,·rho_hat,·long_run],
78 ····columns=cols,78 ····columns=cols,
79 ····index=["delta-or-phi",·"rho",·"long-run·mean"],79 ····index=["delta-or-phi",·"rho",·"long-run·mean"],
80 )80 )
81 [5]: 
82 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
83 |_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8A\x8A_\x8R\x8R_\x8(\x8(_\x80\x80_\x8)\x8)_\x8|_\x8·_\x8S\x8S_\x8A\x8A_\x8R\x8R_\x8I\x8I_\x8M\x8M_\x8A\x8A_\x8X\x8X_\x8|_\x8·_\x8·_\x8·_\x8A\x8A_\x8R\x8R_\x8I\x8I_\x8M\x8M_\x8A\x8A_\x8|_\x8·_\x8A\x8A_\x8u\x8u_\x8t\x8t_\x8o\x8o_\x8R\x8R_\x8e\x8e_\x8g\x8g| 
84 |_\x8d\x8d_\x8e\x8e_\x8l\x8l_\x8t\x8t_\x8a\x8a_\x8-\x8-_\x8o\x8o_\x8r\x8r_\x8-\x8-_\x8p\x8p_\x8h\x8h_\x8i\x8i_\x8·_\x8|_\x89_\x8._\x87_\x87_\x84_\x85_\x8|_\x81_\x8._\x89_\x88_\x85_\x87_\x81_\x84_\x8|_\x89_\x8._\x87_\x87_\x84_\x84_\x89_\x88_\x8|_\x81_\x8._\x89_\x88_\x85_\x87_\x89_\x80| 
85 |_\x8r\x8r_\x8h\x8h_\x8o\x8o_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x8|_\x80_\x8._\x87_\x89_\x86_\x88_\x84_\x86_\x8|_\x80_\x8._\x87_\x89_\x86_\x88_\x87_\x85_\x8|_\x80_\x8._\x87_\x89_\x86_\x88_\x88_\x82| 
86 |_\x8l\x8l_\x8o\x8o_\x8n\x8n_\x8g\x8g_\x8-\x8-_\x8r\x8r_\x8u\x8u_\x8n\x8n_\x8·_\x8m\x8m_\x8e\x8e_\x8a\x8a_\x8n\x8n_\x8|_\x89_\x8._\x87_\x87_\x84_\x85_\x8|_\x89_\x8._\x87_\x87_\x84_\x84_\x82_\x84_\x8|_\x89_\x8._\x87_\x87_\x84_\x84_\x89_\x88_\x8|_\x89_\x8._\x87_\x87_\x86_\x85_\x83_\x87| 
87 *\x8**\x8**\x8**\x8*·D\x8Di\x8if\x8ff\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·b\x8be\x8et\x8tw\x8we\x8ee\x8en\x8n·t\x8tr\x8re\x8en\x8nd\x8d·a\x8an\x8nd\x8d·e\x8ex\x8xo\x8og\x8g·i\x8in\x8n·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8·*\x8**\x8**\x8**\x8*81 *\x8**\x8**\x8**\x8*·D\x8Di\x8if\x8ff\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·b\x8be\x8et\x8tw\x8we\x8ee\x8en\x8n·t\x8tr\x8re\x8en\x8nd\x8d·a\x8an\x8nd\x8d·e\x8ex\x8xo\x8og\x8g·i\x8in\x8n·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8·*\x8**\x8**\x8**\x8*
88 When·SARIMAX·includes·exog·variables,·then·the·exog·are·treated·as·OLS82 When·SARIMAX·includes·exog·variables,·then·the·exog·are·treated·as·OLS
89 regressors,·so·that·the·model·estimated·is83 regressors,·so·that·the·model·estimated·is
90 \[\begin{split}\begin{align}·Y_t·-·X_t·\beta·&·=·\delta·+·\rho·(Y_{t-1}·-·X_{t-84 \[\begin{split}\begin{align}·Y_t·-·X_t·\beta·&·=·\delta·+·\rho·(Y_{t-1}·-·X_{t-
91 1}\beta)·+·\eta_t·\\·\eta_t·&·\sim·WN(0,\sigma^2)·\\·\end{align}\end{split}\]85 1}\beta)·+·\eta_t·\\·\eta_t·&·\sim·WN(0,\sigma^2)·\\·\end{align}\end{split}\]
92 In·the·next·example,·we·omit·the·trend·and·instead·include·a·column·of·1,·which86 In·the·next·example,·we·omit·the·trend·and·instead·include·a·column·of·1,·which
93 produces·a·model·that·is·equivalent,·in·large·samples,·to·the·case·with·no87 produces·a·model·that·is·equivalent,·in·large·samples,·to·the·case·with·no
94 exogenous·regressor·and·trend="c".·Here·the·estimated·value·of·const·matches88 exogenous·regressor·and·trend="c".·Here·the·estimated·value·of·const·matches
95 the·value·estimated·using·ARIMA.·This·happens·since·both·exog·in·SARIMAX·and89 the·value·estimated·using·ARIMA.·This·happens·since·both·exog·in·SARIMAX·and
96 the·trend·in·ARIMA·are·treated·as·linear·regression·models·with·ARMA·errors.90 the·trend·in·ARIMA·are·treated·as·linear·regression·models·with·ARMA·errors.
97 [6]:91 [·]:
98 sarimax_exog_res·=·SARIMAX(y,·exog=np.ones_like(y),·order=(1,·0,·0),92 sarimax_exog_res·=·SARIMAX(y,·exog=np.ones_like(y),·order=(1,·0,·0),
99 trend="n").fit()93 trend="n").fit()
100 print(sarimax_exog_res.summary())94 print(sarimax_exog_res.summary())
101 ·······························SARIMAX·Results 
102 ============================================================================== 
103 Dep.·Variable:······················y···No.·Observations:·················5000 
104 Model:···············SARIMAX(1,·0,·0)···Log·Likelihood···············-7068.656 
105 Date:················Sun,·10·Aug·2025···AIC··························14143.311 
106 Time:························13:13:47···BIC··························14162.863 
107 Sample:·····························0···HQIC·························14150.164 
108 ·······························-·5000 
109 Covariance·Type:··················opg 
110 ============================================================================== 
111 ·················coef····std·err··········z······P>|z|······[0.025······0.975] 
112 ------------------------------------------------------------------------------ 
113 const··········9.7745······0.069····141.177······0.000·······9.639·······9.910 
114 ar.L1··········0.7969······0.009·····93.691······0.000·······0.780·······0.814 
115 sigma2·········0.9894······0.020·····49.921······0.000·······0.951·······1.028 
116 =================================================================================== 
117 Ljung-Box·(L1)·(Q):···················0.42···Jarque-Bera·(JB): 
118 0.08 
119 Prob(Q):······························0.51···Prob(JB): 
120 0.96 
121 Heteroskedasticity·(H):···············0.97···Skew:····························- 
122 0.01 
123 Prob(H)·(two-sided):··················0.47···Kurtosis: 
124 2.99 
125 =================================================================================== 
  
126 Warnings: 
127 [1]·Covariance·matrix·calculated·using·the·outer·product·of·gradients·(complex- 
128 step). 
129 *\x8**\x8**\x8**\x8*·U\x8Us\x8si\x8in\x8ng\x8g·e\x8ex\x8xo\x8og\x8g·i\x8in\x8n·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X·a\x8an\x8nd\x8d·A\x8AR\x8RI\x8IM\x8MA\x8A_\x8?\x8·*\x8**\x8**\x8**\x8*95 *\x8**\x8**\x8**\x8*·U\x8Us\x8si\x8in\x8ng\x8g·e\x8ex\x8xo\x8og\x8g·i\x8in\x8n·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X·a\x8an\x8nd\x8d·A\x8AR\x8RI\x8IM\x8MA\x8A_\x8?\x8·*\x8**\x8**\x8**\x8*
130 While·exog·are·treated·the·same·in·both·models,·the·intercept·continues·to96 While·exog·are·treated·the·same·in·both·models,·the·intercept·continues·to
131 differ.·Below·we·add·an·exogenous·regressor·to·y·and·then·fit·the·model·using97 differ.·Below·we·add·an·exogenous·regressor·to·y·and·then·fit·the·model·using
132 all·three·methods.·The·data·generating·process·is·now98 all·three·methods.·The·data·generating·process·is·now
133 \[\begin{split}\begin{align}·Y_t·&·=·\delta·+·X_t·\beta·+·\epsilon_t·\\99 \[\begin{split}\begin{align}·Y_t·&·=·\delta·+·X_t·\beta·+·\epsilon_t·\\
134 \epsilon_t·&·=·\rho·\epsilon_{t-1}·+·\eta_t·\\·\eta_t·&·\sim·WN(0,\sigma^2)·\\100 \epsilon_t·&·=·\rho·\epsilon_{t-1}·+·\eta_t·\\·\eta_t·&·\sim·WN(0,\sigma^2)·\\
135 \end{align}\end{split}\]101 \end{align}\end{split}\]
136 [7]:102 [·]:
137 full_x·=·rng.standard_normal(eta.shape)103 full_x·=·rng.standard_normal(eta.shape)
138 x·=·full_x[200:]104 x·=·full_x[200:]
139 y·+=·3·*·x105 y·+=·3·*·x
140 [8]:106 [·]:
141 sarimax_exog_res·=·SARIMAX(y,·exog=x,·order=(1,·0,·0),·trend="c").fit()107 sarimax_exog_res·=·SARIMAX(y,·exog=x,·order=(1,·0,·0),·trend="c").fit()
142 arima_exog_res·=·ARIMA(y,·exog=x,·order=(1,·0,·0),·trend="c").fit()108 arima_exog_res·=·ARIMA(y,·exog=x,·order=(1,·0,·0),·trend="c").fit()
143 Examining·the·parameter·tables,·we·see·that·the·parameter·estimates·on·x1·are109 Examining·the·parameter·tables,·we·see·that·the·parameter·estimates·on·x1·are
144 identical·while·the·estimates·of·the·intercept·continue·to·differ·due·to·the110 identical·while·the·estimates·of·the·intercept·continue·to·differ·due·to·the
145 differences·in·the·treatment·of·trends·in·these·estimators.111 differences·in·the·treatment·of·trends·in·these·estimators.
146 *\x8**\x8**\x8*·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8·*\x8**\x8**\x8*112 *\x8**\x8**\x8*·S\x8SA\x8AR\x8RI\x8IM\x8MA\x8AX\x8X_\x8?\x8·*\x8**\x8**\x8*
147 [9]:113 [·]:
148 def·print_params(s):114 def·print_params(s):
149 ····from·io·import·StringIO115 ····from·io·import·StringIO
  
150 ····return·pd.read_csv(StringIO(s.tables[1].as_csv()),·index_col=0)116 ····return·pd.read_csv(StringIO(s.tables[1].as_csv()),·index_col=0)
  
  
151 print_params(sarimax_exog_res.summary())117 print_params(sarimax_exog_res.summary())
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64 <h1>Seasonality·in·time·series·data<a·class="headerlink"·href="#Seasonality-in-time-series-data"·title="Link·to·this·heading">¶</a></h1>64 <h1>Seasonality·in·time·series·data<a·class="headerlink"·href="#Seasonality-in-time-series-data"·title="Link·to·this·heading">¶</a></h1>
65 <p>Consider·the·problem·of·modeling·time·series·data·with·multiple·seasonal·components·with·different·periodicities.·Let·us·take·the·time·series·<span·class="math·notranslate·nohighlight">\(y_t\)</span>·and·decompose·it·explicitly·to·have·a·level·component·and·two·seasonal·components.</p>65 <p>Consider·the·problem·of·modeling·time·series·data·with·multiple·seasonal·components·with·different·periodicities.·Let·us·take·the·time·series·<span·class="math·notranslate·nohighlight">\(y_t\)</span>·and·decompose·it·explicitly·to·have·a·level·component·and·two·seasonal·components.</p>
66 <div·class="math·notranslate·nohighlight">66 <div·class="math·notranslate·nohighlight">
67 \[y_t·=·\mu_t·+·\gamma^{(1)}_t·+·\gamma^{(2)}_t\]</div>67 \[y_t·=·\mu_t·+·\gamma^{(1)}_t·+·\gamma^{(2)}_t\]</div>
68 <p>where·<span·class="math·notranslate·nohighlight">\(\mu_t\)</span>·represents·the·trend·or·level,·<span·class="math·notranslate·nohighlight">\(\gamma^{(1)}_t\)</span>·represents·a·seasonal·component·with·a·relatively·short·period,·and·<span·class="math·notranslate·nohighlight">\(\gamma^{(2)}_t\)</span>·represents·another·seasonal·component·of·longer·period.·We·will·have·a·fixed·intercept·term·for·our·level·and·consider·both·<span·class="math·notranslate·nohighlight">\(\gamma^{(2)}_t\)</span>·and·<span·class="math·notranslate·nohighlight">\(\gamma^{(2)}_t\)</span>·to·be·stochastic·so·that·the·seasonal·patterns·can·vary·over·time.</p>68 <p>where·<span·class="math·notranslate·nohighlight">\(\mu_t\)</span>·represents·the·trend·or·level,·<span·class="math·notranslate·nohighlight">\(\gamma^{(1)}_t\)</span>·represents·a·seasonal·component·with·a·relatively·short·period,·and·<span·class="math·notranslate·nohighlight">\(\gamma^{(2)}_t\)</span>·represents·another·seasonal·component·of·longer·period.·We·will·have·a·fixed·intercept·term·for·our·level·and·consider·both·<span·class="math·notranslate·nohighlight">\(\gamma^{(2)}_t\)</span>·and·<span·class="math·notranslate·nohighlight">\(\gamma^{(2)}_t\)</span>·to·be·stochastic·so·that·the·seasonal·patterns·can·vary·over·time.</p>
69 <p>In·this·notebook,·we·will·generate·synthetic·data·conforming·to·this·model·and·showcase·modeling·of·the·seasonal·terms·in·a·few·different·ways·under·the·unobserved·components·modeling·framework.</p>69 <p>In·this·notebook,·we·will·generate·synthetic·data·conforming·to·this·model·and·showcase·modeling·of·the·seasonal·terms·in·a·few·different·ways·under·the·unobserved·components·modeling·framework.</p>
70 <div·class="nbinput·nblast·docutils·container">70 <div·class="nbinput·nblast·docutils·container">
71 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:71 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
72 </pre></div>72 </pre></div>
73 </div>73 </div>
74 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline74 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
75 </pre></div>75 </pre></div>
76 </div>76 </div>
77 </div>77 </div>
78 <div·class="nbinput·nblast·docutils·container">78 <div·class="nbinput·nblast·docutils·container">
79 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:79 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
80 </pre></div>80 </pre></div>
81 </div>81 </div>
82 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>82 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
83 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>83 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
84 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>84 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
85 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>85 <span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
  
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89 </pre></div>89 </pre></div>
90 </div>90 </div>
91 </div>91 </div>
92 <section·id="Synthetic-data-creation">92 <section·id="Synthetic-data-creation">
93 <h2>Synthetic·data·creation<a·class="headerlink"·href="#Synthetic-data-creation"·title="Link·to·this·heading">¶</a></h2>93 <h2>Synthetic·data·creation<a·class="headerlink"·href="#Synthetic-data-creation"·title="Link·to·this·heading">¶</a></h2>
94 <p>We·will·create·data·with·multiple·seasonal·patterns·by·following·equations·(3.7)·and·(3.8)·in·Durbin·and·Koopman·(2012).·We·will·simulate·300·periods·and·two·seasonal·terms·parametrized·in·the·frequency·domain·having·periods·10·and·100,·respectively,·and·3·and·2·number·of·harmonics,·respectively.·Further,·the·variances·of·their·stochastic·parts·are·4·and·9,·respectively.</p>94 <p>We·will·create·data·with·multiple·seasonal·patterns·by·following·equations·(3.7)·and·(3.8)·in·Durbin·and·Koopman·(2012).·We·will·simulate·300·periods·and·two·seasonal·terms·parametrized·in·the·frequency·domain·having·periods·10·and·100,·respectively,·and·3·and·2·number·of·harmonics,·respectively.·Further,·the·variances·of·their·stochastic·parts·are·4·and·9,·respectively.</p>
95 <div·class="nbinput·nblast·docutils·container">95 <div·class="nbinput·nblast·docutils·container">
96 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:96 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
97 </pre></div>97 </pre></div>
98 </div>98 </div>
99 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·First·we&#39;ll·simulate·the·synthetic·data</span>99 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="c1">#·First·we&#39;ll·simulate·the·synthetic·data</span>
100 <span·class="k">def</span>·<span·class="nf">simulate_seasonal_term</span><span·class="p">(</span><span·class="n">periodicity</span><span·class="p">,</span>·<span·class="n">total_cycles</span><span·class="p">,</span>·<span·class="n">noise_std</span><span·class="o">=</span><span·class="mf">1.</span><span·class="p">,</span>100 <span·class="k">def</span>·<span·class="nf">simulate_seasonal_term</span><span·class="p">(</span><span·class="n">periodicity</span><span·class="p">,</span>·<span·class="n">total_cycles</span><span·class="p">,</span>·<span·class="n">noise_std</span><span·class="o">=</span><span·class="mf">1.</span><span·class="p">,</span>
101 ···························<span·class="n">harmonics</span><span·class="o">=</span><span·class="kc">None</span><span·class="p">):</span>101 ···························<span·class="n">harmonics</span><span·class="o">=</span><span·class="kc">None</span><span·class="p">):</span>
102 ····<span·class="n">duration</span>·<span·class="o">=</span>·<span·class="n">periodicity</span>·<span·class="o">*</span>·<span·class="n">total_cycles</span>102 ····<span·class="n">duration</span>·<span·class="o">=</span>·<span·class="n">periodicity</span>·<span·class="o">*</span>·<span·class="n">total_cycles</span>
103 ····<span·class="k">assert</span>·<span·class="n">duration</span>·<span·class="o">==</span>·<span·class="nb">int</span><span·class="p">(</span><span·class="n">duration</span><span·class="p">)</span>103 ····<span·class="k">assert</span>·<span·class="n">duration</span>·<span·class="o">==</span>·<span·class="nb">int</span><span·class="p">(</span><span·class="n">duration</span><span·class="p">)</span>
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128 ········<span·class="n">gamma_star_jt</span>·<span·class="o">=</span>·<span·class="n">gamma_star_jtp1</span>128 ········<span·class="n">gamma_star_jt</span>·<span·class="o">=</span>·<span·class="n">gamma_star_jtp1</span>
129 ····<span·class="n">wanted_series</span>·<span·class="o">=</span>·<span·class="n">series</span><span·class="p">[</span><span·class="o">-</span><span·class="n">duration</span><span·class="p">:]</span>·<span·class="c1">#·Discard·burn·in</span>129 ····<span·class="n">wanted_series</span>·<span·class="o">=</span>·<span·class="n">series</span><span·class="p">[</span><span·class="o">-</span><span·class="n">duration</span><span·class="p">:]</span>·<span·class="c1">#·Discard·burn·in</span>
  
130 ····<span·class="k">return</span>·<span·class="n">wanted_series</span>130 ····<span·class="k">return</span>·<span·class="n">wanted_series</span>
131 </pre></div>131 </pre></div>
132 </div>132 </div>
133 </div>133 </div>
134 <div·class="nbinput·docutils·container">134 <div·class="nbinput·nblast·docutils·container">
135 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:135 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
136 </pre></div>136 </pre></div>
137 </div>137 </div>
138 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">duration</span>·<span·class="o">=</span>·<span·class="mi">100</span>·<span·class="o">*</span>·<span·class="mi">3</span>138 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">duration</span>·<span·class="o">=</span>·<span·class="mi">100</span>·<span·class="o">*</span>·<span·class="mi">3</span>
139 <span·class="n">periodicities</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mi">10</span><span·class="p">,</span>·<span·class="mi">100</span><span·class="p">]</span>139 <span·class="n">periodicities</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mi">10</span><span·class="p">,</span>·<span·class="mi">100</span><span·class="p">]</span>
140 <span·class="n">num_harmonics</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mi">3</span><span·class="p">,</span>·<span·class="mi">2</span><span·class="p">]</span>140 <span·class="n">num_harmonics</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mi">3</span><span·class="p">,</span>·<span·class="mi">2</span><span·class="p">]</span>
141 <span·class="n">std</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">array</span><span·class="p">([</span><span·class="mi">2</span><span·class="p">,</span>·<span·class="mi">3</span><span·class="p">])</span>141 <span·class="n">std</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">array</span><span·class="p">([</span><span·class="mi">2</span><span·class="p">,</span>·<span·class="mi">3</span><span·class="p">])</span>
142 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">8678309</span><span·class="p">)</span>142 <span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">8678309</span><span·class="p">)</span>
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161 <span·class="n">h3</span><span·class="p">,</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">df</span><span·class="p">[</span><span·class="s1">&#39;100(2)&#39;</span><span·class="p">])</span>161 <span·class="n">h3</span><span·class="p">,</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">df</span><span·class="p">[</span><span·class="s1">&#39;100(2)&#39;</span><span·class="p">])</span>
162 <span·class="n">h4</span><span·class="p">,</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">df</span><span·class="p">[</span><span·class="s1">&#39;level&#39;</span><span·class="p">])</span>162 <span·class="n">h4</span><span·class="p">,</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">df</span><span·class="p">[</span><span·class="s1">&#39;level&#39;</span><span·class="p">])</span>
163 <span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">([</span><span·class="s1">&#39;total&#39;</span><span·class="p">,</span><span·class="s1">&#39;10(3)&#39;</span><span·class="p">,</span><span·class="s1">&#39;100(2)&#39;</span><span·class="p">,</span>·<span·class="s1">&#39;level&#39;</span><span·class="p">])</span>163 <span·class="n">plt</span><span·class="o">.</span><span·class="n">legend</span><span·class="p">([</span><span·class="s1">&#39;total&#39;</span><span·class="p">,</span><span·class="s1">&#39;10(3)&#39;</span><span·class="p">,</span><span·class="s1">&#39;100(2)&#39;</span><span·class="p">,</span>·<span·class="s1">&#39;level&#39;</span><span·class="p">])</span>
164 <span·class="n">plt</span><span·class="o">.</span><span·class="n">show</span><span·class="p">()</span>164 <span·class="n">plt</span><span·class="o">.</span><span·class="n">show</span><span·class="p">()</span>
165 </pre></div>165 </pre></div>
166 </div>166 </div>
167 </div>167 </div>
168 <div·class="nboutput·nblast·docutils·container"> 
169 <div·class="prompt·empty·docutils·container"> 
170 </div> 
171 <div·class="output_area·docutils·container"> 
172 <img·alt="../../../_images/examples_notebooks_generated_statespace_seasonal_5_0.png"·src="../../../_images/examples_notebooks_generated_statespace_seasonal_5_0.png"·/> 
173 </div> 
174 </div> 
175 </section>168 </section>
176 <section·id="Unobserved-components-(frequency-domain-modeling)">169 <section·id="Unobserved-components-(frequency-domain-modeling)">
177 <h2>Unobserved·components·(frequency·domain·modeling)<a·class="headerlink"·href="#Unobserved-components-(frequency-domain-modeling)"·title="Link·to·this·heading">¶</a></h2>170 <h2>Unobserved·components·(frequency·domain·modeling)<a·class="headerlink"·href="#Unobserved-components-(frequency-domain-modeling)"·title="Link·to·this·heading">¶</a></h2>
178 <p>The·next·method·is·an·unobserved·components·model,·where·the·trend·is·modeled·as·a·fixed·intercept·and·the·seasonal·components·are·modeled·using·trigonometric·functions·with·primary·periodicities·of·10·and·100,·respectively,·and·number·of·harmonics·3·and·2,·respectively.·Note·that·this·is·the·correct,·generating·model.·The·process·for·the·time·series·can·be·written·as:</p>171 <p>The·next·method·is·an·unobserved·components·model,·where·the·trend·is·modeled·as·a·fixed·intercept·and·the·seasonal·components·are·modeled·using·trigonometric·functions·with·primary·periodicities·of·10·and·100,·respectively,·and·number·of·harmonics·3·and·2,·respectively.·Note·that·this·is·the·correct,·generating·model.·The·process·for·the·time·series·can·be·written·as:</p>
179 <div·class="math·notranslate·nohighlight">172 <div·class="math·notranslate·nohighlight">
180 \[\begin{split}\begin{align}173 \[\begin{split}\begin{align}
181 y_t·&amp;·=·\mu_t·+·\gamma^{(1)}_t·+·\gamma^{(2)}_t·+·\epsilon_t\\174 y_t·&amp;·=·\mu_t·+·\gamma^{(1)}_t·+·\gamma^{(2)}_t·+·\epsilon_t\\
Offset 184, 16 lines modifiedOffset 177, 16 lines modified
184 \gamma^{(2)}_{t}·&amp;=·\sum_{j=1}^3·\gamma^{(2)}_{j,·t}\\177 \gamma^{(2)}_{t}·&amp;=·\sum_{j=1}^3·\gamma^{(2)}_{j,·t}\\
185 \gamma^{(1)}_{j,·t+1}·&amp;=·\gamma^{(1)}_{j,·t}\cos(\lambda_j)·+·\gamma^{*,·(1)}_{j,·t}\sin(\lambda_j)·+·\omega^{(1)}_{j,t},·~j·=·1,·2,·3\\178 \gamma^{(1)}_{j,·t+1}·&amp;=·\gamma^{(1)}_{j,·t}\cos(\lambda_j)·+·\gamma^{*,·(1)}_{j,·t}\sin(\lambda_j)·+·\omega^{(1)}_{j,t},·~j·=·1,·2,·3\\
186 \gamma^{*,·(1)}_{j,·t+1}·&amp;=·-\gamma^{(1)}_{j,·t}\sin(\lambda_j)·+·\gamma^{*,·(1)}_{j,·t}\cos(\lambda_j)·+·\omega^{*,·(1)}_{j,·t},·~j·=·1,·2,·3\\179 \gamma^{*,·(1)}_{j,·t+1}·&amp;=·-\gamma^{(1)}_{j,·t}\sin(\lambda_j)·+·\gamma^{*,·(1)}_{j,·t}\cos(\lambda_j)·+·\omega^{*,·(1)}_{j,·t},·~j·=·1,·2,·3\\
187 \gamma^{(2)}_{j,·t+1}·&amp;=·\gamma^{(2)}_{j,·t}\cos(\lambda_j)·+·\gamma^{*,·(2)}_{j,·t}\sin(\lambda_j)·+·\omega^{(2)}_{j,t},·~j·=·1,·2\\180 \gamma^{(2)}_{j,·t+1}·&amp;=·\gamma^{(2)}_{j,·t}\cos(\lambda_j)·+·\gamma^{*,·(2)}_{j,·t}\sin(\lambda_j)·+·\omega^{(2)}_{j,t},·~j·=·1,·2\\
188 \gamma^{*,·(2)}_{j,·t+1}·&amp;=·-\gamma^{(2)}_{j,·t}\sin(\lambda_j)·+·\gamma^{*,·(2)}_{j,·t}\cos(\lambda_j)·+·\omega^{*,·(2)}_{j,·t},·~j·=·1,·2\\181 \gamma^{*,·(2)}_{j,·t+1}·&amp;=·-\gamma^{(2)}_{j,·t}\sin(\lambda_j)·+·\gamma^{*,·(2)}_{j,·t}\cos(\lambda_j)·+·\omega^{*,·(2)}_{j,·t},·~j·=·1,·2\\
189 \end{align}\end{split}\]</div>182 \end{align}\end{split}\]</div>
190 <p>where·<span·class="math·notranslate·nohighlight">\(\epsilon_t\)</span>·is·white·noise,·<span·class="math·notranslate·nohighlight">\(\omega^{(1)}_{j,t}\)</span>·are·i.i.d.·<span·class="math·notranslate·nohighlight">\(N(0,·\sigma^2_1)\)</span>,·and·<span·class="math·notranslate·nohighlight">\(\omega^{(2)}_{j,t}\)</span>·are·i.i.d.·<span·class="math·notranslate·nohighlight">\(N(0,·\sigma^2_2)\)</span>,·where·<span·class="math·notranslate·nohighlight">\(\sigma_1·=·2.\)</span></p>183 <p>where·<span·class="math·notranslate·nohighlight">\(\epsilon_t\)</span>·is·white·noise,·<span·class="math·notranslate·nohighlight">\(\omega^{(1)}_{j,t}\)</span>·are·i.i.d.·<span·class="math·notranslate·nohighlight">\(N(0,·\sigma^2_1)\)</span>,·and·<span·class="math·notranslate·nohighlight">\(\omega^{(2)}_{j,t}\)</span>·are·i.i.d.·<span·class="math·notranslate·nohighlight">\(N(0,·\sigma^2_2)\)</span>,·where·<span·class="math·notranslate·nohighlight">\(\sigma_1·=·2.\)</span></p>
191 <div·class="nbinput·docutils·container">184 <div·class="nbinput·nblast·docutils·container">
192 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:185 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
193 </pre></div>186 </pre></div>
194 </div>187 </div>
195 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">model</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">UnobservedComponents</span><span·class="p">(</span><span·class="n">series</span><span·class="o">.</span><span·class="n">values</span><span·class="p">,</span>188 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">model</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">UnobservedComponents</span><span·class="p">(</span><span·class="n">series</span><span·class="o">.</span><span·class="n">values</span><span·class="p">,</span>
196 ····································<span·class="n">level</span><span·class="o">=</span><span·class="s1">&#39;fixed·intercept&#39;</span><span·class="p">,</span>189 ····································<span·class="n">level</span><span·class="o">=</span><span·class="s1">&#39;fixed·intercept&#39;</span><span·class="p">,</span>
197 ····································<span·class="n">freq_seasonal</span><span·class="o">=</span><span·class="p">[{</span><span·class="s1">&#39;period&#39;</span><span·class="p">:</span>·<span·class="mi">10</span><span·class="p">,</span>190 ····································<span·class="n">freq_seasonal</span><span·class="o">=</span><span·class="p">[{</span><span·class="s1">&#39;period&#39;</span><span·class="p">:</span>·<span·class="mi">10</span><span·class="p">,</span>
198 ····················································<span·class="s1">&#39;harmonics&#39;</span><span·class="p">:</span>·<span·class="mi">3</span><span·class="p">},</span>191 ····················································<span·class="s1">&#39;harmonics&#39;</span><span·class="p">:</span>·<span·class="mi">3</span><span·class="p">},</span>
199 ···················································<span·class="p">{</span><span·class="s1">&#39;period&#39;</span><span·class="p">:</span>·<span·class="mi">100</span><span·class="p">,</span>192 ···················································<span·class="p">{</span><span·class="s1">&#39;period&#39;</span><span·class="p">:</span>·<span·class="mi">100</span><span·class="p">,</span>
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204 <span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;fixed·intercept·estimated·as·</span><span·class="si">{0:.3f}</span><span·class="s2">&quot;</span><span·class="o">.</span><span·class="n">format</span><span·class="p">(</span><span·class="n">res_f</span><span·class="o">.</span><span·class="n">smoother_results</span><span·class="o">.</span><span·class="n">smoothed_state</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">,</span><span·class="o">-</span><span·class="mi">1</span><span·class="p">:][</span><span·class="mi">0</span><span·class="p">]))</span>197 <span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;fixed·intercept·estimated·as·</span><span·class="si">{0:.3f}</span><span·class="s2">&quot;</span><span·class="o">.</span><span·class="n">format</span><span·class="p">(</span><span·class="n">res_f</span><span·class="o">.</span><span·class="n">smoother_results</span><span·class="o">.</span><span·class="n">smoothed_state</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">,</span><span·class="o">-</span><span·class="mi">1</span><span·class="p">:][</span><span·class="mi">0</span><span·class="p">]))</span>
  
205 <span·class="n">res_f</span><span·class="o">.</span><span·class="n">plot_components</span><span·class="p">()</span>198 <span·class="n">res_f</span><span·class="o">.</span><span·class="n">plot_components</span><span·class="p">()</span>
206 <span·class="n">plt</span><span·class="o">.</span><span·class="n">show</span><span·class="p">()</span>199 <span·class="n">plt</span><span·class="o">.</span><span·class="n">show</span><span·class="p">()</span>
207 <br/></pre></div>200 <br/></pre></div>
208 </div>201 </div>
209 </div>202 </div>
210 <div·class="nboutput·docutils·container"> 
211 <div·class="prompt·empty·docutils·container"> 
212 </div> 
213 <div·class="output_area·docutils·container"> 
214 <div·class="highlight"><pre> 
215 ································Unobserved·Components·Results 
216 ============================================================================================== 
217 Dep.·Variable:······································y···No.·Observations:··················300 
218 Model:································fixed·intercept···Log·Likelihood···············-1145.631 
219 ····················+·stochastic·freq_seasonal(10(3))···AIC···························2295.261 
220 ···················+·stochastic·freq_seasonal(100(2))···BIC···························2302.594 
221 Date:································Sun,·10·Aug·2025···HQIC··························2298.200 
222 Time:········································13:13:47 
223 Sample:·············································0 
224 ················································-·300 
225 Covariance·Type:··································opg 
226 =============================================================================================== 
227 ··································coef····std·err··········z······P&gt;|z|······[0.025······0.975] 
228 ----------------------------------------------------------------------------------------------- 
229 sigma2.freq_seasonal_10(3)······4.5942······0.565······8.126······0.000·······3.486·······5.702 
230 sigma2.freq_seasonal_100(2)·····9.7904······2.483······3.942······0.000·······4.923······14.658 
231 =================================================================================== 
232 Ljung-Box·(L1)·(Q):···················0.06···Jarque-Bera·(JB):·················0.08 
233 Prob(Q):······························0.81···Prob(JB):·························0.96 
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16 seasonal·component·with·a·relatively·short·period,·and·\(\gamma^{(2)}_t\)16 seasonal·component·with·a·relatively·short·period,·and·\(\gamma^{(2)}_t\)
17 represents·another·seasonal·component·of·longer·period.·We·will·have·a·fixed17 represents·another·seasonal·component·of·longer·period.·We·will·have·a·fixed
18 intercept·term·for·our·level·and·consider·both·\(\gamma^{(2)}_t\)·and·\(\gamma^18 intercept·term·for·our·level·and·consider·both·\(\gamma^{(2)}_t\)·and·\(\gamma^
19 {(2)}_t\)·to·be·stochastic·so·that·the·seasonal·patterns·can·vary·over·time.19 {(2)}_t\)·to·be·stochastic·so·that·the·seasonal·patterns·can·vary·over·time.
20 In·this·notebook,·we·will·generate·synthetic·data·conforming·to·this·model·and20 In·this·notebook,·we·will·generate·synthetic·data·conforming·to·this·model·and
21 showcase·modeling·of·the·seasonal·terms·in·a·few·different·ways·under·the21 showcase·modeling·of·the·seasonal·terms·in·a·few·different·ways·under·the
22 unobserved·components·modeling·framework.22 unobserved·components·modeling·framework.
23 [1]:23 [·]:
24 %matplotlib·inline24 %matplotlib·inline
25 [2]:25 [·]:
26 import·numpy·as·np26 import·numpy·as·np
27 import·pandas·as·pd27 import·pandas·as·pd
28 import·statsmodels.api·as·sm28 import·statsmodels.api·as·sm
29 import·matplotlib.pyplot·as·plt29 import·matplotlib.pyplot·as·plt
  
30 plt.rc("figure",·figsize=(16,8))30 plt.rc("figure",·figsize=(16,8))
31 plt.rc("font",·size=14)31 plt.rc("font",·size=14)
32 *\x8**\x8**\x8**\x8**\x8*·S\x8Sy\x8yn\x8nt\x8th\x8he\x8et\x8ti\x8ic\x8c·d\x8da\x8at\x8ta\x8a·c\x8cr\x8re\x8ea\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*32 *\x8**\x8**\x8**\x8**\x8*·S\x8Sy\x8yn\x8nt\x8th\x8he\x8et\x8ti\x8ic\x8c·d\x8da\x8at\x8ta\x8a·c\x8cr\x8re\x8ea\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
33 We·will·create·data·with·multiple·seasonal·patterns·by·following·equations33 We·will·create·data·with·multiple·seasonal·patterns·by·following·equations
34 (3.7)·and·(3.8)·in·Durbin·and·Koopman·(2012).·We·will·simulate·300·periods·and34 (3.7)·and·(3.8)·in·Durbin·and·Koopman·(2012).·We·will·simulate·300·periods·and
35 two·seasonal·terms·parametrized·in·the·frequency·domain·having·periods·10·and35 two·seasonal·terms·parametrized·in·the·frequency·domain·having·periods·10·and
36 100,·respectively,·and·3·and·2·number·of·harmonics,·respectively.·Further,·the36 100,·respectively,·and·3·and·2·number·of·harmonics,·respectively.·Further,·the
37 variances·of·their·stochastic·parts·are·4·and·9,·respectively.37 variances·of·their·stochastic·parts·are·4·and·9,·respectively.
38 [3]:38 [·]:
39 #·First·we'll·simulate·the·synthetic·data39 #·First·we'll·simulate·the·synthetic·data
40 def·simulate_seasonal_term(periodicity,·total_cycles,·noise_std=1.,40 def·simulate_seasonal_term(periodicity,·total_cycles,·noise_std=1.,
41 ···························harmonics=None):41 ···························harmonics=None):
42 ····duration·=·periodicity·*·total_cycles42 ····duration·=·periodicity·*·total_cycles
43 ····assert·duration·==·int(duration)43 ····assert·duration·==·int(duration)
44 ····duration·=·int(duration)44 ····duration·=·int(duration)
45 ····harmonics·=·harmonics·if·harmonics·else·int(np.floor(periodicity·/·2))45 ····harmonics·=·harmonics·if·harmonics·else·int(np.floor(periodicity·/·2))
Offset 66, 15 lines modifiedOffset 66, 15 lines modified
66 ······································+·noise_std·*·np.random.randn())66 ······································+·noise_std·*·np.random.randn())
67 ········series[t]·=·np.sum(gamma_jtp1)67 ········series[t]·=·np.sum(gamma_jtp1)
68 ········gamma_jt·=·gamma_jtp168 ········gamma_jt·=·gamma_jtp1
69 ········gamma_star_jt·=·gamma_star_jtp169 ········gamma_star_jt·=·gamma_star_jtp1
70 ····wanted_series·=·series[-duration:]·#·Discard·burn·in70 ····wanted_series·=·series[-duration:]·#·Discard·burn·in
  
71 ····return·wanted_series71 ····return·wanted_series
72 [4]:72 [·]:
73 duration·=·100·*·373 duration·=·100·*·3
74 periodicities·=·[10,·100]74 periodicities·=·[10,·100]
75 num_harmonics·=·[3,·2]75 num_harmonics·=·[3,·2]
76 std·=·np.array([2,·3])76 std·=·np.array([2,·3])
77 np.random.seed(8678309)77 np.random.seed(8678309)
  
78 terms·=·[]78 terms·=·[]
Offset 93, 15 lines modifiedOffset 93, 14 lines modified
93 ························'level':terms[2]})93 ························'level':terms[2]})
94 h1,·=·plt.plot(df['total'])94 h1,·=·plt.plot(df['total'])
95 h2,·=·plt.plot(df['10(3)'])95 h2,·=·plt.plot(df['10(3)'])
96 h3,·=·plt.plot(df['100(2)'])96 h3,·=·plt.plot(df['100(2)'])
97 h4,·=·plt.plot(df['level'])97 h4,·=·plt.plot(df['level'])
98 plt.legend(['total','10(3)','100(2)',·'level'])98 plt.legend(['total','10(3)','100(2)',·'level'])
99 plt.show()99 plt.show()
100 [../../../_images/examples_notebooks_generated_statespace_seasonal_5_0.png] 
101 *\x8**\x8**\x8**\x8**\x8*·U\x8Un\x8no\x8ob\x8bs\x8se\x8er\x8rv\x8ve\x8ed\x8d·c\x8co\x8om\x8mp\x8po\x8on\x8ne\x8en\x8nt\x8ts\x8s·(\x8(f\x8fr\x8re\x8eq\x8qu\x8ue\x8en\x8nc\x8cy\x8y·d\x8do\x8om\x8ma\x8ai\x8in\x8n·m\x8mo\x8od\x8de\x8el\x8li\x8in\x8ng\x8g)\x8)_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*100 *\x8**\x8**\x8**\x8**\x8*·U\x8Un\x8no\x8ob\x8bs\x8se\x8er\x8rv\x8ve\x8ed\x8d·c\x8co\x8om\x8mp\x8po\x8on\x8ne\x8en\x8nt\x8ts\x8s·(\x8(f\x8fr\x8re\x8eq\x8qu\x8ue\x8en\x8nc\x8cy\x8y·d\x8do\x8om\x8ma\x8ai\x8in\x8n·m\x8mo\x8od\x8de\x8el\x8li\x8in\x8ng\x8g)\x8)_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
102 The·next·method·is·an·unobserved·components·model,·where·the·trend·is·modeled101 The·next·method·is·an·unobserved·components·model,·where·the·trend·is·modeled
103 as·a·fixed·intercept·and·the·seasonal·components·are·modeled·using102 as·a·fixed·intercept·and·the·seasonal·components·are·modeled·using
104 trigonometric·functions·with·primary·periodicities·of·10·and·100,·respectively,103 trigonometric·functions·with·primary·periodicities·of·10·and·100,·respectively,
105 and·number·of·harmonics·3·and·2,·respectively.·Note·that·this·is·the·correct,104 and·number·of·harmonics·3·and·2,·respectively.·Note·that·this·is·the·correct,
106 generating·model.·The·process·for·the·time·series·can·be·written·as:105 generating·model.·The·process·for·the·time·series·can·be·written·as:
107 \[\begin{split}\begin{align}·y_t·&·=·\mu_t·+·\gamma^{(1)}_t·+·\gamma^{(2)}_t·+106 \[\begin{split}\begin{align}·y_t·&·=·\mu_t·+·\gamma^{(1)}_t·+·\gamma^{(2)}_t·+
Offset 114, 15 lines modifiedOffset 113, 15 lines modified
114 {j,·t}\cos(\lambda_j)·+·\gamma^{*,·(2)}_{j,·t}\sin(\lambda_j)·+·\omega^{(2)}_113 {j,·t}\cos(\lambda_j)·+·\gamma^{*,·(2)}_{j,·t}\sin(\lambda_j)·+·\omega^{(2)}_
115 {j,t},·~j·=·1,·2\\·\gamma^{*,·(2)}_{j,·t+1}·&=·-\gamma^{(2)}_{j,·t}\sin114 {j,t},·~j·=·1,·2\\·\gamma^{*,·(2)}_{j,·t+1}·&=·-\gamma^{(2)}_{j,·t}\sin
116 (\lambda_j)·+·\gamma^{*,·(2)}_{j,·t}\cos(\lambda_j)·+·\omega^{*,·(2)}_{j,·t},115 (\lambda_j)·+·\gamma^{*,·(2)}_{j,·t}\cos(\lambda_j)·+·\omega^{*,·(2)}_{j,·t},
117 ~j·=·1,·2\\·\end{align}\end{split}\]116 ~j·=·1,·2\\·\end{align}\end{split}\]
118 where·\(\epsilon_t\)·is·white·noise,·\(\omega^{(1)}_{j,t}\)·are·i.i.d.·\(N(0,117 where·\(\epsilon_t\)·is·white·noise,·\(\omega^{(1)}_{j,t}\)·are·i.i.d.·\(N(0,
119 \sigma^2_1)\),·and·\(\omega^{(2)}_{j,t}\)·are·i.i.d.·\(N(0,·\sigma^2_2)\),118 \sigma^2_1)\),·and·\(\omega^{(2)}_{j,t}\)·are·i.i.d.·\(N(0,·\sigma^2_2)\),
120 where·\(\sigma_1·=·2.\)119 where·\(\sigma_1·=·2.\)
121 [5]:120 [·]:
122 model·=·sm.tsa.UnobservedComponents(series.values,121 model·=·sm.tsa.UnobservedComponents(series.values,
123 ····································level='fixed·intercept',122 ····································level='fixed·intercept',
124 ····································freq_seasonal=[{'period':·10,123 ····································freq_seasonal=[{'period':·10,
125 ····················································'harmonics':·3},124 ····················································'harmonics':·3},
126 ···················································{'period':·100,125 ···················································{'period':·100,
127 ····················································'harmonics':·2}])126 ····················································'harmonics':·2}])
128 res_f·=·model.fit(disp=False)127 res_f·=·model.fit(disp=False)
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130 #·The·first·state·variable·holds·our·estimate·of·the·intercept129 #·The·first·state·variable·holds·our·estimate·of·the·intercept
131 print("fixed·intercept·estimated·as·{0:.3f}".format130 print("fixed·intercept·estimated·as·{0:.3f}".format
132 (res_f.smoother_results.smoothed_state[0,-1:][0]))131 (res_f.smoother_results.smoothed_state[0,-1:][0]))
  
133 res_f.plot_components()132 res_f.plot_components()
134 plt.show()133 plt.show()
  
135 ································Unobserved·Components·Results 
136 ============================================================================================== 
137 Dep.·Variable:······································y···No.·Observations: 
138 300 
139 Model:································fixed·intercept···Log·Likelihood 
140 -1145.631 
141 ····················+·stochastic·freq_seasonal(10(3))···AIC 
142 2295.261 
143 ···················+·stochastic·freq_seasonal(100(2))···BIC 
144 2302.594 
145 Date:································Sun,·10·Aug·2025···HQIC 
146 2298.200 
147 Time:········································13:13:47 
148 Sample:·············································0 
149 ················································-·300 
150 Covariance·Type:··································opg 
151 =============================================================================================== 
152 ··································coef····std·err··········z······P>|z| 
153 [0.025······0.975] 
154 ------------------------------------------------------------------------------- 
155 ---------------- 
156 sigma2.freq_seasonal_10(3)······4.5942······0.565······8.126······0.000 
157 3.486·······5.702 
158 sigma2.freq_seasonal_100(2)·····9.7904······2.483······3.942······0.000 
159 4.923······14.658 
160 =================================================================================== 
161 Ljung-Box·(L1)·(Q):···················0.06···Jarque-Bera·(JB): 
162 0.08 
163 Prob(Q):······························0.81···Prob(JB): 
164 0.96 
165 Heteroskedasticity·(H):···············1.17···Skew: 
166 0.01 
167 Prob(H)·(two-sided):··················0.45···Kurtosis: 
168 3.08 
169 =================================================================================== 
  
170 Warnings: 
171 [1]·Covariance·matrix·calculated·using·the·outer·product·of·gradients·(complex- 
172 step). 
173 fixed·intercept·estimated·as·4.053 
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65 <p>All·functions·in·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.stats.rates</span></code>·take·summary·statistics·of·the·data·as·arguments.·Those·are·counts·of·events·and·number·of·observations·or·total·exposure.·Some·functions·for·Poisson·have·an·option·for·excess·dispersion.·Functions·for·negative·binomial,·NB2,·require·the·dispersion·parameter.·Excess·dispersion·and·dispersion·parameter·need·to·be·provided·by·the·user·and·can·be·estimated·from·the·original·data·with·GLM-Poisson·and·discrete·NegativeBinomial·model,·respectively.</p>65 <p>All·functions·in·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.stats.rates</span></code>·take·summary·statistics·of·the·data·as·arguments.·Those·are·counts·of·events·and·number·of·observations·or·total·exposure.·Some·functions·for·Poisson·have·an·option·for·excess·dispersion.·Functions·for·negative·binomial,·NB2,·require·the·dispersion·parameter.·Excess·dispersion·and·dispersion·parameter·need·to·be·provided·by·the·user·and·can·be·estimated·from·the·original·data·with·GLM-Poisson·and·discrete·NegativeBinomial·model,·respectively.</p>
66 <p>Note,·some·parts·are·still·experimental·and·will·likely·change,·some·features·are·still·missing·and·will·be·added·in·future·versions.</p>66 <p>Note,·some·parts·are·still·experimental·and·will·likely·change,·some·features·are·still·missing·and·will·be·added·in·future·versions.</p>
67 <div·class="line-block">67 <div·class="line-block">
68 <div·class="line"><a·class="reference·internal"·href="#One-sample-functions"><span·class="std·std-ref">One·sample·functions</span></a></div>68 <div·class="line"><a·class="reference·internal"·href="#One-sample-functions"><span·class="std·std-ref">One·sample·functions</span></a></div>
69 <div·class="line"><a·class="reference·internal"·href="#Two-sample-functions"><span·class="std·std-ref">Two·sample·functions</span></a></div>69 <div·class="line"><a·class="reference·internal"·href="#Two-sample-functions"><span·class="std·std-ref">Two·sample·functions</span></a></div>
70 </div>70 </div>
71 <div·class="nbinput·nblast·docutils·container">71 <div·class="nbinput·nblast·docutils·container">
72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
76 <span·class="kn">from</span>·<span·class="nn">numpy.testing</span>·<span·class="kn">import</span>·<span·class="n">assert_allclose</span>76 <span·class="kn">from</span>·<span·class="nn">numpy.testing</span>·<span·class="kn">import</span>·<span·class="n">assert_allclose</span>
77 <span·class="kn">import</span>·<span·class="nn">statsmodels.stats.rates</span>·<span·class="k">as</span>·<span·class="nn">smr</span>77 <span·class="kn">import</span>·<span·class="nn">statsmodels.stats.rates</span>·<span·class="k">as</span>·<span·class="nn">smr</span>
78 <span·class="kn">from</span>·<span·class="nn">statsmodels.stats.rates</span>·<span·class="kn">import</span>·<span·class="p">(</span>78 <span·class="kn">from</span>·<span·class="nn">statsmodels.stats.rates</span>·<span·class="kn">import</span>·<span·class="p">(</span>
79 ····<span·class="c1">#·functions·for·1·sample</span>79 ····<span·class="c1">#·functions·for·1·sample</span>
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105 </div>105 </div>
106 <section·id="One-sample-functions">106 <section·id="One-sample-functions">
107 <h2>One·sample·functions<a·class="headerlink"·href="#One-sample-functions"·title="Link·to·this·heading">¶</a></h2>107 <h2>One·sample·functions<a·class="headerlink"·href="#One-sample-functions"·title="Link·to·this·heading">¶</a></h2>
108 <div·class="line-block">108 <div·class="line-block">
109 <div·class="line">The·main·functions·for·one·sample·Poisson·rates·currently·are·test_poisson·and·confint_poisson.·Both·have·several·methods·available,·most·of·them·are·consistent·between·hypothesis·test·and·confidence·interval.·Two·additional·functions·are·available·for·tolerance·intervals·and·for·confidence·intervals·of·quantiles.</div>109 <div·class="line">The·main·functions·for·one·sample·Poisson·rates·currently·are·test_poisson·and·confint_poisson.·Both·have·several·methods·available,·most·of·them·are·consistent·between·hypothesis·test·and·confidence·interval.·Two·additional·functions·are·available·for·tolerance·intervals·and·for·confidence·intervals·of·quantiles.</div>
110 <div·class="line">See·docstrings·for·details.</div>110 <div·class="line">See·docstrings·for·details.</div>
111 </div>111 </div>
112 <div·class="nbinput·docutils·container">112 <div·class="nbinput·nblast·docutils·container">
113 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:113 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
114 </pre></div>114 </pre></div>
115 </div>115 </div>
116 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">count1</span><span·class="p">,</span>·<span·class="n">n1</span>·<span·class="o">=</span>·<span·class="mi">60</span><span·class="p">,</span>·<span·class="mf">514.775</span>116 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">count1</span><span·class="p">,</span>·<span·class="n">n1</span>·<span·class="o">=</span>·<span·class="mi">60</span><span·class="p">,</span>·<span·class="mf">514.775</span>
117 <span·class="n">count1</span>·<span·class="o">/</span>·<span·class="n">n1</span>117 <span·class="n">count1</span>·<span·class="o">/</span>·<span·class="n">n1</span>
118 </pre></div>118 </pre></div>
119 </div>119 </div>
120 </div>120 </div>
121 <div·class="nboutput·nblast·docutils·container">121 <div·class="nbinput·nblast·docutils·container">
122 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:122 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
123 </pre></div> 
124 </div> 
125 <div·class="output_area·docutils·container"> 
126 <div·class="highlight"><pre> 
127 0.11655577679568745 
128 </pre></div></div> 
129 </div> 
130 <div·class="nbinput·docutils·container"> 
131 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]: 
132 </pre></div>123 </pre></div>
133 </div>124 </div>
134 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">test_poisson</span><span·class="p">(</span><span·class="n">count1</span><span·class="p">,</span>·<span·class="n">n1</span><span·class="p">,</span>·<span·class="n">value</span><span·class="o">=</span><span·class="mf">0.1</span><span·class="p">,</span>·<span·class="n">method</span><span·class="o">=</span><span·class="s2">&quot;midp-c&quot;</span><span·class="p">)</span>125 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">test_poisson</span><span·class="p">(</span><span·class="n">count1</span><span·class="p">,</span>·<span·class="n">n1</span><span·class="p">,</span>·<span·class="n">value</span><span·class="o">=</span><span·class="mf">0.1</span><span·class="p">,</span>·<span·class="n">method</span><span·class="o">=</span><span·class="s2">&quot;midp-c&quot;</span><span·class="p">)</span>
135 </pre></div>126 </pre></div>
136 </div>127 </div>
137 </div>128 </div>
138 <div·class="nboutput·nblast·docutils·container">129 <div·class="nbinput·nblast·docutils·container">
139 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:130 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
140 </pre></div> 
141 </div> 
142 <div·class="output_area·docutils·container"> 
143 <div·class="highlight"><pre> 
144 &lt;class·&#39;statsmodels.stats.base.HolderTuple&#39;&gt; 
145 statistic·=·nan 
146 pvalue·=·np.float64(0.23913820865664664) 
147 distribution·=·&#39;Poisson&#39; 
148 method·=·&#39;midp-c&#39; 
149 alternative·=·&#39;two-sided&#39; 
150 rate·=·0.11655577679568745 
151 nobs·=·514.775 
152 tuple·=·(nan,·np.float64(0.23913820865664664)) 
153 </pre></div></div> 
154 </div> 
155 <div·class="nbinput·docutils·container"> 
156 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]: 
157 </pre></div>131 </pre></div>
158 </div>132 </div>
159 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">confint_poisson</span><span·class="p">(</span><span·class="n">count1</span><span·class="p">,</span>·<span·class="n">n1</span><span·class="p">,</span>·<span·class="n">method</span><span·class="o">=</span><span·class="s2">&quot;midp-c&quot;</span><span·class="p">)</span>133 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">confint_poisson</span><span·class="p">(</span><span·class="n">count1</span><span·class="p">,</span>·<span·class="n">n1</span><span·class="p">,</span>·<span·class="n">method</span><span·class="o">=</span><span·class="s2">&quot;midp-c&quot;</span><span·class="p">)</span>
160 </pre></div>134 </pre></div>
161 </div>135 </div>
162 </div>136 </div>
163 <div·class="nboutput·nblast·docutils·container"> 
164 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]: 
165 </pre></div> 
166 </div> 
167 <div·class="output_area·docutils·container"> 
168 <div·class="highlight"><pre> 
169 (np.float64(0.0897357524941493),·np.float64(0.1490015282355224)) 
170 </pre></div></div> 
171 </div> 
172 <p>The·available·methods·for·hypothesis·tests·and·confidence·interval·are·available·in·the·dictionary·<code·class="docutils·literal·notranslate"><span·class="pre">method_names_poisson_1samp</span></code>.·See·docstring·for·details.</p>137 <p>The·available·methods·for·hypothesis·tests·and·confidence·interval·are·available·in·the·dictionary·<code·class="docutils·literal·notranslate"><span·class="pre">method_names_poisson_1samp</span></code>.·See·docstring·for·details.</p>
173 <div·class="nbinput·docutils·container">138 <div·class="nbinput·nblast·docutils·container">
174 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:139 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
175 </pre></div>140 </pre></div>
176 </div>141 </div>
177 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">method_names_poisson_1samp</span>142 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">method_names_poisson_1samp</span>
178 </pre></div>143 </pre></div>
179 </div>144 </div>
180 </div>145 </div>
181 <div·class="nboutput·nblast·docutils·container">146 <div·class="nbinput·nblast·docutils·container">
182 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:147 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
183 </pre></div> 
184 </div> 
185 <div·class="output_area·docutils·container"> 
186 <div·class="highlight"><pre> 
187 {&#39;test&#39;:·[&#39;wald&#39;, 
188 ··&#39;score&#39;, 
189 ··&#39;exact-c&#39;, 
190 ··&#39;midp-c&#39;, 
191 ··&#39;waldccv&#39;, 
192 ··&#39;sqrt-a&#39;, 
193 ··&#39;sqrt-v&#39;, 
194 ··&#39;sqrt&#39;], 
195 ·&#39;confint&#39;:·[&#39;wald&#39;, 
196 ··&#39;score&#39;, 
197 ··&#39;exact-c&#39;, 
198 ··&#39;midp-c&#39;, 
199 ··&#39;jeff&#39;, 
200 ··&#39;waldccv&#39;, 
201 ··&#39;sqrt-a&#39;, 
202 ··&#39;sqrt-v&#39;, 
203 ··&#39;sqrt&#39;, 
204 ··&#39;sqrt-cent&#39;, 
205 ··&#39;sqrt-centcc&#39;]} 
206 </pre></div></div> 
207 </div> 
208 <div·class="nbinput·docutils·container"> 
209 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]: 
210 </pre></div>148 </pre></div>
211 </div>149 </div>
212 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">for</span>·<span·class="n">meth</span>·<span·class="ow">in</span>·<span·class="n">method_names_poisson_1samp</span><span·class="p">[</span><span·class="s2">&quot;test&quot;</span><span·class="p">]:</span>150 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">for</span>·<span·class="n">meth</span>·<span·class="ow">in</span>·<span·class="n">method_names_poisson_1samp</span><span·class="p">[</span><span·class="s2">&quot;test&quot;</span><span·class="p">]:</span>
213 ····<span·class="n">tst</span>·<span·class="o">=</span>·<span·class="n">test_poisson</span><span·class="p">(</span><span·class="n">count1</span><span·class="p">,</span>·<span·class="n">n1</span><span·class="p">,</span>·<span·class="n">method</span><span·class="o">=</span><span·class="n">meth</span><span·class="p">,</span>·<span·class="n">value</span><span·class="o">=</span><span·class="mf">0.1</span><span·class="p">,</span>151 ····<span·class="n">tst</span>·<span·class="o">=</span>·<span·class="n">test_poisson</span><span·class="p">(</span><span·class="n">count1</span><span·class="p">,</span>·<span·class="n">n1</span><span·class="p">,</span>·<span·class="n">method</span><span·class="o">=</span><span·class="n">meth</span><span·class="p">,</span>·<span·class="n">value</span><span·class="o">=</span><span·class="mf">0.1</span><span·class="p">,</span>
214 ·······················<span·class="n">alternative</span><span·class="o">=</span><span·class="s1">&#39;two-sided&#39;</span><span·class="p">)</span>152 ·······················<span·class="n">alternative</span><span·class="o">=</span><span·class="s1">&#39;two-sided&#39;</span><span·class="p">)</span>
215 ····<span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;</span><span·class="si">%-12s</span><span·class="s2">&quot;</span>·<span·class="o">%</span>·<span·class="n">meth</span><span·class="p">,</span>·<span·class="n">tst</span><span·class="o">.</span><span·class="n">pvalue</span><span·class="p">)</span>153 ····<span·class="nb">print</span><span·class="p">(</span><span·class="s2">&quot;</span><span·class="si">%-12s</span><span·class="s2">&quot;</span>·<span·class="o">%</span>·<span·class="n">meth</span><span·class="p">,</span>·<span·class="n">tst</span><span·class="o">.</span><span·class="n">pvalue</span><span·class="p">)</span>
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18 dispersion·and·dispersion·parameter·need·to·be·provided·by·the·user·and·can·be18 dispersion·and·dispersion·parameter·need·to·be·provided·by·the·user·and·can·be
19 estimated·from·the·original·data·with·GLM-Poisson·and·discrete·NegativeBinomial19 estimated·from·the·original·data·with·GLM-Poisson·and·discrete·NegativeBinomial
20 model,·respectively.20 model,·respectively.
21 Note,·some·parts·are·still·experimental·and·will·likely·change,·some·features21 Note,·some·parts·are·still·experimental·and·will·likely·change,·some·features
22 are·still·missing·and·will·be·added·in·future·versions.22 are·still·missing·and·will·be·added·in·future·versions.
23 _\x8O_\x8n_\x8e_\x8·_\x8s_\x8a_\x8m_\x8p_\x8l_\x8e_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8s23 _\x8O_\x8n_\x8e_\x8·_\x8s_\x8a_\x8m_\x8p_\x8l_\x8e_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8s
24 _\x8T_\x8w_\x8o_\x8·_\x8s_\x8a_\x8m_\x8p_\x8l_\x8e_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8s24 _\x8T_\x8w_\x8o_\x8·_\x8s_\x8a_\x8m_\x8p_\x8l_\x8e_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8s
25 [1]:25 [·]:
26 import·numpy·as·np26 import·numpy·as·np
27 from·numpy.testing·import·assert_allclose27 from·numpy.testing·import·assert_allclose
28 import·statsmodels.stats.rates·as·smr28 import·statsmodels.stats.rates·as·smr
29 from·statsmodels.stats.rates·import·(29 from·statsmodels.stats.rates·import·(
30 ····#·functions·for·1·sample30 ····#·functions·for·1·sample
31 ····test_poisson,31 ····test_poisson,
32 ····confint_poisson,32 ····confint_poisson,
Offset 54, 88 lines modifiedOffset 54, 35 lines modified
54 *\x8**\x8**\x8**\x8**\x8*·O\x8On\x8ne\x8e·s\x8sa\x8am\x8mp\x8pl\x8le\x8e·f\x8fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*54 *\x8**\x8**\x8**\x8**\x8*·O\x8On\x8ne\x8e·s\x8sa\x8am\x8mp\x8pl\x8le\x8e·f\x8fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
55 The·main·functions·for·one·sample·Poisson·rates·currently·are·test_poisson·and55 The·main·functions·for·one·sample·Poisson·rates·currently·are·test_poisson·and
56 confint_poisson.·Both·have·several·methods·available,·most·of·them·are56 confint_poisson.·Both·have·several·methods·available,·most·of·them·are
57 consistent·between·hypothesis·test·and·confidence·interval.·Two·additional57 consistent·between·hypothesis·test·and·confidence·interval.·Two·additional
58 functions·are·available·for·tolerance·intervals·and·for·confidence·intervals·of58 functions·are·available·for·tolerance·intervals·and·for·confidence·intervals·of
59 quantiles.59 quantiles.
60 See·docstrings·for·details.60 See·docstrings·for·details.
61 [2]:61 [·]:
62 count1,·n1·=·60,·514.77562 count1,·n1·=·60,·514.775
63 count1·/·n163 count1·/·n1
64 [2]:64 [·]:
65 0.11655577679568745 
66 [3]: 
67 test_poisson(count1,·n1,·value=0.1,·method="midp-c")65 test_poisson(count1,·n1,·value=0.1,·method="midp-c")
68 [3]:66 [·]:
69 <class·'statsmodels.stats.base.HolderTuple'> 
70 statistic·=·nan 
71 pvalue·=·np.float64(0.23913820865664664) 
72 distribution·=·'Poisson' 
73 method·=·'midp-c' 
74 alternative·=·'two-sided' 
75 rate·=·0.11655577679568745 
76 nobs·=·514.775 
77 tuple·=·(nan,·np.float64(0.23913820865664664)) 
78 [4]: 
79 confint_poisson(count1,·n1,·method="midp-c")67 confint_poisson(count1,·n1,·method="midp-c")
80 [4]: 
81 (np.float64(0.0897357524941493),·np.float64(0.1490015282355224)) 
82 The·available·methods·for·hypothesis·tests·and·confidence·interval·are68 The·available·methods·for·hypothesis·tests·and·confidence·interval·are
83 available·in·the·dictionary·method_names_poisson_1samp.·See·docstring·for69 available·in·the·dictionary·method_names_poisson_1samp.·See·docstring·for
84 details.70 details.
85 [5]:71 [·]:
86 method_names_poisson_1samp72 method_names_poisson_1samp
87 [5]:73 [·]:
88 {'test':·['wald', 
89 ··'score', 
90 ··'exact-c', 
91 ··'midp-c', 
92 ··'waldccv', 
93 ··'sqrt-a', 
94 ··'sqrt-v', 
95 ··'sqrt'], 
96 ·'confint':·['wald', 
97 ··'score', 
98 ··'exact-c', 
99 ··'midp-c', 
100 ··'jeff', 
101 ··'waldccv', 
102 ··'sqrt-a', 
103 ··'sqrt-v', 
104 ··'sqrt', 
105 ··'sqrt-cent', 
106 ··'sqrt-centcc']} 
107 [6]: 
108 for·meth·in·method_names_poisson_1samp["test"]:74 for·meth·in·method_names_poisson_1samp["test"]:
109 ····tst·=·test_poisson(count1,·n1,·method=meth,·value=0.1,75 ····tst·=·test_poisson(count1,·n1,·method=meth,·value=0.1,
110 ·······················alternative='two-sided')76 ·······················alternative='two-sided')
111 ····print("%-12s"·%·meth,·tst.pvalue)77 ····print("%-12s"·%·meth,·tst.pvalue)
112 wald·········0.2712232025335152 
113 score········0.23489608509894766 
114 exact-c······0.2654698417416039 
115 midp-c·······0.23913820865664664 
116 waldccv······0.27321266612309003 
117 sqrt-a·······0.25489746088635834 
118 sqrt-v·······0.2281700763432699 
119 sqrt·········0.2533006997208508 
120 [7]:78 [·]:
121 for·meth·in·method_names_poisson_1samp["confint"]:79 for·meth·in·method_names_poisson_1samp["confint"]:
122 ····tst·=·confint_poisson(count1,·n1,·method=meth)80 ····tst·=·confint_poisson(count1,·n1,·method=meth)
123 ····print("%-12s"·%·meth,·tst)81 ····print("%-12s"·%·meth,·tst)
124 wald·········(np.float64(0.08706363801159746),·np.float64(0.14604791557977745)) 
125 score········(np.float64(0.0905597500576385),·np.float64(0.15001420714831387)) 
126 exact-c······(np.float64(0.08894433674907924),·np.float64(0.15003038882355074)) 
127 midp-c·······(np.float64(0.0897357524941493),·np.float64(0.1490015282355224)) 
128 jeff·········(np.float64(0.08979284758964944),·np.float64(0.14893677466593855)) 
129 waldccv······(np.float64(0.08694100904696915),·np.float64(0.14617054454440576)) 
130 sqrt-a·······(np.float64(0.08883721953786133),·np.float64(0.14800553586080228)) 
131 sqrt-v·······(np.float64(0.08975547672311084),·np.float64(0.14897854470462502)) 
132 sqrt·········(np.float64(0.08892923891524183),·np.float64(0.14791351648342183)) 
133 sqrt-cent····(np.float64(0.08883721953786133),·np.float64(0.1480055358608023)) 
134 sqrt-centcc··(np.float64(0.0879886777703761),·np.float64(0.1490990831089978)) 
135 Two·additional·functions·are·currently·available·for·one·sample·poisson·rates,82 Two·additional·functions·are·currently·available·for·one·sample·poisson·rates,
136 tolerance_int_poisson·for·tolerance·intervals·and·confint_quantile_poisson·for83 tolerance_int_poisson·for·tolerance·intervals·and·confint_quantile_poisson·for
137 confidence·intervals·of·Poisson·quantiles.84 confidence·intervals·of·Poisson·quantiles.
138 Tolerance·intervals·are·similar·to·prediction·intervals·that·combine·the85 Tolerance·intervals·are·similar·to·prediction·intervals·that·combine·the
139 randomness·of·a·new·observation·and·uncertainty·about·the·estimated·Poisson86 randomness·of·a·new·observation·and·uncertainty·about·the·estimated·Poisson
140 rate.·If·the·rate·were·known,·then·we·can·compute·a·Poisson·interval·for·a·new87 rate.·If·the·rate·were·known,·then·we·can·compute·a·Poisson·interval·for·a·new
141 observation·using·the·inverse·cdf·at·the·given·rate.·The·tolerance·interval88 observation·using·the·inverse·cdf·at·the·given·rate.·The·tolerance·interval
Offset 151, 176 lines modifiedOffset 98, 81 lines modified
151 most·methods·will·not·guarantee·that·the·coverage·inequalities·hold·in·small98 most·methods·will·not·guarantee·that·the·coverage·inequalities·hold·in·small
152 samples·even·if·the·distribution·is·correctly·specified.99 samples·even·if·the·distribution·is·correctly·specified.
153 In·the·following·example,·we·can·expect·to·observe·between·4·and·23·events·if100 In·the·following·example,·we·can·expect·to·observe·between·4·and·23·events·if
154 the·total·exposure·or·number·of·observations·is·100,·at·given·coverage·prob·and101 the·total·exposure·or·number·of·observations·is·100,·at·given·coverage·prob·and
155 confidence·level·alpha.·The·tolerance·interval·is·larger·than·the·Poisson102 confidence·level·alpha.·The·tolerance·interval·is·larger·than·the·Poisson
156 interval·at·the·observed·rate,·(5,·19),·because·the·tolerance·interval·takes103 interval·at·the·observed·rate,·(5,·19),·because·the·tolerance·interval·takes
157 uncertainty·about·the·parameter·estimate·into·account.104 uncertainty·about·the·parameter·estimate·into·account.
158 [8]:105 [·]:
159 exposure_new·=·100106 exposure_new·=·100
160 tolerance_int_poisson(count1,·n1,·prob=0.95,·exposure_new=exposure_new,107 tolerance_int_poisson(count1,·n1,·prob=0.95,·exposure_new=exposure_new,
161 method="score",·alpha=0.05,·alternative='two-sided')108 method="score",·alpha=0.05,·alternative='two-sided')
162 [8]:109 [·]:
163 (np.float64(4.0),·np.float64(23.0)) 
164 [9]: 
165 from·scipy·import·stats110 from·scipy·import·stats
166 stats.poisson.interval(0.95,·count1·/·n1·*·exposure_new)111 stats.poisson.interval(0.95,·count1·/·n1·*·exposure_new)
167 [9]: 
168 (np.float64(5.0),·np.float64(19.0)) 
169 Aside:·We·can·force·the·tolerance·interval·to·ignore·parameter·uncertainty·by112 Aside:·We·can·force·the·tolerance·interval·to·ignore·parameter·uncertainty·by
170 specifying·alpha=1.113 specifying·alpha=1.
171 [10]:114 [·]:
172 tolerance_int_poisson(count1,·n1,·prob=0.95,·exposure_new=exposure_new,115 tolerance_int_poisson(count1,·n1,·prob=0.95,·exposure_new=exposure_new,
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65 <div·class="highlight-none·notranslate"><div·class="highlight"><pre><span></span>p·=·P(x1·&gt;·x2)·+·0.5·*·P(x1·=·x2)65 <div·class="highlight-none·notranslate"><div·class="highlight"><pre><span></span>p·=·P(x1·&gt;·x2)·+·0.5·*·P(x1·=·x2)
66 </pre></div>66 </pre></div>
67 </div>67 </div>
68 <p>This·is·a·measure·underlying·Wilcoxon-Mann-Whitney’s·U·test,·Fligner-Policello·test·and·Brunner-Munzel·test.·Inference·is·based·on·the·asymptotic·distribution·of·the·Brunner-Munzel·test.·The·half·probability·for·ties·corresponds·to·the·use·of·midranks·and·makes·it·valid·for·discrete·variables.</p>68 <p>This·is·a·measure·underlying·Wilcoxon-Mann-Whitney’s·U·test,·Fligner-Policello·test·and·Brunner-Munzel·test.·Inference·is·based·on·the·asymptotic·distribution·of·the·Brunner-Munzel·test.·The·half·probability·for·ties·corresponds·to·the·use·of·midranks·and·makes·it·valid·for·discrete·variables.</p>
69 <p>The·Null·hypothesis·for·stochastic·equality·is·p·=·0.5,·which·corresponds·to·the·Brunner-Munzel·test.</p>69 <p>The·Null·hypothesis·for·stochastic·equality·is·p·=·0.5,·which·corresponds·to·the·Brunner-Munzel·test.</p>
70 <p>This·notebook·provides·a·brief·overview·of·the·statistics·provided·in·statsmodels.</p>70 <p>This·notebook·provides·a·brief·overview·of·the·statistics·provided·in·statsmodels.</p>
71 <div·class="nbinput·nblast·docutils·container">71 <div·class="nbinput·nblast·docutils·container">
72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
  
76 <span·class="kn">from</span>·<span·class="nn">statsmodels.stats.nonparametric</span>·<span·class="kn">import</span>·<span·class="p">(</span>76 <span·class="kn">from</span>·<span·class="nn">statsmodels.stats.nonparametric</span>·<span·class="kn">import</span>·<span·class="p">(</span>
77 ····<span·class="n">rank_compare_2indep</span><span·class="p">,</span>·<span·class="n">rank_compare_2ordinal</span><span·class="p">,</span>·<span·class="n">prob_larger_continuous</span><span·class="p">,</span>77 ····<span·class="n">rank_compare_2indep</span><span·class="p">,</span>·<span·class="n">rank_compare_2ordinal</span><span·class="p">,</span>·<span·class="n">prob_larger_continuous</span><span·class="p">,</span>
78 ····<span·class="n">cohensd2problarger</span><span·class="p">)</span>78 ····<span·class="n">cohensd2problarger</span><span·class="p">)</span>
79 </pre></div>79 </pre></div>
80 </div>80 </div>
81 </div>81 </div>
82 <section·id="Example">82 <section·id="Example">
83 <h2>Example<a·class="headerlink"·href="#Example"·title="Link·to·this·heading">¶</a></h2>83 <h2>Example<a·class="headerlink"·href="#Example"·title="Link·to·this·heading">¶</a></h2>
84 <p>The·main·function·is·<code·class="docutils·literal·notranslate"><span·class="pre">rank_compare_2indep</span></code>·which·computes·the·Brunner-Munzel·test·and·returns·a·<code·class="docutils·literal·notranslate"><span·class="pre">RankCompareResult</span></code>·instance·with·additional·methods.</p>84 <p>The·main·function·is·<code·class="docutils·literal·notranslate"><span·class="pre">rank_compare_2indep</span></code>·which·computes·the·Brunner-Munzel·test·and·returns·a·<code·class="docutils·literal·notranslate"><span·class="pre">RankCompareResult</span></code>·instance·with·additional·methods.</p>
85 <p>The·data·for·the·example·are·taken·from·Munzel·and·Hauschke·2003·and·is·given·in·frequency·counts.·We·need·to·expand·it·to·arrays·of·observations·to·be·able·to·use·it·with·<code·class="docutils·literal·notranslate"><span·class="pre">rank_compare_2indep</span></code>.·See·below·for·a·function·that·directly·takes·frequency·counts.·The·labels·or·levels·are·treated·as·ordinal,·the·specific·values·are·irrelevant·as·long·as·they·define·an·order·(<code·class="docutils·literal·notranslate"><span·class="pre">&gt;</span></code>,·<code·class="docutils·literal·notranslate"><span·class="pre">=</span></code>).</p>85 <p>The·data·for·the·example·are·taken·from·Munzel·and·Hauschke·2003·and·is·given·in·frequency·counts.·We·need·to·expand·it·to·arrays·of·observations·to·be·able·to·use·it·with·<code·class="docutils·literal·notranslate"><span·class="pre">rank_compare_2indep</span></code>.·See·below·for·a·function·that·directly·takes·frequency·counts.·The·labels·or·levels·are·treated·as·ordinal,·the·specific·values·are·irrelevant·as·long·as·they·define·an·order·(<code·class="docutils·literal·notranslate"><span·class="pre">&gt;</span></code>,·<code·class="docutils·literal·notranslate"><span·class="pre">=</span></code>).</p>
86 <div·class="nbinput·docutils·container">86 <div·class="nbinput·nblast·docutils·container">
87 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:87 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
88 </pre></div>88 </pre></div>
89 </div>89 </div>
90 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">levels</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="o">-</span><span·class="mi">2</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">2</span><span·class="p">]</span>90 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">levels</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="o">-</span><span·class="mi">2</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">1</span><span·class="p">,</span>·<span·class="mi">2</span><span·class="p">]</span>
91 <span·class="n">new</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mi">24</span><span·class="p">,</span>·<span·class="mi">37</span><span·class="p">,</span>·<span·class="mi">21</span><span·class="p">,</span>·<span·class="mi">19</span><span·class="p">,</span>·<span·class="mi">6</span><span·class="p">]</span>91 <span·class="n">new</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mi">24</span><span·class="p">,</span>·<span·class="mi">37</span><span·class="p">,</span>·<span·class="mi">21</span><span·class="p">,</span>·<span·class="mi">19</span><span·class="p">,</span>·<span·class="mi">6</span><span·class="p">]</span>
92 <span·class="n">active</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mi">11</span><span·class="p">,</span>·<span·class="mi">51</span><span·class="p">,</span>·<span·class="mi">22</span><span·class="p">,</span>·<span·class="mi">21</span><span·class="p">,</span>·<span·class="mi">7</span><span·class="p">]</span>92 <span·class="n">active</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mi">11</span><span·class="p">,</span>·<span·class="mi">51</span><span·class="p">,</span>·<span·class="mi">22</span><span·class="p">,</span>·<span·class="mi">21</span><span·class="p">,</span>·<span·class="mi">7</span><span·class="p">]</span>
  
93 <span·class="n">x1</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">repeat</span><span·class="p">(</span><span·class="n">levels</span><span·class="p">,</span>·<span·class="n">new</span><span·class="p">)</span>93 <span·class="n">x1</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">repeat</span><span·class="p">(</span><span·class="n">levels</span><span·class="p">,</span>·<span·class="n">new</span><span·class="p">)</span>
94 <span·class="n">x2</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">repeat</span><span·class="p">(</span><span·class="n">levels</span><span·class="p">,</span>·<span·class="n">active</span><span·class="p">)</span>94 <span·class="n">x2</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">repeat</span><span·class="p">(</span><span·class="n">levels</span><span·class="p">,</span>·<span·class="n">active</span><span·class="p">)</span>
95 <span·class="n">np</span><span·class="o">.</span><span·class="n">bincount</span><span·class="p">(</span><span·class="n">x1</span>·<span·class="o">+</span>·<span·class="mi">2</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">bincount</span><span·class="p">(</span><span·class="n">x2</span>·<span·class="o">+</span>·<span·class="mi">2</span><span·class="p">)</span>95 <span·class="n">np</span><span·class="o">.</span><span·class="n">bincount</span><span·class="p">(</span><span·class="n">x1</span>·<span·class="o">+</span>·<span·class="mi">2</span><span·class="p">),</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">bincount</span><span·class="p">(</span><span·class="n">x2</span>·<span·class="o">+</span>·<span·class="mi">2</span><span·class="p">)</span>
96 </pre></div>96 </pre></div>
97 </div>97 </div>
98 </div>98 </div>
99 <div·class="nboutput·nblast·docutils·container">99 <div·class="nbinput·nblast·docutils·container">
100 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:100 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
101 </pre></div> 
102 </div> 
103 <div·class="output_area·docutils·container"> 
104 <div·class="highlight"><pre> 
105 (array([24,·37,·21,·19,··6]),·array([11,·51,·22,·21,··7])) 
106 </pre></div></div> 
107 </div> 
108 <div·class="nbinput·docutils·container"> 
109 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]: 
110 </pre></div>101 </pre></div>
111 </div>102 </div>
112 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">rank_compare_2indep</span><span·class="p">(</span><span·class="n">x1</span><span·class="p">,</span>·<span·class="n">x2</span><span·class="p">)</span>·<span·class="c1">#,·use_t=False)</span>103 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">rank_compare_2indep</span><span·class="p">(</span><span·class="n">x1</span><span·class="p">,</span>·<span·class="n">x2</span><span·class="p">)</span>·<span·class="c1">#,·use_t=False)</span>
113 <span·class="n">res</span>104 <span·class="n">res</span>
114 </pre></div>105 </pre></div>
115 </div>106 </div>
116 </div>107 </div>
117 <div·class="nboutput·nblast·docutils·container"> 
118 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]: 
119 </pre></div> 
120 </div> 
121 <div·class="output_area·docutils·container"> 
122 <div·class="highlight"><pre> 
123 &lt;class·&#39;statsmodels.stats.nonparametric.RankCompareResult&#39;&gt; 
124 statistic·=·np.float64(-1.1757561456581607) 
125 pvalue·=·np.float64(0.24106066495471642) 
126 s1·=·np.float64(1164.3327014635863) 
127 s2·=·np.float64(701.9050836550837) 
128 var1·=·np.float64(0.09281989010392111) 
129 var2·=·np.float64(0.06130710836361985) 
130 var·=·np.float64(0.3098544504968025) 
131 var_prob·=·np.float64(0.0014148605045516095) 
132 nobs1·=·107 
133 nobs2·=·112 
134 nobs·=·219 
135 mean1·=·np.float64(105.04672897196262) 
136 mean2·=·np.float64(114.73214285714286) 
137 prob1·=·np.float64(0.4557743658210948) 
138 prob2·=·np.float64(0.5442256341789052) 
139 somersd1·=·np.float64(-0.08845126835781036) 
140 somersd2·=·np.float64(0.08845126835781048) 
141 df·=·np.float64(204.29842398679557) 
142 use_t·=·True 
143 tuple·=·(np.float64(-1.1757561456581607),·np.float64(0.24106066495471642)) 
144 </pre></div></div> 
145 </div> 
146 <p>The·methods·of·the·results·instance·are</p>108 <p>The·methods·of·the·results·instance·are</p>
147 <div·class="nbinput·docutils·container">109 <div·class="nbinput·nblast·docutils·container">
148 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:110 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
149 </pre></div>111 </pre></div>
150 </div>112 </div>
151 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="p">[</span><span·class="n">i</span>·<span·class="k">for</span>·<span·class="n">i</span>·<span·class="ow">in</span>·<span·class="nb">dir</span><span·class="p">(</span><span·class="n">res</span><span·class="p">)</span>·<span·class="k">if</span>·<span·class="ow">not</span>·<span·class="n">i</span><span·class="o">.</span><span·class="n">startswith</span><span·class="p">(</span><span·class="s2">&quot;_&quot;</span><span·class="p">)</span>·<span·class="ow">and</span>·<span·class="nb">callable</span><span·class="p">(</span><span·class="nb">getattr</span><span·class="p">(</span><span·class="n">res</span><span·class="p">,</span>·<span·class="n">i</span><span·class="p">))]</span>113 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="p">[</span><span·class="n">i</span>·<span·class="k">for</span>·<span·class="n">i</span>·<span·class="ow">in</span>·<span·class="nb">dir</span><span·class="p">(</span><span·class="n">res</span><span·class="p">)</span>·<span·class="k">if</span>·<span·class="ow">not</span>·<span·class="n">i</span><span·class="o">.</span><span·class="n">startswith</span><span·class="p">(</span><span·class="s2">&quot;_&quot;</span><span·class="p">)</span>·<span·class="ow">and</span>·<span·class="nb">callable</span><span·class="p">(</span><span·class="nb">getattr</span><span·class="p">(</span><span·class="n">res</span><span·class="p">,</span>·<span·class="n">i</span><span·class="p">))]</span>
152 </pre></div>114 </pre></div>
153 </div>115 </div>
154 </div>116 </div>
155 <div·class="nboutput·nblast·docutils·container">117 <div·class="nbinput·nblast·docutils·container">
156 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:118 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
157 </pre></div> 
158 </div> 
159 <div·class="output_area·docutils·container"> 
160 <div·class="highlight"><pre> 
161 [&#39;conf_int&#39;, 
162 ·&#39;confint_lintransf&#39;, 
163 ·&#39;effectsize_normal&#39;, 
164 ·&#39;summary&#39;, 
165 ·&#39;test_prob_superior&#39;, 
166 ·&#39;tost_prob_superior&#39;] 
167 </pre></div></div> 
168 </div> 
169 <div·class="nbinput·docutils·container"> 
170 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]: 
171 </pre></div>119 </pre></div>
172 </div>120 </div>
173 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>··<span·class="c1">#·returns·SimpleTable</span>121 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">res</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>··<span·class="c1">#·returns·SimpleTable</span>
174 </pre></div>122 </pre></div>
175 </div>123 </div>
176 </div>124 </div>
177 <div·class="nboutput·nblast·docutils·container">125 <div·class="nbinput·nblast·docutils·container">
178 <div·class="prompt·empty·docutils·container"> 
179 </div> 
180 <div·class="output_area·docutils·container"> 
181 <div·class="highlight"><pre> 
182 ··················Probability·sample·1·is·stochastically·larger 
183 ================================================================================== 
184 ·····················coef····std·err··········t······P&gt;|t|······[0.025······0.975] 
185 ---------------------------------------------------------------------------------- 
186 prob(x1&gt;x2)·c0·····0.4558······0.038·····-1.176······0.241·······0.382·······0.530 
187 ================================================================================== 
188 </pre></div></div> 
189 </div> 
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18 test·and·Brunner-Munzel·test.·Inference·is·based·on·the·asymptotic·distribution18 test·and·Brunner-Munzel·test.·Inference·is·based·on·the·asymptotic·distribution
19 of·the·Brunner-Munzel·test.·The·half·probability·for·ties·corresponds·to·the19 of·the·Brunner-Munzel·test.·The·half·probability·for·ties·corresponds·to·the
20 use·of·midranks·and·makes·it·valid·for·discrete·variables.20 use·of·midranks·and·makes·it·valid·for·discrete·variables.
21 The·Null·hypothesis·for·stochastic·equality·is·p·=·0.5,·which·corresponds·to21 The·Null·hypothesis·for·stochastic·equality·is·p·=·0.5,·which·corresponds·to
22 the·Brunner-Munzel·test.22 the·Brunner-Munzel·test.
23 This·notebook·provides·a·brief·overview·of·the·statistics·provided·in23 This·notebook·provides·a·brief·overview·of·the·statistics·provided·in
24 statsmodels.24 statsmodels.
25 [1]:25 [·]:
26 import·numpy·as·np26 import·numpy·as·np
  
27 from·statsmodels.stats.nonparametric·import·(27 from·statsmodels.stats.nonparametric·import·(
28 ····rank_compare_2indep,·rank_compare_2ordinal,·prob_larger_continuous,28 ····rank_compare_2indep,·rank_compare_2ordinal,·prob_larger_continuous,
29 ····cohensd2problarger)29 ····cohensd2problarger)
30 *\x8**\x8**\x8**\x8**\x8*·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*30 *\x8**\x8**\x8**\x8**\x8*·E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
31 The·main·function·is·rank_compare_2indep·which·computes·the·Brunner-Munzel·test31 The·main·function·is·rank_compare_2indep·which·computes·the·Brunner-Munzel·test
32 and·returns·a·RankCompareResult·instance·with·additional·methods.32 and·returns·a·RankCompareResult·instance·with·additional·methods.
33 The·data·for·the·example·are·taken·from·Munzel·and·Hauschke·2003·and·is·given33 The·data·for·the·example·are·taken·from·Munzel·and·Hauschke·2003·and·is·given
34 in·frequency·counts.·We·need·to·expand·it·to·arrays·of·observations·to·be·able34 in·frequency·counts.·We·need·to·expand·it·to·arrays·of·observations·to·be·able
35 to·use·it·with·rank_compare_2indep.·See·below·for·a·function·that·directly35 to·use·it·with·rank_compare_2indep.·See·below·for·a·function·that·directly
36 takes·frequency·counts.·The·labels·or·levels·are·treated·as·ordinal,·the36 takes·frequency·counts.·The·labels·or·levels·are·treated·as·ordinal,·the
37 specific·values·are·irrelevant·as·long·as·they·define·an·order·(>,·=).37 specific·values·are·irrelevant·as·long·as·they·define·an·order·(>,·=).
38 [2]:38 [·]:
39 levels·=·[-2,·-1,·0,·1,·2]39 levels·=·[-2,·-1,·0,·1,·2]
40 new·=·[24,·37,·21,·19,·6]40 new·=·[24,·37,·21,·19,·6]
41 active·=·[11,·51,·22,·21,·7]41 active·=·[11,·51,·22,·21,·7]
  
42 x1·=·np.repeat(levels,·new)42 x1·=·np.repeat(levels,·new)
43 x2·=·np.repeat(levels,·active)43 x2·=·np.repeat(levels,·active)
44 np.bincount(x1·+·2),·np.bincount(x2·+·2)44 np.bincount(x1·+·2),·np.bincount(x2·+·2)
45 [2]:45 [·]:
46 (array([24,·37,·21,·19,··6]),·array([11,·51,·22,·21,··7])) 
47 [3]: 
48 res·=·rank_compare_2indep(x1,·x2)·#,·use_t=False)46 res·=·rank_compare_2indep(x1,·x2)·#,·use_t=False)
49 res47 res
50 [3]: 
51 <class·'statsmodels.stats.nonparametric.RankCompareResult'> 
52 statistic·=·np.float64(-1.1757561456581607) 
53 pvalue·=·np.float64(0.24106066495471642) 
54 s1·=·np.float64(1164.3327014635863) 
55 s2·=·np.float64(701.9050836550837) 
56 var1·=·np.float64(0.09281989010392111) 
57 var2·=·np.float64(0.06130710836361985) 
58 var·=·np.float64(0.3098544504968025) 
59 var_prob·=·np.float64(0.0014148605045516095) 
60 nobs1·=·107 
61 nobs2·=·112 
62 nobs·=·219 
63 mean1·=·np.float64(105.04672897196262) 
64 mean2·=·np.float64(114.73214285714286) 
65 prob1·=·np.float64(0.4557743658210948) 
66 prob2·=·np.float64(0.5442256341789052) 
67 somersd1·=·np.float64(-0.08845126835781036) 
68 somersd2·=·np.float64(0.08845126835781048) 
69 df·=·np.float64(204.29842398679557) 
70 use_t·=·True 
71 tuple·=·(np.float64(-1.1757561456581607),·np.float64(0.24106066495471642)) 
72 The·methods·of·the·results·instance·are48 The·methods·of·the·results·instance·are
73 [4]:49 [·]:
74 [i·for·i·in·dir(res)·if·not·i.startswith("_")·and·callable(getattr(res,·i))]50 [i·for·i·in·dir(res)·if·not·i.startswith("_")·and·callable(getattr(res,·i))]
75 [4]:51 [·]:
76 ['conf_int', 
77 ·'confint_lintransf', 
78 ·'effectsize_normal', 
79 ·'summary', 
80 ·'test_prob_superior', 
81 ·'tost_prob_superior'] 
82 [5]: 
83 print(res.summary())··#·returns·SimpleTable52 print(res.summary())··#·returns·SimpleTable
84 ··················Probability·sample·1·is·stochastically·larger 
85 ================================================================================== 
86 ·····················coef····std·err··········t······P>|t|······[0.025 
87 0.975] 
88 ------------------------------------------------------------------------------- 
89 --- 
90 prob(x1>x2)·c0·····0.4558······0.038·····-1.176······0.241·······0.382 
91 0.530 
92 ================================================================================== 
93 [6]:53 [·]:
94 ci·=·res.conf_int()54 ci·=·res.conf_int()
95 ci55 ci
96 [6]:56 [·]:
97 (np.float64(0.3816117144128266),·np.float64(0.529937017229363)) 
98 [7]: 
99 res.test_prob_superior()57 res.test_prob_superior()
100 [7]: 
101 <class·'statsmodels.stats.base.HolderTuple'> 
102 statistic·=·np.float64(-1.1757561456581602) 
103 pvalue·=·np.float64(0.24106066495471665) 
104 df·=·np.float64(204.29842398679557) 
105 distribution·=·'t' 
106 tuple·=·(np.float64(-1.1757561456581602),·np.float64(0.24106066495471665)) 
107 [·]:58 [·]:
108 *\x8**\x8**\x8**\x8**\x8*·O\x8On\x8ne\x8e-\x8-s\x8si\x8id\x8de\x8ed\x8d·t\x8te\x8es\x8st\x8ts\x8s,\x8,·s\x8su\x8up\x8pe\x8er\x8ri\x8io\x8or\x8ri\x8it\x8ty\x8y·a\x8an\x8nd\x8d·n\x8no\x8on\x8ni\x8in\x8nf\x8fe\x8er\x8ri\x8io\x8or\x8ri\x8it\x8ty\x8y·t\x8te\x8es\x8st\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*59 *\x8**\x8**\x8**\x8**\x8*·O\x8On\x8ne\x8e-\x8-s\x8si\x8id\x8de\x8ed\x8d·t\x8te\x8es\x8st\x8ts\x8s,\x8,·s\x8su\x8up\x8pe\x8er\x8ri\x8io\x8or\x8ri\x8it\x8ty\x8y·a\x8an\x8nd\x8d·n\x8no\x8on\x8ni\x8in\x8nf\x8fe\x8er\x8ri\x8io\x8or\x8ri\x8it\x8ty\x8y·t\x8te\x8es\x8st\x8ts\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
109 The·hypothesis·tests·functions·have·a·alternative·keyword·to·specify·one-sided60 The·hypothesis·tests·functions·have·a·alternative·keyword·to·specify·one-sided
110 tests·and·a·value·keyword·to·specify·nonzero·or·nonequality·hypothesis.·Both61 tests·and·a·value·keyword·to·specify·nonzero·or·nonequality·hypothesis.·Both
111 keywords·together·can·be·used·for·noninferiority·tests·or·superiority·tests62 keywords·together·can·be·used·for·noninferiority·tests·or·superiority·tests
112 with·a·margin.63 with·a·margin.
113 A·noninferiority·test·specifies·a·margin·and·alternative·so·we·can·test·the64 A·noninferiority·test·specifies·a·margin·and·alternative·so·we·can·test·the
Offset 175, 37 lines modifiedOffset 126, 23 lines modified
175 better.126 better.
176 E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·n\x8no\x8on\x8ni\x8in\x8nf\x8fe\x8er\x8ri\x8io\x8or\x8ri\x8it\x8ty\x8y·s\x8sm\x8ma\x8al\x8ll\x8le\x8er\x8r·i\x8is\x8s·b\x8be\x8et\x8tt\x8te\x8er\x8r127 E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·n\x8no\x8on\x8ni\x8in\x8nf\x8fe\x8er\x8ri\x8io\x8or\x8ri\x8it\x8ty\x8y·s\x8sm\x8ma\x8al\x8ll\x8le\x8er\x8r·i\x8is\x8s·b\x8be\x8et\x8tt\x8te\x8er\x8r
177 Suppose·our·noninferiority·threshold·is·p0·=·0.55.·The·one-sided·test·with128 Suppose·our·noninferiority·threshold·is·p0·=·0.55.·The·one-sided·test·with
178 alternative·“smaller”·has·a·pvalue·around·0.0065·and·we·reject·the·null129 alternative·“smaller”·has·a·pvalue·around·0.0065·and·we·reject·the·null
179 hypothesis·at·an·alpha·of·0.05.·The·data·provides·evidence·that·the·treatment130 hypothesis·at·an·alpha·of·0.05.·The·data·provides·evidence·that·the·treatment
180 (sample·1)·is·noninferior·to·the·control·(sample2),·that·is·we·have·evidence131 (sample·1)·is·noninferior·to·the·control·(sample2),·that·is·we·have·evidence
181 that·the·treatment·is·at·most·5·percentage·points·worse·than·the·control.132 that·the·treatment·is·at·most·5·percentage·points·worse·than·the·control.
182 [8]:133 [·]:
183 res.test_prob_superior(value=0.55,·alternative="smaller")134 res.test_prob_superior(value=0.55,·alternative="smaller")
184 [8]: 
185 <class·'statsmodels.stats.base.HolderTuple'> 
186 statistic·=·np.float64(-2.505026112598482) 
187 pvalue·=·np.float64(0.006512753894336686) 
188 df·=·np.float64(204.29842398679557) 
189 distribution·=·'t' 
190 tuple·=·(np.float64(-2.505026112598482),·np.float64(0.006512753894336686)) 
191 E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·n\x8no\x8on\x8ni\x8in\x8nf\x8fe\x8er\x8ri\x8io\x8or\x8ri\x8it\x8ty\x8y·l\x8la\x8ar\x8rg\x8ge\x8er\x8r·i\x8is\x8s·b\x8be\x8et\x8tt\x8te\x8er\x8r135 E\x8Ex\x8xa\x8am\x8mp\x8pl\x8le\x8e:\x8:·n\x8no\x8on\x8ni\x8in\x8nf\x8fe\x8er\x8ri\x8io\x8or\x8ri\x8it\x8ty\x8y·l\x8la\x8ar\x8rg\x8ge\x8er\x8r·i\x8is\x8s·b\x8be\x8et\x8tt\x8te\x8er\x8r
192 Now·consider·the·case·when·having·larger·values·is·better·and·the136 Now·consider·the·case·when·having·larger·values·is·better·and·the
193 noninferiority·threshold·is·0.45.·The·one-sided·test·has·a·p-value·of·0.44·and137 noninferiority·threshold·is·0.45.·The·one-sided·test·has·a·p-value·of·0.44·and
194 we·cannot·reject·the·null·hypothesis.·Therefore,·we·do·not·have·evidence·for138 we·cannot·reject·the·null·hypothesis.·Therefore,·we·do·not·have·evidence·for
195 the·treatment·to·be·at·most·5·percentage·points·worse·than·the·control.139 the·treatment·to·be·at·most·5·percentage·points·worse·than·the·control.
196 [9]:140 [·]:
197 res.test_prob_superior(value=0.45,·alternative="larger")141 res.test_prob_superior(value=0.45,·alternative="larger")
198 [9]: 
199 <class·'statsmodels.stats.base.HolderTuple'> 
200 statistic·=·np.float64(0.15351382128216023) 
201 pvalue·=·np.float64(0.43907230923278956) 
202 df·=·np.float64(204.29842398679557) 
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Offset 66, 41 lines modifiedOffset 66, 41 lines modified
66 <ul·class="simple">66 <ul·class="simple">
67 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">season</span></code>·-·The·length·of·the·seasonal·smoother.·Must·be·odd.</p></li>67 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">season</span></code>·-·The·length·of·the·seasonal·smoother.·Must·be·odd.</p></li>
68 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">trend</span></code>·-·The·length·of·the·trend·smoother,·usually·around·150%·of·<code·class="docutils·literal·notranslate"><span·class="pre">season</span></code>.·Must·be·odd·and·larger·than·<code·class="docutils·literal·notranslate"><span·class="pre">season</span></code>.</p></li>68 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">trend</span></code>·-·The·length·of·the·trend·smoother,·usually·around·150%·of·<code·class="docutils·literal·notranslate"><span·class="pre">season</span></code>.·Must·be·odd·and·larger·than·<code·class="docutils·literal·notranslate"><span·class="pre">season</span></code>.</p></li>
69 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">low_pass</span></code>·-·The·length·of·the·low-pass·estimation·window,·usually·the·smallest·odd·number·larger·than·the·periodicity·of·the·data.</p></li>69 <li><p><code·class="docutils·literal·notranslate"><span·class="pre">low_pass</span></code>·-·The·length·of·the·low-pass·estimation·window,·usually·the·smallest·odd·number·larger·than·the·periodicity·of·the·data.</p></li>
70 </ul>70 </ul>
71 <p>First·we·import·the·required·packages,·prepare·the·graphics·environment,·and·prepare·the·data.</p>71 <p>First·we·import·the·required·packages,·prepare·the·graphics·environment,·and·prepare·the·data.</p>
72 <div·class="nbinput·nblast·docutils·container">72 <div·class="nbinput·nblast·docutils·container">
73 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:73 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
74 </pre></div>74 </pre></div>
75 </div>75 </div>
76 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>76 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
77 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>77 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
78 <span·class="kn">import</span>·<span·class="nn">seaborn</span>·<span·class="k">as</span>·<span·class="nn">sns</span>78 <span·class="kn">import</span>·<span·class="nn">seaborn</span>·<span·class="k">as</span>·<span·class="nn">sns</span>
79 <span·class="kn">from</span>·<span·class="nn">pandas.plotting</span>·<span·class="kn">import</span>·<span·class="n">register_matplotlib_converters</span>79 <span·class="kn">from</span>·<span·class="nn">pandas.plotting</span>·<span·class="kn">import</span>·<span·class="n">register_matplotlib_converters</span>
  
80 <span·class="n">register_matplotlib_converters</span><span·class="p">()</span>80 <span·class="n">register_matplotlib_converters</span><span·class="p">()</span>
81 <span·class="n">sns</span><span·class="o">.</span><span·class="n">set_style</span><span·class="p">(</span><span·class="s2">&quot;darkgrid&quot;</span><span·class="p">)</span>81 <span·class="n">sns</span><span·class="o">.</span><span·class="n">set_style</span><span·class="p">(</span><span·class="s2">&quot;darkgrid&quot;</span><span·class="p">)</span>
82 </pre></div>82 </pre></div>
83 </div>83 </div>
84 </div>84 </div>
85 <div·class="nbinput·nblast·docutils·container">85 <div·class="nbinput·nblast·docutils·container">
86 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:86 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
87 </pre></div>87 </pre></div>
88 </div>88 </div>
89 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;figure&quot;</span><span·class="p">,</span>·<span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">16</span><span·class="p">,</span>·<span·class="mi">12</span><span·class="p">))</span>89 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;figure&quot;</span><span·class="p">,</span>·<span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">16</span><span·class="p">,</span>·<span·class="mi">12</span><span·class="p">))</span>
90 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;font&quot;</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">13</span><span·class="p">)</span>90 <span·class="n">plt</span><span·class="o">.</span><span·class="n">rc</span><span·class="p">(</span><span·class="s2">&quot;font&quot;</span><span·class="p">,</span>·<span·class="n">size</span><span·class="o">=</span><span·class="mi">13</span><span·class="p">)</span>
91 </pre></div>91 </pre></div>
92 </div>92 </div>
93 </div>93 </div>
94 <section·id="Atmospheric-CO2">94 <section·id="Atmospheric-CO2">
95 <h2>Atmospheric·CO2<a·class="headerlink"·href="#Atmospheric-CO2"·title="Link·to·this·heading">¶</a></h2>95 <h2>Atmospheric·CO2<a·class="headerlink"·href="#Atmospheric-CO2"·title="Link·to·this·heading">¶</a></h2>
96 <p>The·example·in·Cleveland,·Cleveland,·McRae,·and·Terpenning·(1990)·uses·CO2·data,·which·is·in·the·list·below.·This·monthly·data·(January·1959·to·December·1987)·has·a·clear·trend·and·seasonality·across·the·sample.</p>96 <p>The·example·in·Cleveland,·Cleveland,·McRae,·and·Terpenning·(1990)·uses·CO2·data,·which·is·in·the·list·below.·This·monthly·data·(January·1959·to·December·1987)·has·a·clear·trend·and·seasonality·across·the·sample.</p>
97 <div·class="nbinput·docutils·container">97 <div·class="nbinput·nblast·docutils·container">
98 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:98 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
99 </pre></div>99 </pre></div>
100 </div>100 </div>
101 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">co2</span>·<span·class="o">=</span>·<span·class="p">[</span>101 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">co2</span>·<span·class="o">=</span>·<span·class="p">[</span>
102 ····<span·class="mf">315.58</span><span·class="p">,</span>102 ····<span·class="mf">315.58</span><span·class="p">,</span>
103 ····<span·class="mf">316.39</span><span·class="p">,</span>103 ····<span·class="mf">316.39</span><span·class="p">,</span>
104 ····<span·class="mf">316.79</span><span·class="p">,</span>104 ····<span·class="mf">316.79</span><span·class="p">,</span>
105 ····<span·class="mf">317.82</span><span·class="p">,</span>105 ····<span·class="mf">317.82</span><span·class="p">,</span>
Offset 452, 69 lines modifiedOffset 452, 45 lines modified
452 <span·class="n">co2</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">Series</span><span·class="p">(</span>452 <span·class="n">co2</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">Series</span><span·class="p">(</span>
453 ····<span·class="n">co2</span><span·class="p">,</span>·<span·class="n">index</span><span·class="o">=</span><span·class="n">pd</span><span·class="o">.</span><span·class="n">date_range</span><span·class="p">(</span><span·class="s2">&quot;1-1-1959&quot;</span><span·class="p">,</span>·<span·class="n">periods</span><span·class="o">=</span><span·class="nb">len</span><span·class="p">(</span><span·class="n">co2</span><span·class="p">),</span>·<span·class="n">freq</span><span·class="o">=</span><span·class="s2">&quot;ME&quot;</span><span·class="p">),</span>·<span·class="n">name</span><span·class="o">=</span><span·class="s2">&quot;CO2&quot;</span>453 ····<span·class="n">co2</span><span·class="p">,</span>·<span·class="n">index</span><span·class="o">=</span><span·class="n">pd</span><span·class="o">.</span><span·class="n">date_range</span><span·class="p">(</span><span·class="s2">&quot;1-1-1959&quot;</span><span·class="p">,</span>·<span·class="n">periods</span><span·class="o">=</span><span·class="nb">len</span><span·class="p">(</span><span·class="n">co2</span><span·class="p">),</span>·<span·class="n">freq</span><span·class="o">=</span><span·class="s2">&quot;ME&quot;</span><span·class="p">),</span>·<span·class="n">name</span><span·class="o">=</span><span·class="s2">&quot;CO2&quot;</span>
454 <span·class="p">)</span>454 <span·class="p">)</span>
455 <span·class="n">co2</span><span·class="o">.</span><span·class="n">describe</span><span·class="p">()</span>455 <span·class="n">co2</span><span·class="o">.</span><span·class="n">describe</span><span·class="p">()</span>
456 </pre></div>456 </pre></div>
457 </div>457 </div>
458 </div>458 </div>
459 <div·class="nboutput·nblast·docutils·container"> 
460 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]: 
461 </pre></div> 
462 </div> 
463 <div·class="output_area·docutils·container"> 
464 <div·class="highlight"><pre> 
465 count····348.000000 
466 mean·····330.123879 
467 std·······10.059747 
468 min······313.550000 
469 25%······321.302500 
470 50%······328.820000 
471 75%······338.002500 
472 max······351.340000 
473 Name:·CO2,·dtype:·float64 
474 </pre></div></div> 
475 </div> 
476 <p>The·decomposition·requires·1·input,·the·data·series.·If·the·data·series·does·not·have·a·frequency,·then·you·must·also·specify·<code·class="docutils·literal·notranslate"><span·class="pre">period</span></code>.·The·default·value·for·<code·class="docutils·literal·notranslate"><span·class="pre">seasonal</span></code>·is·7,·and·so·should·also·be·changed·in·most·applications.</p>459 <p>The·decomposition·requires·1·input,·the·data·series.·If·the·data·series·does·not·have·a·frequency,·then·you·must·also·specify·<code·class="docutils·literal·notranslate"><span·class="pre">period</span></code>.·The·default·value·for·<code·class="docutils·literal·notranslate"><span·class="pre">seasonal</span></code>·is·7,·and·so·should·also·be·changed·in·most·applications.</p>
477 <div·class="nbinput·docutils·container">460 <div·class="nbinput·nblast·docutils·container">
478 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:461 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
479 </pre></div>462 </pre></div>
480 </div>463 </div>
481 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.seasonal</span>·<span·class="kn">import</span>·<span·class="n">STL</span>464 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.seasonal</span>·<span·class="kn">import</span>·<span·class="n">STL</span>
  
482 <span·class="n">stl</span>·<span·class="o">=</span>·<span·class="n">STL</span><span·class="p">(</span><span·class="n">co2</span><span·class="p">,</span>·<span·class="n">seasonal</span><span·class="o">=</span><span·class="mi">13</span><span·class="p">)</span>465 <span·class="n">stl</span>·<span·class="o">=</span>·<span·class="n">STL</span><span·class="p">(</span><span·class="n">co2</span><span·class="p">,</span>·<span·class="n">seasonal</span><span·class="o">=</span><span·class="mi">13</span><span·class="p">)</span>
483 <span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">stl</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>466 <span·class="n">res</span>·<span·class="o">=</span>·<span·class="n">stl</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
484 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">res</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">()</span>467 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">res</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">()</span>
485 </pre></div>468 </pre></div>
486 </div>469 </div>
487 </div>470 </div>
488 <div·class="nboutput·nblast·docutils·container"> 
489 <div·class="prompt·empty·docutils·container"> 
490 </div> 
491 <div·class="output_area·docutils·container"> 
492 <img·alt="../../../_images/examples_notebooks_generated_stl_decomposition_6_0.png"·src="../../../_images/examples_notebooks_generated_stl_decomposition_6_0.png"·/> 
493 </div> 
494 </div> 
495 </section>471 </section>
496 <section·id="Robust-Fitting">472 <section·id="Robust-Fitting">
497 <h2>Robust·Fitting<a·class="headerlink"·href="#Robust-Fitting"·title="Link·to·this·heading">¶</a></h2>473 <h2>Robust·Fitting<a·class="headerlink"·href="#Robust-Fitting"·title="Link·to·this·heading">¶</a></h2>
498 <p>Setting·<code·class="docutils·literal·notranslate"><span·class="pre">robust</span></code>·uses·a·data-dependent·weighting·function·that·re-weights·data·when·estimating·the·LOESS·(and·so·is·using·LOWESS).·Using·robust·estimation·allows·the·model·to·tolerate·larger·errors·that·are·visible·on·the·bottom·plot.</p>474 <p>Setting·<code·class="docutils·literal·notranslate"><span·class="pre">robust</span></code>·uses·a·data-dependent·weighting·function·that·re-weights·data·when·estimating·the·LOESS·(and·so·is·using·LOWESS).·Using·robust·estimation·allows·the·model·to·tolerate·larger·errors·that·are·visible·on·the·bottom·plot.</p>
499 <p>Here·we·use·a·series·the·measures·the·production·of·electrical·equipment·in·the·EU.</p>475 <p>Here·we·use·a·series·the·measures·the·production·of·electrical·equipment·in·the·EU.</p>
500 <div·class="nbinput·nblast·docutils·container">476 <div·class="nbinput·nblast·docutils·container">
501 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:477 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
502 </pre></div>478 </pre></div>
503 </div>479 </div>
504 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.datasets</span>·<span·class="kn">import</span>·<span·class="n">elec_equip</span>·<span·class="k">as</span>·<span·class="n">ds</span>480 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.datasets</span>·<span·class="kn">import</span>·<span·class="n">elec_equip</span>·<span·class="k">as</span>·<span·class="n">ds</span>
  
505 <span·class="n">elec_equip</span>·<span·class="o">=</span>·<span·class="n">ds</span><span·class="o">.</span><span·class="n">load</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span><span·class="o">.</span><span·class="n">iloc</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">]</span>481 <span·class="n">elec_equip</span>·<span·class="o">=</span>·<span·class="n">ds</span><span·class="o">.</span><span·class="n">load</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span><span·class="o">.</span><span·class="n">iloc</span><span·class="p">[:,</span>·<span·class="mi">0</span><span·class="p">]</span>
506 </pre></div>482 </pre></div>
507 </div>483 </div>
508 </div>484 </div>
509 <p>Next,·we·estimate·the·model·with·and·without·robust·weighting.·The·difference·is·minor·and·is·most·pronounced·during·the·financial·crisis·of·2008.·The·non-robust·estimate·places·equal·weights·on·all·observations·and·so·produces·smaller·errors,·on·average.·The·weights·vary·between·0·and·1.</p>485 <p>Next,·we·estimate·the·model·with·and·without·robust·weighting.·The·difference·is·minor·and·is·most·pronounced·during·the·financial·crisis·of·2008.·The·non-robust·estimate·places·equal·weights·on·all·observations·and·so·produces·smaller·errors,·on·average.·The·weights·vary·between·0·and·1.</p>
510 <div·class="nbinput·docutils·container">486 <div·class="nbinput·nblast·docutils·container">
511 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:487 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
512 </pre></div>488 </pre></div>
513 </div>489 </div>
514 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">add_stl_plot</span><span·class="p">(</span><span·class="n">fig</span><span·class="p">,</span>·<span·class="n">res</span><span·class="p">,</span>·<span·class="n">legend</span><span·class="p">):</span>490 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">add_stl_plot</span><span·class="p">(</span><span·class="n">fig</span><span·class="p">,</span>·<span·class="n">res</span><span·class="p">,</span>·<span·class="n">legend</span><span·class="p">):</span>
515 <span·class="w">····</span><span·class="sd">&quot;&quot;&quot;Add·3·plots·from·a·second·STL·fit&quot;&quot;&quot;</span>491 <span·class="w">····</span><span·class="sd">&quot;&quot;&quot;Add·3·plots·from·a·second·STL·fit&quot;&quot;&quot;</span>
516 ····<span·class="n">axs</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">get_axes</span><span·class="p">()</span>492 ····<span·class="n">axs</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">get_axes</span><span·class="p">()</span>
517 ····<span·class="n">comps</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;trend&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;seasonal&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;resid&quot;</span><span·class="p">]</span>493 ····<span·class="n">comps</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;trend&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;seasonal&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;resid&quot;</span><span·class="p">]</span>
518 ····<span·class="k">for</span>·<span·class="n">ax</span><span·class="p">,</span>·<span·class="n">comp</span>·<span·class="ow">in</span>·<span·class="nb">zip</span><span·class="p">(</span><span·class="n">axs</span><span·class="p">[</span><span·class="mi">1</span><span·class="p">:],</span>·<span·class="n">comps</span><span·class="p">):</span>494 ····<span·class="k">for</span>·<span·class="n">ax</span><span·class="p">,</span>·<span·class="n">comp</span>·<span·class="ow">in</span>·<span·class="nb">zip</span><span·class="p">(</span><span·class="n">axs</span><span·class="p">[</span><span·class="mi">1</span><span·class="p">:],</span>·<span·class="n">comps</span><span·class="p">):</span>
Offset 531, 76 lines modifiedOffset 507, 55 lines modified
531 <span·class="n">res_robust</span>·<span·class="o">=</span>·<span·class="n">stl</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>507 <span·class="n">res_robust</span>·<span·class="o">=</span>·<span·class="n">stl</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
532 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">res_robust</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">()</span>508 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">res_robust</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">()</span>
533 <span·class="n">res_non_robust</span>·<span·class="o">=</span>·<span·class="n">STL</span><span·class="p">(</span><span·class="n">elec_equip</span><span·class="p">,</span>·<span·class="n">period</span><span·class="o">=</span><span·class="mi">12</span><span·class="p">,</span>·<span·class="n">robust</span><span·class="o">=</span><span·class="kc">False</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>509 <span·class="n">res_non_robust</span>·<span·class="o">=</span>·<span·class="n">STL</span><span·class="p">(</span><span·class="n">elec_equip</span><span·class="p">,</span>·<span·class="n">period</span><span·class="o">=</span><span·class="mi">12</span><span·class="p">,</span>·<span·class="n">robust</span><span·class="o">=</span><span·class="kc">False</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
534 <span·class="n">add_stl_plot</span><span·class="p">(</span><span·class="n">fig</span><span·class="p">,</span>·<span·class="n">res_non_robust</span><span·class="p">,</span>·<span·class="p">[</span><span·class="s2">&quot;Robust&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Non-robust&quot;</span><span·class="p">])</span>510 <span·class="n">add_stl_plot</span><span·class="p">(</span><span·class="n">fig</span><span·class="p">,</span>·<span·class="n">res_non_robust</span><span·class="p">,</span>·<span·class="p">[</span><span·class="s2">&quot;Robust&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;Non-robust&quot;</span><span·class="p">])</span>
535 </pre></div>511 </pre></div>
536 </div>512 </div>
537 </div>513 </div>
538 <div·class="nboutput·nblast·docutils·container">514 <div·class="nbinput·nblast·docutils·container">
539 <div·class="prompt·empty·docutils·container"> 
540 </div> 
541 <div·class="output_area·docutils·container"> 
542 <img·alt="../../../_images/examples_notebooks_generated_stl_decomposition_10_0.png"·src="../../../_images/examples_notebooks_generated_stl_decomposition_10_0.png"·/> 
543 </div> 
544 </div> 
545 <div·class="nbinput·docutils·container"> 
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14 ····*·season·-·The·length·of·the·seasonal·smoother.·Must·be·odd.14 ····*·season·-·The·length·of·the·seasonal·smoother.·Must·be·odd.
15 ····*·trend·-·The·length·of·the·trend·smoother,·usually·around·150%·of·season.15 ····*·trend·-·The·length·of·the·trend·smoother,·usually·around·150%·of·season.
16 ······Must·be·odd·and·larger·than·season.16 ······Must·be·odd·and·larger·than·season.
17 ····*·low_pass·-·The·length·of·the·low-pass·estimation·window,·usually·the17 ····*·low_pass·-·The·length·of·the·low-pass·estimation·window,·usually·the
18 ······smallest·odd·number·larger·than·the·periodicity·of·the·data.18 ······smallest·odd·number·larger·than·the·periodicity·of·the·data.
19 First·we·import·the·required·packages,·prepare·the·graphics·environment,·and19 First·we·import·the·required·packages,·prepare·the·graphics·environment,·and
20 prepare·the·data.20 prepare·the·data.
21 [1]:21 [·]:
22 import·matplotlib.pyplot·as·plt22 import·matplotlib.pyplot·as·plt
23 import·pandas·as·pd23 import·pandas·as·pd
24 import·seaborn·as·sns24 import·seaborn·as·sns
25 from·pandas.plotting·import·register_matplotlib_converters25 from·pandas.plotting·import·register_matplotlib_converters
  
26 register_matplotlib_converters()26 register_matplotlib_converters()
27 sns.set_style("darkgrid")27 sns.set_style("darkgrid")
28 [2]:28 [·]:
29 plt.rc("figure",·figsize=(16,·12))29 plt.rc("figure",·figsize=(16,·12))
30 plt.rc("font",·size=13)30 plt.rc("font",·size=13)
31 *\x8**\x8**\x8**\x8**\x8*·A\x8At\x8tm\x8mo\x8os\x8sp\x8ph\x8he\x8er\x8ri\x8ic\x8c·C\x8CO\x8O2\x82_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*31 *\x8**\x8**\x8**\x8**\x8*·A\x8At\x8tm\x8mo\x8os\x8sp\x8ph\x8he\x8er\x8ri\x8ic\x8c·C\x8CO\x8O2\x82_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
32 The·example·in·Cleveland,·Cleveland,·McRae,·and·Terpenning·(1990)·uses·CO232 The·example·in·Cleveland,·Cleveland,·McRae,·and·Terpenning·(1990)·uses·CO2
33 data,·which·is·in·the·list·below.·This·monthly·data·(January·1959·to·December33 data,·which·is·in·the·list·below.·This·monthly·data·(January·1959·to·December
34 1987)·has·a·clear·trend·and·seasonality·across·the·sample.34 1987)·has·a·clear·trend·and·seasonality·across·the·sample.
35 [3]:35 [·]:
36 co2·=·[36 co2·=·[
37 ····315.58,37 ····315.58,
38 ····316.39,38 ····316.39,
39 ····316.79,39 ····316.79,
40 ····317.82,40 ····317.82,
41 ····318.39,41 ····318.39,
42 ····318.22,42 ····318.22,
Offset 385, 49 lines modifiedOffset 385, 38 lines modified
385 ····348.67,385 ····348.67,
386 ]386 ]
387 co2·=·pd.Series(387 co2·=·pd.Series(
388 ····co2,·index=pd.date_range("1-1-1959",·periods=len(co2),·freq="ME"),388 ····co2,·index=pd.date_range("1-1-1959",·periods=len(co2),·freq="ME"),
389 name="CO2"389 name="CO2"
390 )390 )
391 co2.describe()391 co2.describe()
392 [3]: 
393 count····348.000000 
394 mean·····330.123879 
395 std·······10.059747 
396 min······313.550000 
397 25%······321.302500 
398 50%······328.820000 
399 75%······338.002500 
400 max······351.340000 
401 Name:·CO2,·dtype:·float64 
402 The·decomposition·requires·1·input,·the·data·series.·If·the·data·series·does392 The·decomposition·requires·1·input,·the·data·series.·If·the·data·series·does
403 not·have·a·frequency,·then·you·must·also·specify·period.·The·default·value·for393 not·have·a·frequency,·then·you·must·also·specify·period.·The·default·value·for
404 seasonal·is·7,·and·so·should·also·be·changed·in·most·applications.394 seasonal·is·7,·and·so·should·also·be·changed·in·most·applications.
405 [4]:395 [·]:
406 from·statsmodels.tsa.seasonal·import·STL396 from·statsmodels.tsa.seasonal·import·STL
  
407 stl·=·STL(co2,·seasonal=13)397 stl·=·STL(co2,·seasonal=13)
408 res·=·stl.fit()398 res·=·stl.fit()
409 fig·=·res.plot()399 fig·=·res.plot()
410 [../../../_images/examples_notebooks_generated_stl_decomposition_6_0.png] 
411 *\x8**\x8**\x8**\x8**\x8*·R\x8Ro\x8ob\x8bu\x8us\x8st\x8t·F\x8Fi\x8it\x8tt\x8ti\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*400 *\x8**\x8**\x8**\x8**\x8*·R\x8Ro\x8ob\x8bu\x8us\x8st\x8t·F\x8Fi\x8it\x8tt\x8ti\x8in\x8ng\x8g_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
412 Setting·robust·uses·a·data-dependent·weighting·function·that·re-weights·data401 Setting·robust·uses·a·data-dependent·weighting·function·that·re-weights·data
413 when·estimating·the·LOESS·(and·so·is·using·LOWESS).·Using·robust·estimation402 when·estimating·the·LOESS·(and·so·is·using·LOWESS).·Using·robust·estimation
414 allows·the·model·to·tolerate·larger·errors·that·are·visible·on·the·bottom·plot.403 allows·the·model·to·tolerate·larger·errors·that·are·visible·on·the·bottom·plot.
415 Here·we·use·a·series·the·measures·the·production·of·electrical·equipment·in·the404 Here·we·use·a·series·the·measures·the·production·of·electrical·equipment·in·the
416 EU.405 EU.
417 [5]:406 [·]:
418 from·statsmodels.datasets·import·elec_equip·as·ds407 from·statsmodels.datasets·import·elec_equip·as·ds
  
419 elec_equip·=·ds.load().data.iloc[:,·0]408 elec_equip·=·ds.load().data.iloc[:,·0]
420 Next,·we·estimate·the·model·with·and·without·robust·weighting.·The·difference409 Next,·we·estimate·the·model·with·and·without·robust·weighting.·The·difference
421 is·minor·and·is·most·pronounced·during·the·financial·crisis·of·2008.·The·non-410 is·minor·and·is·most·pronounced·during·the·financial·crisis·of·2008.·The·non-
422 robust·estimate·places·equal·weights·on·all·observations·and·so·produces411 robust·estimate·places·equal·weights·on·all·observations·and·so·produces
423 smaller·errors,·on·average.·The·weights·vary·between·0·and·1.412 smaller·errors,·on·average.·The·weights·vary·between·0·and·1.
424 [6]:413 [·]:
425 def·add_stl_plot(fig,·res,·legend):414 def·add_stl_plot(fig,·res,·legend):
426 ····"""Add·3·plots·from·a·second·STL·fit"""415 ····"""Add·3·plots·from·a·second·STL·fit"""
427 ····axs·=·fig.get_axes()416 ····axs·=·fig.get_axes()
428 ····comps·=·["trend",·"seasonal",·"resid"]417 ····comps·=·["trend",·"seasonal",·"resid"]
429 ····for·ax,·comp·in·zip(axs[1:],·comps):418 ····for·ax,·comp·in·zip(axs[1:],·comps):
430 ········series·=·getattr(res,·comp)419 ········series·=·getattr(res,·comp)
431 ········if·comp·==·"resid":420 ········if·comp·==·"resid":
Offset 439, 156 lines modifiedOffset 428, 107 lines modified
  
  
439 stl·=·STL(elec_equip,·period=12,·robust=True)428 stl·=·STL(elec_equip,·period=12,·robust=True)
440 res_robust·=·stl.fit()429 res_robust·=·stl.fit()
441 fig·=·res_robust.plot()430 fig·=·res_robust.plot()
442 res_non_robust·=·STL(elec_equip,·period=12,·robust=False).fit()431 res_non_robust·=·STL(elec_equip,·period=12,·robust=False).fit()
443 add_stl_plot(fig,·res_non_robust,·["Robust",·"Non-robust"])432 add_stl_plot(fig,·res_non_robust,·["Robust",·"Non-robust"])
444 [../../../_images/examples_notebooks_generated_stl_decomposition_10_0.png] 
445 [7]:433 [·]:
446 fig·=·plt.figure(figsize=(16,·5))434 fig·=·plt.figure(figsize=(16,·5))
447 lines·=·plt.plot(res_robust.weights,·marker="o",·linestyle="none")435 lines·=·plt.plot(res_robust.weights,·marker="o",·linestyle="none")
448 ax·=·plt.gca()436 ax·=·plt.gca()
449 xlim·=·ax.set_xlim(elec_equip.index[0],·elec_equip.index[-1])437 xlim·=·ax.set_xlim(elec_equip.index[0],·elec_equip.index[-1])
450 [../../../_images/examples_notebooks_generated_stl_decomposition_11_0.png] 
451 *\x8**\x8**\x8**\x8**\x8*·L\x8LO\x8OE\x8ES\x8SS\x8S·d\x8de\x8eg\x8gr\x8re\x8ee\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*438 *\x8**\x8**\x8**\x8**\x8*·L\x8LO\x8OE\x8ES\x8SS\x8S·d\x8de\x8eg\x8gr\x8re\x8ee\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
452 The·default·configuration·estimates·the·LOESS·model·with·both·a·constant·and·a439 The·default·configuration·estimates·the·LOESS·model·with·both·a·constant·and·a
453 trend.·This·can·be·changed·to·only·include·a·constant·by·setting·COMPONENT_deg440 trend.·This·can·be·changed·to·only·include·a·constant·by·setting·COMPONENT_deg
454 to·0.·Here·the·degree·makes·little·difference·except·in·the·trend·around·the441 to·0.·Here·the·degree·makes·little·difference·except·in·the·trend·around·the
455 financial·crisis·of·2008.442 financial·crisis·of·2008.
456 [8]:443 [·]:
457 stl·=·STL(444 stl·=·STL(
458 ····elec_equip,·period=12,·seasonal_deg=0,·trend_deg=0,·low_pass_deg=0,445 ····elec_equip,·period=12,·seasonal_deg=0,·trend_deg=0,·low_pass_deg=0,
459 robust=True446 robust=True
460 )447 )
461 res_deg_0·=·stl.fit()448 res_deg_0·=·stl.fit()
462 fig·=·res_robust.plot()449 fig·=·res_robust.plot()
463 add_stl_plot(fig,·res_deg_0,·["Degree·1",·"Degree·0"])450 add_stl_plot(fig,·res_deg_0,·["Degree·1",·"Degree·0"])
464 [../../../_images/examples_notebooks_generated_stl_decomposition_13_0.png] 
465 *\x8**\x8**\x8**\x8**\x8*·P\x8Pe\x8er\x8rf\x8fo\x8or\x8rm\x8ma\x8an\x8nc\x8ce\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*451 *\x8**\x8**\x8**\x8**\x8*·P\x8Pe\x8er\x8rf\x8fo\x8or\x8rm\x8ma\x8an\x8nc\x8ce\x8e_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
466 Three·options·can·be·used·to·reduce·the·computational·cost·of·the·STL452 Three·options·can·be·used·to·reduce·the·computational·cost·of·the·STL
467 decomposition:453 decomposition:
468 ····*·seasonal_jump454 ····*·seasonal_jump
469 ····*·trend_jump455 ····*·trend_jump
470 ····*·low_pass_jump456 ····*·low_pass_jump
471 When·these·are·non-zero,·the·LOESS·for·component·COMPONENT·is·only·estimated457 When·these·are·non-zero,·the·LOESS·for·component·COMPONENT·is·only·estimated
472 ever·COMPONENT_jump·observations,·and·linear·interpolation·is·used·between458 ever·COMPONENT_jump·observations,·and·linear·interpolation·is·used·between
473 points.·These·values·should·not·normally·be·more·than·10-20%·of·the·size·of459 points.·These·values·should·not·normally·be·more·than·10-20%·of·the·size·of
474 seasonal,·trend·or·low_pass,·respectively.460 seasonal,·trend·or·low_pass,·respectively.
475 The·example·below·shows·how·these·can·reduce·the·computational·cost·by·a·factor461 The·example·below·shows·how·these·can·reduce·the·computational·cost·by·a·factor
476 of·15·using·simulated·data·with·both·a·low-frequency·cosinusoidal·trend·and·a462 of·15·using·simulated·data·with·both·a·low-frequency·cosinusoidal·trend·and·a
477 sinusoidal·seasonal·pattern.463 sinusoidal·seasonal·pattern.
478 [9]:464 [·]:
479 import·numpy·as·np465 import·numpy·as·np
  
480 rs·=·np.random.RandomState(0xA4FD94BC)466 rs·=·np.random.RandomState(0xA4FD94BC)
481 tau·=·2000467 tau·=·2000
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64 <p>This·notebook·illustrates·the·basic·usage·of·the·new·treatment·effect·functionality·in·statsmodels.</p>64 <p>This·notebook·illustrates·the·basic·usage·of·the·new·treatment·effect·functionality·in·statsmodels.</p>
65 <p>The·main·class·is·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.treatment.treatment_effects.TreatmentEffect</span></code>.</p>65 <p>The·main·class·is·<code·class="docutils·literal·notranslate"><span·class="pre">statsmodels.treatment.treatment_effects.TreatmentEffect</span></code>.</p>
66 <p>This·class·estimates·treatment·effect·and·potential·outcome·using·5·different·methods,·ipw,·ra,·aipw,·aipw-wls,·ipw-ra.·The·last·three·methods·require·both·a·treatment·or·selection·model·and·an·outcome·model.·Standard·errors·and·inference·are·based·on·the·joint·GMM·representation·of·selection·or·treatment·model,·outcome·model·and·effect·functions.·The·approach·for·inference·follows·Stata,·however·Stata·support·a·wider·range·of·models.·Estimation·and·inference·are·valid·under·conditional66 <p>This·class·estimates·treatment·effect·and·potential·outcome·using·5·different·methods,·ipw,·ra,·aipw,·aipw-wls,·ipw-ra.·The·last·three·methods·require·both·a·treatment·or·selection·model·and·an·outcome·model.·Standard·errors·and·inference·are·based·on·the·joint·GMM·representation·of·selection·or·treatment·model,·outcome·model·and·effect·functions.·The·approach·for·inference·follows·Stata,·however·Stata·support·a·wider·range·of·models.·Estimation·and·inference·are·valid·under·conditional
67 independence·or·ignorability.</p>67 independence·or·ignorability.</p>
68 <p>The·outcome·model·is·currently·limited·to·a·linear·model·based·on·OLS.·Treatment·is·currently·restricted·to·binary·treatment·which·can·be·either·Logit·or·Probit.</p>68 <p>The·outcome·model·is·currently·limited·to·a·linear·model·based·on·OLS.·Treatment·is·currently·restricted·to·binary·treatment·which·can·be·either·Logit·or·Probit.</p>
69 <p>The·example·follows·Cattaneo.</p>69 <p>The·example·follows·Cattaneo.</p>
70 <div·class="nbinput·nblast·docutils·container">70 <div·class="nbinput·nblast·docutils·container">
71 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:71 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
72 </pre></div>72 </pre></div>
73 </div>73 </div>
74 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">os</span>74 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">os</span>
75 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>75 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
76 <span·class="kn">from</span>·<span·class="nn">numpy.testing</span>·<span·class="kn">import</span>·<span·class="n">assert_allclose</span>76 <span·class="kn">from</span>·<span·class="nn">numpy.testing</span>·<span·class="kn">import</span>·<span·class="n">assert_allclose</span>
77 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>77 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
  
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100 ····<span·class="p">]</span>100 ····<span·class="p">]</span>
  
101 <span·class="c1">#·allow·wider·display·of·data·frames</span>101 <span·class="c1">#·allow·wider·display·of·data·frames</span>
102 <span·class="n">pd</span><span·class="o">.</span><span·class="n">set_option</span><span·class="p">(</span><span·class="s1">&#39;display.width&#39;</span><span·class="p">,</span>·<span·class="mi">500</span><span·class="p">)</span>102 <span·class="n">pd</span><span·class="o">.</span><span·class="n">set_option</span><span·class="p">(</span><span·class="s1">&#39;display.width&#39;</span><span·class="p">,</span>·<span·class="mi">500</span><span·class="p">)</span>
103 </pre></div>103 </pre></div>
104 </div>104 </div>
105 </div>105 </div>
106 <div·class="nbinput·docutils·container">106 <div·class="nbinput·nblast·docutils·container">
107 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:107 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
108 </pre></div>108 </pre></div>
109 </div>109 </div>
110 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta_cat</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>110 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta_cat</span><span·class="o">.</span><span·class="n">head</span><span·class="p">()</span>
111 </pre></div>111 </pre></div>
112 </div>112 </div>
113 </div>113 </div>
114 <div·class="nboutput·nblast·docutils·container"> 
115 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]: 
116 </pre></div> 
117 </div> 
118 <div·class="output_area·rendered_html·docutils·container"> 
119 <div> 
120 <style·scoped> 
121 ····.dataframe·tbody·tr·th:only-of-type·{ 
122 ········vertical-align:·middle; 
123 ····} 
  
124 ····.dataframe·tbody·tr·th·{ 
125 ········vertical-align:·top; 
126 ····} 
  
127 ····.dataframe·thead·th·{ 
128 ········text-align:·right; 
129 ····} 
130 </style> 
131 <table·border="1"·class="dataframe"> 
132 ··<thead> 
133 ····<tr·style="text-align:·right;"> 
134 ······<th></th> 
135 ······<th>bweight</th> 
136 ······<th>mmarried</th> 
137 ······<th>mhisp</th> 
138 ······<th>fhisp</th> 
139 ······<th>foreign</th> 
140 ······<th>alcohol</th> 
141 ······<th>deadkids</th> 
142 ······<th>mage</th> 
143 ······<th>medu</th> 
144 ······<th>fage</th> 
145 ······<th>...</th> 
146 ······<th>prenatal</th> 
147 ······<th>birthmonth</th> 
148 ······<th>lbweight</th> 
149 ······<th>fbaby</th> 
150 ······<th>prenatal1</th> 
151 ······<th>mbsmoke_</th> 
152 ······<th>mmarried_</th> 
153 ······<th>fbaby_</th> 
154 ······<th>prenatal1_</th> 
155 ······<th>mage2</th> 
156 ····</tr> 
157 ··</thead> 
158 ··<tbody> 
159 ····<tr> 
160 ······<th>0</th> 
161 ······<td>3459</td> 
162 ······<td>married</td> 
163 ······<td>0</td> 
164 ······<td>0</td> 
165 ······<td>0</td> 
166 ······<td>0</td> 
167 ······<td>0</td> 
168 ······<td>24</td> 
169 ······<td>14</td> 
170 ······<td>28</td> 
171 ······<td>...</td> 
172 ······<td>1</td> 
173 ······<td>12</td> 
174 ······<td>0</td> 
175 ······<td>No</td> 
176 ······<td>Yes</td> 
177 ······<td>0</td> 
178 ······<td>1</td> 
179 ······<td>0</td> 
180 ······<td>1</td> 
181 ······<td>576.0</td> 
182 ····</tr> 
183 ····<tr> 
184 ······<th>1</th> 
185 ······<td>3260</td> 
186 ······<td>notmarried</td> 
187 ······<td>0</td> 
188 ······<td>0</td> 
189 ······<td>1</td> 
190 ······<td>0</td> 
191 ······<td>0</td> 
192 ······<td>20</td> 
193 ······<td>10</td> 
194 ······<td>0</td> 
195 ······<td>...</td> 
196 ······<td>1</td> 
197 ······<td>7</td> 
198 ······<td>0</td> 
199 ······<td>No</td> 
200 ······<td>Yes</td> 
201 ······<td>0</td> 
202 ······<td>0</td> 
203 ······<td>0</td> 
204 ······<td>1</td> 
205 ······<td>400.0</td> 
206 ····</tr> 
207 ····<tr> 
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18 model,·outcome·model·and·effect·functions.·The·approach·for·inference·follows18 model,·outcome·model·and·effect·functions.·The·approach·for·inference·follows
19 Stata,·however·Stata·support·a·wider·range·of·models.·Estimation·and·inference19 Stata,·however·Stata·support·a·wider·range·of·models.·Estimation·and·inference
20 are·valid·under·conditional·independence·or·ignorability.20 are·valid·under·conditional·independence·or·ignorability.
21 The·outcome·model·is·currently·limited·to·a·linear·model·based·on·OLS.21 The·outcome·model·is·currently·limited·to·a·linear·model·based·on·OLS.
22 Treatment·is·currently·restricted·to·binary·treatment·which·can·be·either·Logit22 Treatment·is·currently·restricted·to·binary·treatment·which·can·be·either·Logit
23 or·Probit.23 or·Probit.
24 The·example·follows·Cattaneo.24 The·example·follows·Cattaneo.
25 [1]:25 [·]:
26 import·os26 import·os
27 import·numpy·as·np27 import·numpy·as·np
28 from·numpy.testing·import·assert_allclose28 from·numpy.testing·import·assert_allclose
29 import·pandas·as·pd29 import·pandas·as·pd
  
30 from·statsmodels.regression.linear_model·import·OLS30 from·statsmodels.regression.linear_model·import·OLS
31 from·statsmodels.discrete.discrete_model·import·Probit31 from·statsmodels.discrete.discrete_model·import·Probit
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49 ····("aipw",·res_st.results_aipw),49 ····("aipw",·res_st.results_aipw),
50 ····("aipw_wls",·res_st.results_aipw_wls),50 ····("aipw_wls",·res_st.results_aipw_wls),
51 ····("ipw_ra",·res_st.results_ipwra),51 ····("ipw_ra",·res_st.results_ipwra),
52 ····]52 ····]
  
53 #·allow·wider·display·of·data·frames53 #·allow·wider·display·of·data·frames
54 pd.set_option('display.width',·500)54 pd.set_option('display.width',·500)
55 [2]:55 [·]:
56 dta_cat.head()56 dta_cat.head()
57 [2]: 
58 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
59 |_\x8·_\x8|_\x8b\x8b_\x8w\x8w_\x8e\x8e_\x8i\x8i_\x8g\x8g_\x8h\x8h_\x8t\x8t_\x8|_\x8·_\x8·_\x8m\x8m_\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8e\x8e_\x8d\x8d_\x8|_\x8m\x8m_\x8h\x8h_\x8i\x8i_\x8s\x8s_\x8p\x8p_\x8|_\x8f\x8f_\x8h\x8h_\x8i\x8i_\x8s\x8s_\x8p\x8p_\x8|_\x8f\x8f_\x8o\x8o_\x8r\x8r_\x8e\x8e_\x8i\x8i_\x8g\x8g_\x8n\x8n_\x8|_\x8a\x8a_\x8l\x8l_\x8c\x8c_\x8o\x8o_\x8h\x8h_\x8o\x8o_\x8l\x8l_\x8|_\x8d\x8d_\x8e\x8e_\x8a\x8a_\x8d\x8d_\x8k\x8k_\x8i\x8i_\x8d\x8d_\x8s\x8s_\x8|_\x8m\x8m_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8m\x8m_\x8e\x8e_\x8d\x8d_\x8u\x8u_\x8|_\x8f\x8f_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x8|_\x8.\x8._\x8.\x8._\x8.\x8._\x8|_\x8p\x8p_\x8r\x8r_\x8e\x8e_\x8n\x8n_\x8a\x8a_\x8t\x8t_\x8a\x8a_\x8l\x8l_\x8|_\x8b\x8b_\x8i\x8i_\x8r\x8r_\x8t\x8t_\x8h\x8h_\x8m\x8m_\x8o\x8o_\x8n\x8n_\x8t\x8t_\x8h\x8h_\x8|_\x8l\x8l_\x8b\x8b_\x8w\x8w_\x8e\x8e_\x8i\x8i_\x8g\x8g_\x8h\x8h_\x8t\x8t_\x8|_\x8f\x8f_\x8b\x8b_\x8a\x8a_\x8b\x8b_\x8y\x8y_\x8|_\x8p\x8p_\x8r\x8r_\x8e\x8e_\x8n\x8n_\x8a\x8a_\x8t\x8t_\x8a\x8a_\x8l\x8l_\x81\x81_\x8|_\x8m\x8m_\x8b\x8b_\x8s\x8s_\x8m\x8m_\x8o\x8o_\x8k\x8k_\x8e\x8e_\x8_\x8__\x8|_\x8m\x8m_\x8m\x8m_\x8a\x8a_\x8r\x8r_\x8r\x8r_\x8i\x8i_\x8e\x8e_\x8d\x8d_\x8_\x8__\x8|_\x8f\x8f_\x8b\x8b_\x8a\x8a_\x8b\x8b_\x8y\x8y_\x8_\x8__\x8|_\x8p\x8p_\x8r\x8r_\x8e\x8e_\x8n\x8n_\x8a\x8a_\x8t\x8t_\x8a\x8a_\x8l\x8l_\x81\x81_\x8_\x8__\x8|_\x8m\x8m_\x8a\x8a_\x8g\x8g_\x8e\x8e_\x82\x82| 
60 |_\x80\x80_\x8|_\x83_\x84_\x85_\x89_\x8·_\x8·_\x8·_\x8|_\x8m_\x8a_\x8r_\x8r_\x8i_\x8e_\x8d_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x84_\x8·_\x8·_\x8|_\x81_\x84_\x8·_\x8·_\x8|_\x82_\x88_\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x82_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8N_\x8o_\x8·_\x8·_\x8·_\x8|_\x8Y_\x8e_\x8s_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x85_\x87_\x86_\x8._\x80| 
61 |_\x81\x81_\x8|_\x83_\x82_\x86_\x80_\x8·_\x8·_\x8·_\x8|_\x8n_\x8o_\x8t_\x8m_\x8a_\x8r_\x8r_\x8i_\x8e_\x8d_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x80_\x8·_\x8·_\x8|_\x81_\x80_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x87_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8N_\x8o_\x8·_\x8·_\x8·_\x8|_\x8Y_\x8e_\x8s_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x84_\x80_\x80_\x8._\x80| 
62 |_\x82\x82_\x8|_\x83_\x85_\x87_\x82_\x8·_\x8·_\x8·_\x8|_\x8m_\x8a_\x8r_\x8r_\x8i_\x8e_\x8d_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x82_\x8·_\x8·_\x8|_\x89_\x8·_\x8·_\x8·_\x8|_\x83_\x80_\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8N_\x8o_\x8·_\x8·_\x8·_\x8|_\x8Y_\x8e_\x8s_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x84_\x88_\x84_\x8._\x80| 
63 |_\x83\x83_\x8|_\x82_\x89_\x84_\x88_\x8·_\x8·_\x8·_\x8|_\x8m_\x8a_\x8r_\x8r_\x8i_\x8e_\x8d_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x86_\x8·_\x8·_\x8|_\x81_\x82_\x8·_\x8·_\x8|_\x83_\x80_\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8N_\x8o_\x8·_\x8·_\x8·_\x8|_\x8Y_\x8e_\x8s_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x86_\x87_\x86_\x8._\x80| 
64 |_\x84\x84_\x8|_\x82_\x84_\x81_\x80_\x8·_\x8·_\x8·_\x8|_\x8m_\x8a_\x8r_\x8r_\x8i_\x8e_\x8d_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x82_\x80_\x8·_\x8·_\x8|_\x81_\x82_\x8·_\x8·_\x8|_\x82_\x81_\x8·_\x8·_\x8|_\x8._\x8._\x8._\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x83_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8Y_\x8e_\x8s_\x8·_\x8·_\x8|_\x8Y_\x8e_\x8s_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x80_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x81_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x84_\x80_\x80_\x8._\x80| 
65 5·rows·×·28·columns 
66 *\x8**\x8**\x8**\x8**\x8*·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·T\x8Tr\x8re\x8ea\x8at\x8tm\x8me\x8en\x8nt\x8tE\x8Ef\x8ff\x8fe\x8ec\x8ct\x8t·i\x8in\x8ns\x8st\x8ta\x8an\x8nc\x8ce\x8e·a\x8an\x8nd\x8d·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8e·i\x8ip\x8pw\x8w_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*57 *\x8**\x8**\x8**\x8**\x8*·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·T\x8Tr\x8re\x8ea\x8at\x8tm\x8me\x8en\x8nt\x8tE\x8Ef\x8ff\x8fe\x8ec\x8ct\x8t·i\x8in\x8ns\x8st\x8ta\x8an\x8nc\x8ce\x8e·a\x8an\x8nd\x8d·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8e·i\x8ip\x8pw\x8w_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
67 The·TreatmentEffect·class·requires·-·a·OLS·model·instance·for·the·outcome58 The·TreatmentEffect·class·requires·-·a·OLS·model·instance·for·the·outcome
68 model,·-·a·results·instance·of·the·selection·model·and·-·a·treatment·indicator59 model,·-·a·results·instance·of·the·selection·model·and·-·a·treatment·indicator
69 variable.60 variable.
70 In·the·following·example·we·use·Probit·as·the·selection·model.·Using·Logit·is61 In·the·following·example·we·use·Probit·as·the·selection·model.·Using·Logit·is
71 also·supported.62 also·supported.
72 [3]:63 [·]:
73 #·treatment·selection·model64 #·treatment·selection·model
74 formula·=·'mbsmoke_·~·mmarried_·+·mage·+·mage2·+·fbaby_·+·medu'65 formula·=·'mbsmoke_·~·mmarried_·+·mage·+·mage2·+·fbaby_·+·medu'
75 res_probit·=·Probit.from_formula(formula,·dta_cat).fit()66 res_probit·=·Probit.from_formula(formula,·dta_cat).fit()
  
76 #·outcome·model67 #·outcome·model
77 formula_outcome·=·'bweight·~·prenatal1_·+·mmarried_·+·mage·+·fbaby_'68 formula_outcome·=·'bweight·~·prenatal1_·+·mmarried_·+·mage·+·fbaby_'
78 mod·=·OLS.from_formula(formula_outcome,·dta_cat)69 mod·=·OLS.from_formula(formula_outcome,·dta_cat)
  
79 #·treatment·indicator·variable70 #·treatment·indicator·variable
80 tind·=·np.asarray(dta_cat['mbsmoke_'])71 tind·=·np.asarray(dta_cat['mbsmoke_'])
  
81 teff·=·TreatmentEffect(mod,·tind,·results_select=res_probit)72 teff·=·TreatmentEffect(mod,·tind,·results_select=res_probit)
82 Optimization·terminated·successfully. 
83 ·········Current·function·value:·0.439575 
84 ·········Iterations·6 
85 After·creating·the·TreatmentEffect·instance,·we·can·call·any·of·the·5·methods73 After·creating·the·TreatmentEffect·instance,·we·can·call·any·of·the·5·methods
86 to·compute·potential·outcomes,·POM0,·POM1,·and·average·treatment·effect,·ATE.74 to·compute·potential·outcomes,·POM0,·POM1,·and·average·treatment·effect,·ATE.
87 POM0·is·the·potential·outcome·for·the·no·treatment·group,·POM1·is·the·potential75 POM0·is·the·potential·outcome·for·the·no·treatment·group,·POM1·is·the·potential
88 outcome·for·the·treatment·group,·treatment·effect·is·POM1·-·POM0.76 outcome·for·the·treatment·group,·treatment·effect·is·POM1·-·POM0.
89 For·example·teff.ipw()·computes·POM·and·ATE·using·inverse·probability77 For·example·teff.ipw()·computes·POM·and·ATE·using·inverse·probability
90 weighting.·The·probability·of·treatment·is·also·commonly·called·the·propensity78 weighting.·The·probability·of·treatment·is·also·commonly·called·the·propensity
91 score.·The·summary·of·the·estimation·includes·standard·errors·and·confidence79 score.·The·summary·of·the·estimation·includes·standard·errors·and·confidence
Offset 106, 342 lines modifiedOffset 94, 91 lines modified
106 and·ATE.94 and·ATE.
107 The·internal·gmm·results·are·attached·to·the·treatment·results·as·results_gmm.95 The·internal·gmm·results·are·attached·to·the·treatment·results·as·results_gmm.
108 By·default·the·treatment·effect·methods·computes·average·treatment·effect,96 By·default·the·treatment·effect·methods·computes·average·treatment·effect,
109 where·average·is·take·over·the·sample·observations.·Option·effect_group·can·be97 where·average·is·take·over·the·sample·observations.·Option·effect_group·can·be
110 used·to·compute·either·average·treatment·effect·on·the·treated,·ATT,·using98 used·to·compute·either·average·treatment·effect·on·the·treated,·ATT,·using
111 effect_group=1·or·average·treatment·effect·on·the·non-treated·using99 effect_group=1·or·average·treatment·effect·on·the·non-treated·using
112 effect_group=0.100 effect_group=0.
113 [4]:101 [·]:
114 res·=·teff.ipw()102 res·=·teff.ipw()
115 res103 res
116 [4]:104 [·]:
117 <class·'statsmodels.treatment.treatment_effects.TreatmentEffectResults'> 
118 ·····························Test·for·Constraints 
119 ============================================================================== 
120 ·················coef····std·err··········z······P>|z|······[0.025······0.975] 
121 ------------------------------------------------------------------------------ 
122 ATE·········-230.6891·····25.817·····-8.936······0.000····-281.289····-180.089 
123 POM0········3403.4632······9.571····355.586······0.000····3384.704····3422.223 
124 POM1········3172.7741·····24.001····132.193······0.000····3125.733····3219.815 
125 ============================================================================== 
126 [5]: 
127 res.summary_frame()105 res.summary_frame()
128 [5]:106 [·]:
129 ·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8· 
130 |····|·······c\x8co\x8oe\x8ef\x8f|··s\x8st\x8td\x8d·e\x8er\x8rr\x8r|·········z\x8z|·······P\x8P>\x8>|\x8|z\x8z|\x8||C\x8Co\x8on\x8nf\x8f.\x8.·I\x8In\x8nt\x8t.\x8.·L\x8Lo\x8ow\x8w|·C\x8Co\x8on\x8nf\x8f.\x8.·I\x8In\x8nt\x8t.\x8.| 
131 |_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8|_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8·_\x8U\x8U_\x8p\x8p_\x8p\x8p_\x8.\x8.| 
132 |_\x8A\x8A_\x8T\x8T_\x8E\x8E_\x8·_\x8|_\x8-_\x82_\x83_\x80_\x8._\x86_\x88_\x89_\x80_\x87_\x80_\x8|_\x82_\x85_\x8._\x88_\x81_\x86_\x87_\x85_\x88_\x8|_\x8-_\x88_\x8._\x89_\x83_\x85_\x86_\x83_\x83_\x8·_\x8|_\x84_\x8._\x80_\x84_\x88_\x85_\x84_\x82_\x8e_\x8-_\x81_\x89_\x8|_\x8-_\x82_\x88_\x81_\x8._\x82_\x88_\x88_\x89_\x88_\x85_\x8·_\x8·_\x8·_\x8|_\x8-_\x81_\x88_\x80_\x8._\x80_\x88_\x89_\x81_\x85_\x84| 
133 |_\x8P\x8P_\x8O\x8O_\x8M\x8M_\x80\x80_\x8|_\x83_\x84_\x80_\x83_\x8._\x84_\x86_\x83_\x81_\x86_\x83_\x8|_\x89_\x8._\x85_\x87_\x81_\x84_\x81_\x82_\x8·_\x8|_\x83_\x85_\x85_\x8._\x85_\x88_\x86_\x83_\x82_\x84_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8+_\x80_\x80_\x8|_\x83_\x83_\x88_\x84_\x8._\x87_\x80_\x83_\x85_\x84_\x80_\x8·_\x8·_\x8·_\x8|_\x83_\x84_\x82_\x82_\x8._\x82_\x82_\x82_\x87_\x88_\x85| 
134 |_\x8P\x8P_\x8O\x8O_\x8M\x8M_\x81\x81_\x8|_\x83_\x81_\x87_\x82_\x8._\x87_\x87_\x84_\x80_\x89_\x83_\x8|_\x82_\x84_\x8._\x80_\x80_\x81_\x80_\x85_\x89_\x8|_\x81_\x83_\x82_\x8._\x81_\x89_\x83_\x80_\x88_\x85_\x8|_\x80_\x8._\x80_\x80_\x80_\x80_\x80_\x80_\x8e_\x8+_\x80_\x80_\x8|_\x83_\x81_\x82_\x85_\x8._\x87_\x83_\x82_\x88_\x88_\x81_\x8·_\x8·_\x8·_\x8|_\x83_\x82_\x81_\x89_\x8._\x88_\x81_\x85_\x83_\x80_\x85| 
135 [6]: 
136 print(res.results_gmm.summary())107 print(res.results_gmm.summary())
137 ·······························_IPWGMM·Results 
138 ============================================================================== 
139 Dep.·Variable:······················y···Hansen·J:····················3.988e-09 
140 Model:························_IPWGMM···Prob·(Hansen·J):···················nan 
141 Method:···························GMM 
142 Date:················Sun,·10·Aug·2025 
143 Time:························13:13:47 
144 No.·Observations:················4642 
145 ============================================================================== 
146 ·················coef····std·err··········z······P>|z|······[0.025······0.975] 
147 ------------------------------------------------------------------------------ 
148 p·0·········-230.6891·····25.817·····-8.936······0.000····-281.289····-180.089 
149 p·1·········3403.4632······9.571····355.586······0.000····3384.704····3422.223 
150 p·2···········-1.5583······0.461·····-3.380······0.001······-2.462······-0.655 
151 p·3···········-0.6485······0.055····-11.711······0.000······-0.757······-0.540 
152 p·4············0.1744······0.036······4.836······0.000·······0.104·······0.245 
153 p·5···········-0.0033······0.001·····-4.921······0.000······-0.005······-0.002 
154 p·6···········-0.2176······0.050·····-4.390······0.000······-0.315······-0.120 
155 p·7···········-0.0864······0.010·····-8.630······0.000······-0.106······-0.067 
156 ============================================================================== 
157 a\x8av\x8ve\x8er\x8ra\x8ag\x8ge\x8e·t\x8tr\x8re\x8ea\x8at\x8tm\x8me\x8en\x8nt\x8t·e\x8ef\x8ff\x8fe\x8ec\x8ct\x8t·o\x8on\x8n·t\x8th\x8he\x8e·t\x8tr\x8re\x8ea\x8at\x8te\x8ed\x8d108 a\x8av\x8ve\x8er\x8ra\x8ag\x8ge\x8e·t\x8tr\x8re\x8ea\x8at\x8tm\x8me\x8en\x8nt\x8t·e\x8ef\x8ff\x8fe\x8ec\x8ct\x8t·o\x8on\x8n·t\x8th\x8he\x8e·t\x8tr\x8re\x8ea\x8at\x8te\x8ed\x8d
158 see·more·below109 see·more·below
159 [7]:110 [·]:
160 teff.ipw(effect_group=1)111 teff.ipw(effect_group=1)
161 [7]: 
162 <class·'statsmodels.treatment.treatment_effects.TreatmentEffectResults'> 
163 ·····························Test·for·Constraints 
164 ============================================================================== 
165 ·················coef····std·err··········z······P>|z|······[0.025······0.975] 
166 ------------------------------------------------------------------------------ 
167 ATE·········-225.1796·····23.658·····-9.518······0.000····-271.549····-178.811 
168 POM0········3362.8393·····14.198····236.855······0.000····3335.012····3390.667 
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57 ······<div·class="documentwrapper">57 ······<div·class="documentwrapper">
58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Autoregressive-Moving-Average-(ARMA):-Sunspots-data">61 ··<section·id="Autoregressive-Moving-Average-(ARMA):-Sunspots-data">
62 <h1>Autoregressive·Moving·Average·(ARMA):·Sunspots·data<a·class="headerlink"·href="#Autoregressive-Moving-Average-(ARMA):-Sunspots-data"·title="Link·to·this·heading">¶</a></h1>62 <h1>Autoregressive·Moving·Average·(ARMA):·Sunspots·data<a·class="headerlink"·href="#Autoregressive-Moving-Average-(ARMA):-Sunspots-data"·title="Link·to·this·heading">¶</a></h1>
63 <div·class="nbinput·nblast·docutils·container">63 <div·class="nbinput·nblast·docutils·container">
64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
65 </pre></div>65 </pre></div>
66 </div>66 </div>
67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 </div>70 </div>
71 <div·class="nbinput·nblast·docutils·container">71 <div·class="nbinput·nblast·docutils·container">
72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
76 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>76 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
77 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>77 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
78 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>78 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
79 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>79 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>
80 <span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.arima.model</span>·<span·class="kn">import</span>·<span·class="n">ARIMA</span>80 <span·class="kn">from</span>·<span·class="nn">statsmodels.tsa.arima.model</span>·<span·class="kn">import</span>·<span·class="n">ARIMA</span>
81 </pre></div>81 </pre></div>
82 </div>82 </div>
83 </div>83 </div>
84 <div·class="nbinput·nblast·docutils·container">84 <div·class="nbinput·nblast·docutils·container">
85 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:85 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
86 </pre></div>86 </pre></div>
87 </div>87 </div>
88 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.graphics.api</span>·<span·class="kn">import</span>·<span·class="n">qqplot</span>88 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">from</span>·<span·class="nn">statsmodels.graphics.api</span>·<span·class="kn">import</span>·<span·class="n">qqplot</span>
89 </pre></div>89 </pre></div>
90 </div>90 </div>
91 </div>91 </div>
92 <section·id="Sunspots-Data">92 <section·id="Sunspots-Data">
93 <h2>Sunspots·Data<a·class="headerlink"·href="#Sunspots-Data"·title="Link·to·this·heading">¶</a></h2>93 <h2>Sunspots·Data<a·class="headerlink"·href="#Sunspots-Data"·title="Link·to·this·heading">¶</a></h2>
94 <div·class="nbinput·docutils·container">94 <div·class="nbinput·nblast·docutils·container">
95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:95 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
96 </pre></div>96 </pre></div>
97 </div>97 </div>
98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">sunspots</span><span·class="o">.</span><span·class="n">NOTE</span><span·class="p">)</span>98 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="nb">print</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">sunspots</span><span·class="o">.</span><span·class="n">NOTE</span><span·class="p">)</span>
99 </pre></div>99 </pre></div>
100 </div>100 </div>
101 </div>101 </div>
102 <div·class="nboutput·nblast·docutils·container"> 
103 <div·class="prompt·empty·docutils·container"> 
104 </div> 
105 <div·class="output_area·docutils·container"> 
106 <div·class="highlight"><pre> 
107 :: 
  
108 ····Number·of·Observations·-·309·(Annual·1700·-·2008) 
109 ····Number·of·Variables·-·1 
110 ····Variable·name·definitions:: 
  
111 ········SUNACTIVITY·-·Number·of·sunspots·for·each·year 
  
112 ····The·data·file·contains·a·&#39;YEAR&#39;·variable·that·is·not·returned·by·load. 
  
113 </pre></div></div> 
114 </div> 
115 <div·class="nbinput·nblast·docutils·container">102 <div·class="nbinput·nblast·docutils·container">
116 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:103 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
117 </pre></div>104 </pre></div>
118 </div>105 </div>
119 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">sunspots</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>106 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">datasets</span><span·class="o">.</span><span·class="n">sunspots</span><span·class="o">.</span><span·class="n">load_pandas</span><span·class="p">()</span><span·class="o">.</span><span·class="n">data</span>
120 </pre></div>107 </pre></div>
121 </div>108 </div>
122 </div>109 </div>
123 <div·class="nbinput·nblast·docutils·container">110 <div·class="nbinput·nblast·docutils·container">
124 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:111 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
125 </pre></div>112 </pre></div>
126 </div>113 </div>
127 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">Index</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">datetools</span><span·class="o">.</span><span·class="n">dates_from_range</span><span·class="p">(</span><span·class="s2">&quot;1700&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;2008&quot;</span><span·class="p">))</span>114 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span><span·class="o">.</span><span·class="n">index</span>·<span·class="o">=</span>·<span·class="n">pd</span><span·class="o">.</span><span·class="n">Index</span><span·class="p">(</span><span·class="n">sm</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">datetools</span><span·class="o">.</span><span·class="n">dates_from_range</span><span·class="p">(</span><span·class="s2">&quot;1700&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;2008&quot;</span><span·class="p">))</span>
128 <span·class="n">dta</span><span·class="o">.</span><span·class="n">index</span><span·class="o">.</span><span·class="n">freq</span>·<span·class="o">=</span>·<span·class="n">dta</span><span·class="o">.</span><span·class="n">index</span><span·class="o">.</span><span·class="n">inferred_freq</span>115 <span·class="n">dta</span><span·class="o">.</span><span·class="n">index</span><span·class="o">.</span><span·class="n">freq</span>·<span·class="o">=</span>·<span·class="n">dta</span><span·class="o">.</span><span·class="n">index</span><span·class="o">.</span><span·class="n">inferred_freq</span>
129 <span·class="k">del</span>·<span·class="n">dta</span><span·class="p">[</span><span·class="s2">&quot;YEAR&quot;</span><span·class="p">]</span>116 <span·class="k">del</span>·<span·class="n">dta</span><span·class="p">[</span><span·class="s2">&quot;YEAR&quot;</span><span·class="p">]</span>
130 </pre></div>117 </pre></div>
131 </div>118 </div>
132 </div>119 </div>
133 <div·class="nbinput·docutils·container">120 <div·class="nbinput·nblast·docutils·container">
134 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:121 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
135 </pre></div>122 </pre></div>
136 </div>123 </div>
137 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>124 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">dta</span><span·class="o">.</span><span·class="n">plot</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>
138 </pre></div>125 </pre></div>
139 </div>126 </div>
140 </div>127 </div>
141 <div·class="nboutput·docutils·container">128 <div·class="nbinput·nblast·docutils·container">
142 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:129 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
143 </pre></div> 
144 </div> 
145 <div·class="output_area·docutils·container"> 
146 <div·class="highlight"><pre> 
147 &lt;Axes:·&gt; 
148 </pre></div></div> 
149 </div> 
150 <div·class="nboutput·nblast·docutils·container"> 
151 <div·class="prompt·empty·docutils·container"> 
152 </div> 
153 <div·class="output_area·docutils·container"> 
154 <img·alt="../../../_images/examples_notebooks_generated_tsa_arma_0_8_1.png"·src="../../../_images/examples_notebooks_generated_tsa_arma_0_8_1.png"·/> 
155 </div> 
156 </div> 
157 <div·class="nbinput·docutils·container"> 
158 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[8]: 
159 </pre></div>130 </pre></div>
160 </div>131 </div>
161 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>132 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">plt</span><span·class="o">.</span><span·class="n">figure</span><span·class="p">(</span><span·class="n">figsize</span><span·class="o">=</span><span·class="p">(</span><span·class="mi">12</span><span·class="p">,</span>·<span·class="mi">8</span><span·class="p">))</span>
162 <span·class="n">ax1</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">211</span><span·class="p">)</span>133 <span·class="n">ax1</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">211</span><span·class="p">)</span>
163 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">plot_acf</span><span·class="p">(</span><span·class="n">dta</span><span·class="o">.</span><span·class="n">values</span><span·class="o">.</span><span·class="n">squeeze</span><span·class="p">(),</span>·<span·class="n">lags</span><span·class="o">=</span><span·class="mi">40</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax1</span><span·class="p">)</span>134 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">plot_acf</span><span·class="p">(</span><span·class="n">dta</span><span·class="o">.</span><span·class="n">values</span><span·class="o">.</span><span·class="n">squeeze</span><span·class="p">(),</span>·<span·class="n">lags</span><span·class="o">=</span><span·class="mi">40</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax1</span><span·class="p">)</span>
164 <span·class="n">ax2</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">212</span><span·class="p">)</span>135 <span·class="n">ax2</span>·<span·class="o">=</span>·<span·class="n">fig</span><span·class="o">.</span><span·class="n">add_subplot</span><span·class="p">(</span><span·class="mi">212</span><span·class="p">)</span>
165 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">plot_pacf</span><span·class="p">(</span><span·class="n">dta</span><span·class="p">,</span>·<span·class="n">lags</span><span·class="o">=</span><span·class="mi">40</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax2</span><span·class="p">)</span>136 <span·class="n">fig</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">graphics</span><span·class="o">.</span><span·class="n">tsa</span><span·class="o">.</span><span·class="n">plot_pacf</span><span·class="p">(</span><span·class="n">dta</span><span·class="p">,</span>·<span·class="n">lags</span><span·class="o">=</span><span·class="mi">40</span><span·class="p">,</span>·<span·class="n">ax</span><span·class="o">=</span><span·class="n">ax2</span><span·class="p">)</span>
166 </pre></div>137 </pre></div>
167 </div>138 </div>
168 </div>139 </div>
169 <div·class="nboutput·nblast·docutils·container"> 
170 <div·class="prompt·empty·docutils·container"> 
171 </div> 
172 <div·class="output_area·docutils·container"> 
173 <img·alt="../../../_images/examples_notebooks_generated_tsa_arma_0_9_0.png"·src="../../../_images/examples_notebooks_generated_tsa_arma_0_9_0.png"·/> 
174 </div> 
175 </div> 
176 <div·class="nbinput·nblast·docutils·container">140 <div·class="nbinput·nblast·docutils·container">
177 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:141 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
178 </pre></div>142 </pre></div>
179 </div>143 </div>
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Autoregressive·Moving·Average·(ARMA):·Sunspots·data8 ····*·Autoregressive·Moving·Average·(ARMA):·Sunspots·data
9 *\x8**\x8**\x8**\x8**\x8**\x8*·A\x8Au\x8ut\x8to\x8or\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8iv\x8ve\x8e·M\x8Mo\x8ov\x8vi\x8in\x8ng\x8g·A\x8Av\x8ve\x8er\x8ra\x8ag\x8ge\x8e·(\x8(A\x8AR\x8RM\x8MA\x8A)\x8):\x8:·S\x8Su\x8un\x8ns\x8sp\x8po\x8ot\x8ts\x8s·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·A\x8Au\x8ut\x8to\x8or\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8iv\x8ve\x8e·M\x8Mo\x8ov\x8vi\x8in\x8ng\x8g·A\x8Av\x8ve\x8er\x8ra\x8ag\x8ge\x8e·(\x8(A\x8AR\x8RM\x8MA\x8A)\x8):\x8:·S\x8Su\x8un\x8ns\x8sp\x8po\x8ot\x8ts\x8s·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 %matplotlib·inline11 %matplotlib·inline
12 [2]:12 [·]:
13 import·matplotlib.pyplot·as·plt13 import·matplotlib.pyplot·as·plt
14 import·numpy·as·np14 import·numpy·as·np
15 import·pandas·as·pd15 import·pandas·as·pd
16 import·statsmodels.api·as·sm16 import·statsmodels.api·as·sm
17 from·scipy·import·stats17 from·scipy·import·stats
18 from·statsmodels.tsa.arima.model·import·ARIMA18 from·statsmodels.tsa.arima.model·import·ARIMA
19 [3]:19 [·]:
20 from·statsmodels.graphics.api·import·qqplot20 from·statsmodels.graphics.api·import·qqplot
21 *\x8**\x8**\x8**\x8**\x8*·S\x8Su\x8un\x8ns\x8sp\x8po\x8ot\x8ts\x8s·D\x8Da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*21 *\x8**\x8**\x8**\x8**\x8*·S\x8Su\x8un\x8ns\x8sp\x8po\x8ot\x8ts\x8s·D\x8Da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
22 [4]:22 [·]:
23 print(sm.datasets.sunspots.NOTE)23 print(sm.datasets.sunspots.NOTE)
24 :: 
  
25 ····Number·of·Observations·-·309·(Annual·1700·-·2008) 
26 ····Number·of·Variables·-·1 
27 ····Variable·name·definitions:: 
  
28 ········SUNACTIVITY·-·Number·of·sunspots·for·each·year 
  
29 ····The·data·file·contains·a·'YEAR'·variable·that·is·not·returned·by·load. 
30 [5]:24 [·]:
31 dta·=·sm.datasets.sunspots.load_pandas().data25 dta·=·sm.datasets.sunspots.load_pandas().data
32 [6]:26 [·]:
33 dta.index·=·pd.Index(sm.tsa.datetools.dates_from_range("1700",·"2008"))27 dta.index·=·pd.Index(sm.tsa.datetools.dates_from_range("1700",·"2008"))
34 dta.index.freq·=·dta.index.inferred_freq28 dta.index.freq·=·dta.index.inferred_freq
35 del·dta["YEAR"]29 del·dta["YEAR"]
36 [7]:30 [·]:
37 dta.plot(figsize=(12,·8))31 dta.plot(figsize=(12,·8))
38 [7]:32 [·]:
39 <Axes:·> 
40 [../../../_images/examples_notebooks_generated_tsa_arma_0_8_1.png] 
41 [8]: 
42 fig·=·plt.figure(figsize=(12,·8))33 fig·=·plt.figure(figsize=(12,·8))
43 ax1·=·fig.add_subplot(211)34 ax1·=·fig.add_subplot(211)
44 fig·=·sm.graphics.tsa.plot_acf(dta.values.squeeze(),·lags=40,·ax=ax1)35 fig·=·sm.graphics.tsa.plot_acf(dta.values.squeeze(),·lags=40,·ax=ax1)
45 ax2·=·fig.add_subplot(212)36 ax2·=·fig.add_subplot(212)
46 fig·=·sm.graphics.tsa.plot_pacf(dta,·lags=40,·ax=ax2)37 fig·=·sm.graphics.tsa.plot_pacf(dta,·lags=40,·ax=ax2)
47 [../../../_images/examples_notebooks_generated_tsa_arma_0_9_0.png] 
48 [·]:38 [·]:
49 [9]:39 [·]:
50 arma_mod20·=·ARIMA(dta,·order=(2,·0,·0)).fit()40 arma_mod20·=·ARIMA(dta,·order=(2,·0,·0)).fit()
51 print(arma_mod20.params)41 print(arma_mod20.params)
 42 [·]:
52 const······49.746198 
53 ar.L1·······1.390633 
54 ar.L2······-0.688573 
55 sigma2····274.727183 
56 dtype:·float64 
57 [10]: 
58 arma_mod30·=·ARIMA(dta,·order=(3,·0,·0)).fit()43 arma_mod30·=·ARIMA(dta,·order=(3,·0,·0)).fit()
59 [11]:44 [·]:
60 print(arma_mod20.aic,·arma_mod20.bic,·arma_mod20.hqic)45 print(arma_mod20.aic,·arma_mod20.bic,·arma_mod20.hqic)
 46 [·]:
61 2622.637093301387·2637.5704584089776·2628.607481146633 
62 [12]: 
63 print(arma_mod30.params)47 print(arma_mod30.params)
 48 [·]:
64 const······49.751911 
65 ar.L1·······1.300818 
66 ar.L2······-0.508102 
67 ar.L3······-0.129644 
68 sigma2····270.101139 
69 dtype:·float64 
70 [13]: 
71 print(arma_mod30.aic,·arma_mod30.bic,·arma_mod30.hqic)49 print(arma_mod30.aic,·arma_mod30.bic,·arma_mod30.hqic)
72 2619.4036292456676·2638.0703356301565·2626.866614052225 
73 ····*·Does·our·model·obey·the·theory?50 ····*·Does·our·model·obey·the·theory?
74 [14]:51 [·]:
75 sm.stats.durbin_watson(arma_mod30.resid.values)52 sm.stats.durbin_watson(arma_mod30.resid.values)
 53 [·]:
76 [14]: 
77 np.float64(1.9564953616072376) 
78 [15]: 
79 fig·=·plt.figure(figsize=(12,·8))54 fig·=·plt.figure(figsize=(12,·8))
80 ax·=·fig.add_subplot(111)55 ax·=·fig.add_subplot(111)
81 ax·=·arma_mod30.resid.plot(ax=ax)56 ax·=·arma_mod30.resid.plot(ax=ax)
 57 [·]:
82 [../../../_images/examples_notebooks_generated_tsa_arma_0_18_0.png] 
83 [16]: 
84 resid·=·arma_mod30.resid58 resid·=·arma_mod30.resid
85 [17]:59 [·]:
86 stats.normaltest(resid)60 stats.normaltest(resid)
 61 [·]:
87 [17]: 
88 NormaltestResult(statistic=np.float64(49.84393220876942),·pvalue=np.float64 
89 (1.5015079731491487e-11)) 
90 [18]: 
91 fig·=·plt.figure(figsize=(12,·8))62 fig·=·plt.figure(figsize=(12,·8))
92 ax·=·fig.add_subplot(111)63 ax·=·fig.add_subplot(111)
93 fig·=·qqplot(resid,·line="q",·ax=ax,·fit=True)64 fig·=·qqplot(resid,·line="q",·ax=ax,·fit=True)
 65 [·]:
94 [../../../_images/examples_notebooks_generated_tsa_arma_0_21_0.png] 
95 [19]: 
96 fig·=·plt.figure(figsize=(12,·8))66 fig·=·plt.figure(figsize=(12,·8))
97 ax1·=·fig.add_subplot(211)67 ax1·=·fig.add_subplot(211)
98 fig·=·sm.graphics.tsa.plot_acf(resid.values.squeeze(),·lags=40,·ax=ax1)68 fig·=·sm.graphics.tsa.plot_acf(resid.values.squeeze(),·lags=40,·ax=ax1)
99 ax2·=·fig.add_subplot(212)69 ax2·=·fig.add_subplot(212)
100 fig·=·sm.graphics.tsa.plot_pacf(resid,·lags=40,·ax=ax2)70 fig·=·sm.graphics.tsa.plot_pacf(resid,·lags=40,·ax=ax2)
 71 [·]:
101 [../../../_images/examples_notebooks_generated_tsa_arma_0_22_0.png] 
102 [20]: 
103 r,·q,·p·=·sm.tsa.acf(resid.values.squeeze(),·fft=True,·qstat=True)72 r,·q,·p·=·sm.tsa.acf(resid.values.squeeze(),·fft=True,·qstat=True)
104 data·=·np.c_[np.arange(1,·25),·r[1:],·q,·p]73 data·=·np.c_[np.arange(1,·25),·r[1:],·q,·p]
105 [21]:74 [·]:
106 table·=·pd.DataFrame(data,·columns=["lag",·"AC",·"Q",·"Prob(>Q)"])75 table·=·pd.DataFrame(data,·columns=["lag",·"AC",·"Q",·"Prob(>Q)"])
107 print(table.set_index("lag"))76 print(table.set_index("lag"))
108 ············AC··········Q······Prob(>Q) 
109 lag 
110 1.0···0.009170···0.026239··8.713184e-01 
111 2.0···0.041793···0.572982··7.508939e-01 
112 3.0··-0.001338···0.573544··9.024612e-01 
113 4.0···0.136086···6.408642··1.706385e-01 
114 5.0···0.092465···9.111351··1.047043e-01 
115 6.0···0.091947··11.792661··6.675737e-02 
116 7.0···0.068747··13.296552··6.520425e-02 
117 8.0··-0.015022··13.368601··9.978086e-02 
118 9.0···0.187590··24.641072··3.394963e-03 
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56 ····<div·class="document">56 ····<div·class="document">
57 ······<div·class="documentwrapper">57 ······<div·class="documentwrapper">
58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Autoregressive-Moving-Average-(ARMA):-Artificial-data">61 ··<section·id="Autoregressive-Moving-Average-(ARMA):-Artificial-data">
62 <h1>Autoregressive·Moving·Average·(ARMA):·Artificial·data<a·class="headerlink"·href="#Autoregressive-Moving-Average-(ARMA):-Artificial-data"·title="Link·to·this·heading">¶</a></h1>62 <h1>Autoregressive·Moving·Average·(ARMA):·Artificial·data<a·class="headerlink"·href="#Autoregressive-Moving-Average-(ARMA):-Artificial-data"·title="Link·to·this·heading">¶</a></h1>
63 <div·class="nbinput·nblast·docutils·container">63 <div·class="nbinput·docutils·container">
64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:
65 </pre></div>65 </pre></div>
66 </div>66 </div>
67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 </div>70 </div>
 71 <div·class="nboutput·nblast·docutils·container">
 72 <div·class="prompt·empty·docutils·container">
 73 </div>
 74 <div·class="output_area·stderr·docutils·container">
 75 <div·class="highlight"><pre>
 76 Matplotlib·is·building·the·font·cache;·this·may·take·a·moment.
 77 Could·not·save·font_manager·cache·Lock·error:·Matplotlib·failed·to·acquire·the·following·lock·file:
 78 ····/build/reproducible-path/statsmodels-0.14.5+dfsg/build/fontlist-v390.json.matplotlib-lock
 79 This·maybe·due·to·another·process·holding·this·lock·file.··If·you·are·sure·no
 80 other·Matplotlib·process·is·running,·remove·this·file·and·try·again.
 81 </pre></div></div>
 82 </div>
71 <div·class="nbinput·nblast·docutils·container">83 <div·class="nbinput·nblast·docutils·container">
72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:84 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:
73 </pre></div>85 </pre></div>
74 </div>86 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>87 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
76 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>88 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
  
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5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Autoregressive·Moving·Average·(ARMA):·Artificial·data8 ····*·Autoregressive·Moving·Average·(ARMA):·Artificial·data
9 *\x8**\x8**\x8**\x8**\x8**\x8*·A\x8Au\x8ut\x8to\x8or\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8iv\x8ve\x8e·M\x8Mo\x8ov\x8vi\x8in\x8ng\x8g·A\x8Av\x8ve\x8er\x8ra\x8ag\x8ge\x8e·(\x8(A\x8AR\x8RM\x8MA\x8A)\x8):\x8:·A\x8Ar\x8rt\x8ti\x8if\x8fi\x8ic\x8ci\x8ia\x8al\x8l·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·A\x8Au\x8ut\x8to\x8or\x8re\x8eg\x8gr\x8re\x8es\x8ss\x8si\x8iv\x8ve\x8e·M\x8Mo\x8ov\x8vi\x8in\x8ng\x8g·A\x8Av\x8ve\x8er\x8ra\x8ag\x8ge\x8e·(\x8(A\x8AR\x8RM\x8MA\x8A)\x8):\x8:·A\x8Ar\x8rt\x8ti\x8if\x8fi\x8ic\x8ci\x8ia\x8al\x8l·d\x8da\x8at\x8ta\x8a_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [1]:
11 %matplotlib·inline11 %matplotlib·inline
 12 Matplotlib·is·building·the·font·cache;·this·may·take·a·moment.
 13 Could·not·save·font_manager·cache·Lock·error:·Matplotlib·failed·to·acquire·the
 14 following·lock·file:
 15 ····/build/reproducible-path/statsmodels-0.14.5+dfsg/build/fontlist-
 16 v390.json.matplotlib-lock
 17 This·maybe·due·to·another·process·holding·this·lock·file.··If·you·are·sure·no
 18 other·Matplotlib·process·is·running,·remove·this·file·and·try·again.
12 [2]:19 [2]:
13 import·numpy·as·np20 import·numpy·as·np
14 import·pandas·as·pd21 import·pandas·as·pd
  
15 from·statsmodels.graphics.tsaplots·import·plot_predict22 from·statsmodels.graphics.tsaplots·import·plot_predict
16 from·statsmodels.tsa.arima_process·import·arma_generate_sample23 from·statsmodels.tsa.arima_process·import·arma_generate_sample
17 from·statsmodels.tsa.arima.model·import·ARIMA24 from·statsmodels.tsa.arima.model·import·ARIMA
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9 ········},9 ········},
10 ········{10 ········{
11 ············"cell_type":·"code",11 ············"cell_type":·"code",
12 ············"execution_count":·1,12 ············"execution_count":·1,
13 ············"metadata":·{13 ············"metadata":·{
14 ················"execution":·{}14 ················"execution":·{}
15 ············},15 ············},
16 ············"outputs":·[],16 ············"outputs":·[
 17 ················{
 18 ····················"name":·"stderr",
 19 ····················"output_type":·"stream",
 20 ····················"text":·[
 21 ························"Matplotlib·is·building·the·font·cache;·this·may·take·a·moment.\n"
 22 ····················]
 23 ················},
 24 ················{
 25 ····················"name":·"stderr",
 26 ····················"output_type":·"stream",
 27 ····················"text":·[
 28 ························"Could·not·save·font_manager·cache·Lock·error:·Matplotlib·failed·to·acquire·the·following·lock·file:\n",
 29 ························"····/build/reproducible-path/statsmodels-0.14.5+dfsg/build/fontlist-v390.json.matplotlib-lock\n",
 30 ························"This·maybe·due·to·another·process·holding·this·lock·file.··If·you·are·sure·no\n",
 31 ························"other·Matplotlib·process·is·running,·remove·this·file·and·try·again.\n"
 32 ····················]
 33 ················}
 34 ············],
17 ············"source":·[35 ············"source":·[
18 ················"%matplotlib·inline"36 ················"%matplotlib·inline"
19 ············]37 ············]
20 ········},38 ········},
21 ········{39 ········{
22 ············"cell_type":·"code",40 ············"cell_type":·"code",
23 ············"execution_count":·2,41 ············"execution_count":·2,
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Offset 58, 39 lines modifiedOffset 58, 39 lines modified
58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Variance-Component-Analysis">61 ··<section·id="Variance-Component-Analysis">
62 <h1>Variance·Component·Analysis<a·class="headerlink"·href="#Variance-Component-Analysis"·title="Link·to·this·heading">¶</a></h1>62 <h1>Variance·Component·Analysis<a·class="headerlink"·href="#Variance-Component-Analysis"·title="Link·to·this·heading">¶</a></h1>
63 <p>This·notebook·illustrates·variance·components·analysis·for·two-level·nested·and·crossed·designs.</p>63 <p>This·notebook·illustrates·variance·components·analysis·for·two-level·nested·and·crossed·designs.</p>
64 <div·class="nbinput·nblast·docutils·container">64 <div·class="nbinput·nblast·docutils·container">
65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:65 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
66 </pre></div>66 </pre></div>
67 </div>67 </div>
68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>68 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
69 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>69 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
70 <span·class="kn">from</span>·<span·class="nn">statsmodels.regression.mixed_linear_model</span>·<span·class="kn">import</span>·<span·class="n">VCSpec</span>70 <span·class="kn">from</span>·<span·class="nn">statsmodels.regression.mixed_linear_model</span>·<span·class="kn">import</span>·<span·class="n">VCSpec</span>
71 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>71 <span·class="kn">import</span>·<span·class="nn">pandas</span>·<span·class="k">as</span>·<span·class="nn">pd</span>
72 </pre></div>72 </pre></div>
73 </div>73 </div>
74 </div>74 </div>
75 <p>Make·the·notebook·reproducible</p>75 <p>Make·the·notebook·reproducible</p>
76 <div·class="nbinput·nblast·docutils·container">76 <div·class="nbinput·nblast·docutils·container">
77 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:77 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
78 </pre></div>78 </pre></div>
79 </div>79 </div>
80 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">3123</span><span·class="p">)</span>80 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">np</span><span·class="o">.</span><span·class="n">random</span><span·class="o">.</span><span·class="n">seed</span><span·class="p">(</span><span·class="mi">3123</span><span·class="p">)</span>
81 </pre></div>81 </pre></div>
82 </div>82 </div>
83 </div>83 </div>
84 <section·id="Nested-analysis">84 <section·id="Nested-analysis">
85 <h2>Nested·analysis<a·class="headerlink"·href="#Nested-analysis"·title="Link·to·this·heading">¶</a></h2>85 <h2>Nested·analysis<a·class="headerlink"·href="#Nested-analysis"·title="Link·to·this·heading">¶</a></h2>
86 <p>In·our·discussion·below,·“Group·2”·is·nested·within·“Group·1”.·As·a·concrete·example,·“Group·1”·might·be·school·districts,·with·“Group·2”·being·individual·schools.·The·function·below·generates·data·from·such·a·population.·In·a·nested·analysis,·the·group·2·labels·that·are·nested·within·different·group·1·labels·are·treated·as·independent·groups,·even·if·they·have·the·same·label.·For·example,·two·schools·labeled·“school·1”·that·are·in·two·different·school·districts·are·treated·as·independent86 <p>In·our·discussion·below,·“Group·2”·is·nested·within·“Group·1”.·As·a·concrete·example,·“Group·1”·might·be·school·districts,·with·“Group·2”·being·individual·schools.·The·function·below·generates·data·from·such·a·population.·In·a·nested·analysis,·the·group·2·labels·that·are·nested·within·different·group·1·labels·are·treated·as·independent·groups,·even·if·they·have·the·same·label.·For·example,·two·schools·labeled·“school·1”·that·are·in·two·different·school·districts·are·treated·as·independent
87 schools,·even·though·they·have·the·same·label.</p>87 schools,·even·though·they·have·the·same·label.</p>
88 <div·class="nbinput·nblast·docutils·container">88 <div·class="nbinput·nblast·docutils·container">
89 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:89 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
90 </pre></div>90 </pre></div>
91 </div>91 </div>
92 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">generate_nested</span><span·class="p">(</span>92 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">generate_nested</span><span·class="p">(</span>
93 ····<span·class="n">n_group1</span><span·class="o">=</span><span·class="mi">200</span><span·class="p">,</span>·<span·class="n">n_group2</span><span·class="o">=</span><span·class="mi">20</span><span·class="p">,</span>·<span·class="n">n_rep</span><span·class="o">=</span><span·class="mi">10</span><span·class="p">,</span>·<span·class="n">group1_sd</span><span·class="o">=</span><span·class="mi">2</span><span·class="p">,</span>·<span·class="n">group2_sd</span><span·class="o">=</span><span·class="mi">3</span><span·class="p">,</span>·<span·class="n">unexplained_sd</span><span·class="o">=</span><span·class="mi">4</span>93 ····<span·class="n">n_group1</span><span·class="o">=</span><span·class="mi">200</span><span·class="p">,</span>·<span·class="n">n_group2</span><span·class="o">=</span><span·class="mi">20</span><span·class="p">,</span>·<span·class="n">n_rep</span><span·class="o">=</span><span·class="mi">10</span><span·class="p">,</span>·<span·class="n">group1_sd</span><span·class="o">=</span><span·class="mi">2</span><span·class="p">,</span>·<span·class="n">group2_sd</span><span·class="o">=</span><span·class="mi">3</span><span·class="p">,</span>·<span·class="n">unexplained_sd</span><span·class="o">=</span><span·class="mi">4</span>
94 <span·class="p">):</span>94 <span·class="p">):</span>
  
95 ····<span·class="c1">#·Group·1·indicators</span>95 ····<span·class="c1">#·Group·1·indicators</span>
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114 ····<span·class="k">return</span>·<span·class="n">df</span>114 ····<span·class="k">return</span>·<span·class="n">df</span>
115 </pre></div>115 </pre></div>
116 </div>116 </div>
117 </div>117 </div>
118 <p>Generate·a·data·set·to·analyze.</p>118 <p>Generate·a·data·set·to·analyze.</p>
119 <div·class="nbinput·nblast·docutils·container">119 <div·class="nbinput·nblast·docutils·container">
120 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:120 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
121 </pre></div>121 </pre></div>
122 </div>122 </div>
123 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">generate_nested</span><span·class="p">()</span>123 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">df</span>·<span·class="o">=</span>·<span·class="n">generate_nested</span><span·class="p">()</span>
124 </pre></div>124 </pre></div>
125 </div>125 </div>
126 </div>126 </div>
127 <p>Using·all·the·default·arguments·for·<code·class="docutils·literal·notranslate"><span·class="pre">generate_nested</span></code>,·the·population·values·of·“group·1·Var”·and·“group·2·Var”·are·2^2=4·and·3^2=9,·respectively.·The·unexplained·variance,·listed·as·“scale”·at·the·top·of·the·summary·table,·has·population·value·4^2=16.</p>127 <p>Using·all·the·default·arguments·for·<code·class="docutils·literal·notranslate"><span·class="pre">generate_nested</span></code>,·the·population·values·of·“group·1·Var”·and·“group·2·Var”·are·2^2=4·and·3^2=9,·respectively.·The·unexplained·variance,·listed·as·“scale”·at·the·top·of·the·summary·table,·has·population·value·4^2=16.</p>
128 <div·class="nbinput·docutils·container">128 <div·class="nbinput·nblast·docutils·container">
129 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:129 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
130 </pre></div>130 </pre></div>
131 </div>131 </div>
132 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">model1</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">MixedLM</span><span·class="o">.</span><span·class="n">from_formula</span><span·class="p">(</span>132 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">model1</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">MixedLM</span><span·class="o">.</span><span·class="n">from_formula</span><span·class="p">(</span>
133 ····<span·class="s2">&quot;y·~·1&quot;</span><span·class="p">,</span>133 ····<span·class="s2">&quot;y·~·1&quot;</span><span·class="p">,</span>
134 ····<span·class="n">re_formula</span><span·class="o">=</span><span·class="s2">&quot;1&quot;</span><span·class="p">,</span>134 ····<span·class="n">re_formula</span><span·class="o">=</span><span·class="s2">&quot;1&quot;</span><span·class="p">,</span>
135 ····<span·class="n">vc_formula</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;group2&quot;</span><span·class="p">:</span>·<span·class="s2">&quot;0·+·C(group2)&quot;</span><span·class="p">},</span>135 ····<span·class="n">vc_formula</span><span·class="o">=</span><span·class="p">{</span><span·class="s2">&quot;group2&quot;</span><span·class="p">:</span>·<span·class="s2">&quot;0·+·C(group2)&quot;</span><span·class="p">},</span>
136 ····<span·class="n">groups</span><span·class="o">=</span><span·class="s2">&quot;group1&quot;</span><span·class="p">,</span>136 ····<span·class="n">groups</span><span·class="o">=</span><span·class="s2">&quot;group1&quot;</span><span·class="p">,</span>
137 ····<span·class="n">data</span><span·class="o">=</span><span·class="n">df</span><span·class="p">,</span>137 ····<span·class="n">data</span><span·class="o">=</span><span·class="n">df</span><span·class="p">,</span>
138 <span·class="p">)</span>138 <span·class="p">)</span>
139 <span·class="n">result1</span>·<span·class="o">=</span>·<span·class="n">model1</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>139 <span·class="n">result1</span>·<span·class="o">=</span>·<span·class="n">model1</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
140 <span·class="nb">print</span><span·class="p">(</span><span·class="n">result1</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>140 <span·class="nb">print</span><span·class="p">(</span><span·class="n">result1</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
141 </pre></div>141 </pre></div>
142 </div>142 </div>
143 </div>143 </div>
144 <div·class="nboutput·nblast·docutils·container"> 
145 <div·class="prompt·empty·docutils·container"> 
146 </div> 
147 <div·class="output_area·docutils·container"> 
148 <div·class="highlight"><pre> 
149 ··········Mixed·Linear·Model·Regression·Results 
150 ========================================================== 
151 Model:············MixedLM·Dependent·Variable:·y 
152 No.·Observations:·40000···Method:·············REML 
153 No.·Groups:·······200·····Scale:··············15.8825 
154 Min.·group·size:··200·····Log-Likelihood:·····-116022.3805 
155 Max.·group·size:··200·····Converged:··········Yes 
156 Mean·group·size:··200.0 
157 ----------------------------------------------------------- 
158 ············Coef.···Std.Err.····z·····P&gt;|z|··[0.025··0.975] 
159 ----------------------------------------------------------- 
160 Intercept···-0.035·····0.149··-0.232··0.817··-0.326···0.257 
161 group1·Var···3.917·····0.112 
162 group2·Var···8.742·····0.063 
163 ========================================================== 
  
164 </pre></div></div> 
165 </div> 
166 <p>If·we·wish·to·avoid·the·formula·interface,·we·can·fit·the·same·model·by·building·the·design·matrices·manually.</p>144 <p>If·we·wish·to·avoid·the·formula·interface,·we·can·fit·the·same·model·by·building·the·design·matrices·manually.</p>
167 <div·class="nbinput·nblast·docutils·container">145 <div·class="nbinput·nblast·docutils·container">
168 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:146 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
169 </pre></div>147 </pre></div>
170 </div>148 </div>
171 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">f</span><span·class="p">(</span><span·class="n">x</span><span·class="p">):</span>149 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="k">def</span>·<span·class="nf">f</span><span·class="p">(</span><span·class="n">x</span><span·class="p">):</span>
172 ····<span·class="n">n</span>·<span·class="o">=</span>·<span·class="n">x</span><span·class="o">.</span><span·class="n">shape</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">]</span>150 ····<span·class="n">n</span>·<span·class="o">=</span>·<span·class="n">x</span><span·class="o">.</span><span·class="n">shape</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">]</span>
173 ····<span·class="n">g2</span>·<span·class="o">=</span>·<span·class="n">x</span><span·class="o">.</span><span·class="n">group2</span>151 ····<span·class="n">g2</span>·<span·class="o">=</span>·<span·class="n">x</span><span·class="o">.</span><span·class="n">group2</span>
174 ····<span·class="n">u</span>·<span·class="o">=</span>·<span·class="n">g2</span><span·class="o">.</span><span·class="n">unique</span><span·class="p">()</span>152 ····<span·class="n">u</span>·<span·class="o">=</span>·<span·class="n">g2</span><span·class="o">.</span><span·class="n">unique</span><span·class="p">()</span>
175 ····<span·class="n">u</span><span·class="o">.</span><span·class="n">sort</span><span·class="p">()</span>153 ····<span·class="n">u</span><span·class="o">.</span><span·class="n">sort</span><span·class="p">()</span>
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181 ········<span·class="n">mat</span><span·class="p">[</span><span·class="n">i</span><span·class="p">,</span>·<span·class="n">uv</span><span·class="p">[</span><span·class="n">g2</span><span·class="o">.</span><span·class="n">iloc</span><span·class="p">[</span><span·class="n">i</span><span·class="p">]]]</span>·<span·class="o">=</span>·<span·class="mi">1</span>158 ········<span·class="n">mat</span><span·class="p">[</span><span·class="n">i</span><span·class="p">,</span>·<span·class="n">uv</span><span·class="p">[</span><span·class="n">g2</span><span·class="o">.</span><span·class="n">iloc</span><span·class="p">[</span><span·class="n">i</span><span·class="p">]]]</span>·<span·class="o">=</span>·<span·class="mi">1</span>
182 ····<span·class="n">colnames</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;</span><span·class="si">%d</span><span·class="s2">&quot;</span>·<span·class="o">%</span>·<span·class="n">z</span>·<span·class="k">for</span>·<span·class="n">z</span>·<span·class="ow">in</span>·<span·class="n">u</span><span·class="p">]</span>159 ····<span·class="n">colnames</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;</span><span·class="si">%d</span><span·class="s2">&quot;</span>·<span·class="o">%</span>·<span·class="n">z</span>·<span·class="k">for</span>·<span·class="n">z</span>·<span·class="ow">in</span>·<span·class="n">u</span><span·class="p">]</span>
183 ····<span·class="k">return</span>·<span·class="n">mat</span><span·class="p">,</span>·<span·class="n">colnames</span>160 ····<span·class="k">return</span>·<span·class="n">mat</span><span·class="p">,</span>·<span·class="n">colnames</span>
184 </pre></div>161 </pre></div>
185 </div>162 </div>
186 </div>163 </div>
187 <p>Then·we·set·up·the·variance·components·using·the·VCSpec·class.</p>164 <p>Then·we·set·up·the·variance·components·using·the·VCSpec·class.</p>
188 <div·class="nbinput·docutils·container">165 <div·class="nbinput·nblast·docutils·container">
189 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[7]:166 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
190 </pre></div>167 </pre></div>
191 </div>168 </div>
192 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">vcm</span>·<span·class="o">=</span>·<span·class="n">df</span><span·class="o">.</span><span·class="n">groupby</span><span·class="p">(</span><span·class="s2">&quot;group1&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">apply</span><span·class="p">(</span><span·class="n">f</span><span·class="p">)</span><span·class="o">.</span><span·class="n">to_list</span><span·class="p">()</span>169 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">vcm</span>·<span·class="o">=</span>·<span·class="n">df</span><span·class="o">.</span><span·class="n">groupby</span><span·class="p">(</span><span·class="s2">&quot;group1&quot;</span><span·class="p">)</span><span·class="o">.</span><span·class="n">apply</span><span·class="p">(</span><span·class="n">f</span><span·class="p">)</span><span·class="o">.</span><span·class="n">to_list</span><span·class="p">()</span>
193 <span·class="n">mats</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">x</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">]</span>·<span·class="k">for</span>·<span·class="n">x</span>·<span·class="ow">in</span>·<span·class="n">vcm</span><span·class="p">]</span>170 <span·class="n">mats</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">x</span><span·class="p">[</span><span·class="mi">0</span><span·class="p">]</span>·<span·class="k">for</span>·<span·class="n">x</span>·<span·class="ow">in</span>·<span·class="n">vcm</span><span·class="p">]</span>
194 <span·class="n">colnames</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">x</span><span·class="p">[</span><span·class="mi">1</span><span·class="p">]</span>·<span·class="k">for</span>·<span·class="n">x</span>·<span·class="ow">in</span>·<span·class="n">vcm</span><span·class="p">]</span>171 <span·class="n">colnames</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="n">x</span><span·class="p">[</span><span·class="mi">1</span><span·class="p">]</span>·<span·class="k">for</span>·<span·class="n">x</span>·<span·class="ow">in</span>·<span·class="n">vcm</span><span·class="p">]</span>
195 <span·class="n">names</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;group2&quot;</span><span·class="p">]</span>172 <span·class="n">names</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;group2&quot;</span><span·class="p">]</span>
196 <span·class="n">vcs</span>·<span·class="o">=</span>·<span·class="n">VCSpec</span><span·class="p">(</span><span·class="n">names</span><span·class="p">,</span>·<span·class="p">[</span><span·class="n">colnames</span><span·class="p">],</span>·<span·class="p">[</span><span·class="n">mats</span><span·class="p">])</span>173 <span·class="n">vcs</span>·<span·class="o">=</span>·<span·class="n">VCSpec</span><span·class="p">(</span><span·class="n">names</span><span·class="p">,</span>·<span·class="p">[</span><span·class="n">colnames</span><span·class="p">],</span>·<span·class="p">[</span><span·class="n">mats</span><span·class="p">])</span>
197 </pre></div>174 </pre></div>
198 </div>175 </div>
199 </div>176 </div>
200 <div·class="nboutput·nblast·docutils·container"> 
201 <div·class="prompt·empty·docutils·container"> 
202 </div> 
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5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Variance·Component·Analysis8 ····*·Variance·Component·Analysis
9 *\x8**\x8**\x8**\x8**\x8**\x8*·V\x8Va\x8ar\x8ri\x8ia\x8an\x8nc\x8ce\x8e·C\x8Co\x8om\x8mp\x8po\x8on\x8ne\x8en\x8nt\x8t·A\x8An\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·V\x8Va\x8ar\x8ri\x8ia\x8an\x8nc\x8ce\x8e·C\x8Co\x8om\x8mp\x8po\x8on\x8ne\x8en\x8nt\x8t·A\x8An\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 This·notebook·illustrates·variance·components·analysis·for·two-level·nested·and10 This·notebook·illustrates·variance·components·analysis·for·two-level·nested·and
11 crossed·designs.11 crossed·designs.
12 [1]:12 [·]:
13 import·numpy·as·np13 import·numpy·as·np
14 import·statsmodels.api·as·sm14 import·statsmodels.api·as·sm
15 from·statsmodels.regression.mixed_linear_model·import·VCSpec15 from·statsmodels.regression.mixed_linear_model·import·VCSpec
16 import·pandas·as·pd16 import·pandas·as·pd
17 Make·the·notebook·reproducible17 Make·the·notebook·reproducible
18 [2]:18 [·]:
19 np.random.seed(3123)19 np.random.seed(3123)
20 *\x8**\x8**\x8**\x8**\x8*·N\x8Ne\x8es\x8st\x8te\x8ed\x8d·a\x8an\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8**\x8*·N\x8Ne\x8es\x8st\x8te\x8ed\x8d·a\x8an\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
21 In·our·discussion·below,·“Group·2”·is·nested·within·“Group·1”.·As·a·concrete21 In·our·discussion·below,·“Group·2”·is·nested·within·“Group·1”.·As·a·concrete
22 example,·“Group·1”·might·be·school·districts,·with·“Group·2”·being·individual22 example,·“Group·1”·might·be·school·districts,·with·“Group·2”·being·individual
23 schools.·The·function·below·generates·data·from·such·a·population.·In·a·nested23 schools.·The·function·below·generates·data·from·such·a·population.·In·a·nested
24 analysis,·the·group·2·labels·that·are·nested·within·different·group·1·labels24 analysis,·the·group·2·labels·that·are·nested·within·different·group·1·labels
25 are·treated·as·independent·groups,·even·if·they·have·the·same·label.·For25 are·treated·as·independent·groups,·even·if·they·have·the·same·label.·For
26 example,·two·schools·labeled·“school·1”·that·are·in·two·different·school26 example,·two·schools·labeled·“school·1”·that·are·in·two·different·school
27 districts·are·treated·as·independent·schools,·even·though·they·have·the·same27 districts·are·treated·as·independent·schools,·even·though·they·have·the·same
28 label.28 label.
29 [3]:29 [·]:
30 def·generate_nested(30 def·generate_nested(
31 ····n_group1=200,·n_group2=20,·n_rep=10,·group1_sd=2,·group2_sd=3,31 ····n_group1=200,·n_group2=20,·n_rep=10,·group1_sd=2,·group2_sd=3,
32 unexplained_sd=432 unexplained_sd=4
33 ):33 ):
  
34 ····#·Group·1·indicators34 ····#·Group·1·indicators
35 ····group1·=·np.kron(np.arange(n_group1),·np.ones(n_group2·*·n_rep))35 ····group1·=·np.kron(np.arange(n_group1),·np.ones(n_group2·*·n_rep))
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50 ····e·=·unexplained_sd·*·np.random.normal(size=n_group1·*·n_group2·*·n_rep)50 ····e·=·unexplained_sd·*·np.random.normal(size=n_group1·*·n_group2·*·n_rep)
51 ····y·=·effects1·+·effects2·+·e51 ····y·=·effects1·+·effects2·+·e
  
52 ····df·=·pd.DataFrame({"y":·y,·"group1":·group1,·"group2":·group2})52 ····df·=·pd.DataFrame({"y":·y,·"group1":·group1,·"group2":·group2})
  
53 ····return·df53 ····return·df
54 Generate·a·data·set·to·analyze.54 Generate·a·data·set·to·analyze.
55 [4]:55 [·]:
56 df·=·generate_nested()56 df·=·generate_nested()
57 Using·all·the·default·arguments·for·generate_nested,·the·population·values·of57 Using·all·the·default·arguments·for·generate_nested,·the·population·values·of
58 “group·1·Var”·and·“group·2·Var”·are·2^2=4·and·3^2=9,·respectively.·The58 “group·1·Var”·and·“group·2·Var”·are·2^2=4·and·3^2=9,·respectively.·The
59 unexplained·variance,·listed·as·“scale”·at·the·top·of·the·summary·table,·has59 unexplained·variance,·listed·as·“scale”·at·the·top·of·the·summary·table,·has
60 population·value·4^2=16.60 population·value·4^2=16.
61 [5]:61 [·]:
62 model1·=·sm.MixedLM.from_formula(62 model1·=·sm.MixedLM.from_formula(
63 ····"y·~·1",63 ····"y·~·1",
64 ····re_formula="1",64 ····re_formula="1",
65 ····vc_formula={"group2":·"0·+·C(group2)"},65 ····vc_formula={"group2":·"0·+·C(group2)"},
66 ····groups="group1",66 ····groups="group1",
67 ····data=df,67 ····data=df,
68 )68 )
69 result1·=·model1.fit()69 result1·=·model1.fit()
70 print(result1.summary())70 print(result1.summary())
71 ··········Mixed·Linear·Model·Regression·Results 
72 ========================================================== 
73 Model:············MixedLM·Dependent·Variable:·y 
74 No.·Observations:·40000···Method:·············REML 
75 No.·Groups:·······200·····Scale:··············15.8825 
76 Min.·group·size:··200·····Log-Likelihood:·····-116022.3805 
77 Max.·group·size:··200·····Converged:··········Yes 
78 Mean·group·size:··200.0 
79 ----------------------------------------------------------- 
80 ············Coef.···Std.Err.····z·····P>|z|··[0.025··0.975] 
81 ----------------------------------------------------------- 
82 Intercept···-0.035·····0.149··-0.232··0.817··-0.326···0.257 
83 group1·Var···3.917·····0.112 
84 group2·Var···8.742·····0.063 
85 ========================================================== 
86 If·we·wish·to·avoid·the·formula·interface,·we·can·fit·the·same·model·by71 If·we·wish·to·avoid·the·formula·interface,·we·can·fit·the·same·model·by
87 building·the·design·matrices·manually.72 building·the·design·matrices·manually.
88 [6]:73 [·]:
89 def·f(x):74 def·f(x):
90 ····n·=·x.shape[0]75 ····n·=·x.shape[0]
91 ····g2·=·x.group276 ····g2·=·x.group2
92 ····u·=·g2.unique()77 ····u·=·g2.unique()
93 ····u.sort()78 ····u.sort()
94 ····uv·=·{v:·k·for·k,·v·in·enumerate(u)}79 ····uv·=·{v:·k·for·k,·v·in·enumerate(u)}
95 ····mat·=·np.zeros((n,·len(u)))80 ····mat·=·np.zeros((n,·len(u)))
96 ····for·i·in·range(n):81 ····for·i·in·range(n):
97 ········mat[i,·uv[g2.iloc[i]]]·=·182 ········mat[i,·uv[g2.iloc[i]]]·=·1
98 ····colnames·=·["%d"·%·z·for·z·in·u]83 ····colnames·=·["%d"·%·z·for·z·in·u]
99 ····return·mat,·colnames84 ····return·mat,·colnames
100 Then·we·set·up·the·variance·components·using·the·VCSpec·class.85 Then·we·set·up·the·variance·components·using·the·VCSpec·class.
101 [7]:86 [·]:
102 vcm·=·df.groupby("group1").apply(f).to_list()87 vcm·=·df.groupby("group1").apply(f).to_list()
103 mats·=·[x[0]·for·x·in·vcm]88 mats·=·[x[0]·for·x·in·vcm]
104 colnames·=·[x[1]·for·x·in·vcm]89 colnames·=·[x[1]·for·x·in·vcm]
105 names·=·["group2"]90 names·=·["group2"]
106 vcs·=·VCSpec(names,·[colnames],·[mats])91 vcs·=·VCSpec(names,·[colnames],·[mats])
107 /tmp/ipykernel_nnnnnnn/1119967950.py:1:·DeprecationWarning: 
108 DataFrameGroupBy.apply·operated·on·the·grouping·columns.·This·behavior·is 
109 deprecated,·and·in·a·future·version·of·pandas·the·grouping·columns·will·be 
110 excluded·from·the·operation.·Either·pass·`include_groups=False`·to·exclude·the 
111 groupings·or·explicitly·select·the·grouping·columns·after·groupby·to·silence 
112 this·warning. 
113 ··vcm·=·df.groupby("group1").apply(f).to_list() 
114 Finally·we·fit·the·model.·It·can·be·seen·that·the·results·of·the·two·fits·are92 Finally·we·fit·the·model.·It·can·be·seen·that·the·results·of·the·two·fits·are
115 identical.93 identical.
116 [8]:94 [·]:
117 oo·=·np.ones(df.shape[0])95 oo·=·np.ones(df.shape[0])
118 model2·=·sm.MixedLM(df.y,·oo,·exog_re=oo,·groups=df.group1,·exog_vc=vcs)96 model2·=·sm.MixedLM(df.y,·oo,·exog_re=oo,·groups=df.group1,·exog_vc=vcs)
119 result2·=·model2.fit()97 result2·=·model2.fit()
120 print(result2.summary())98 print(result2.summary())
121 ··········Mixed·Linear·Model·Regression·Results 
122 ========================================================== 
123 Model:············MixedLM·Dependent·Variable:·y 
124 No.·Observations:·40000···Method:·············REML 
125 No.·Groups:·······200·····Scale:··············15.8825 
126 Min.·group·size:··200·····Log-Likelihood:·····-116022.3805 
127 Max.·group·size:··200·····Converged:··········Yes 
128 Mean·group·size:··200.0 
129 ----------------------------------------------------------- 
130 ············Coef.···Std.Err.····z·····P>|z|··[0.025··0.975] 
131 ----------------------------------------------------------- 
132 const·······-0.035·····0.149··-0.232··0.817··-0.326···0.257 
133 x_re1·Var····3.917·····0.112 
134 group2·Var···8.742·····0.063 
135 ========================================================== 
136 *\x8**\x8**\x8**\x8**\x8*·C\x8Cr\x8ro\x8os\x8ss\x8se\x8ed\x8d·a\x8an\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*99 *\x8**\x8**\x8**\x8**\x8*·C\x8Cr\x8ro\x8os\x8ss\x8se\x8ed\x8d·a\x8an\x8na\x8al\x8ly\x8ys\x8si\x8is\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
137 In·a·crossed·analysis,·the·levels·of·one·group·can·occur·in·any·combination100 In·a·crossed·analysis,·the·levels·of·one·group·can·occur·in·any·combination
138 with·the·levels·of·the·another·group.·The·groups·in·Statsmodels·MixedLM·are101 with·the·levels·of·the·another·group.·The·groups·in·Statsmodels·MixedLM·are
139 always·nested,·but·it·is·possible·to·fit·a·crossed·model·by·having·only·one102 always·nested,·but·it·is·possible·to·fit·a·crossed·model·by·having·only·one
140 group,·and·specifying·all·random·effects·as·variance·components.·Many,·but·not103 group,·and·specifying·all·random·effects·as·variance·components.·Many,·but·not
141 all·crossed·models·can·be·fit·in·this·way.·The·function·below·generates·a104 all·crossed·models·can·be·fit·in·this·way.·The·function·below·generates·a
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58 ········<div·class="bodywrapper">58 ········<div·class="bodywrapper">
59 ··········<div·class="body"·role="main">59 ··········<div·class="body"·role="main">
60 ············60 ············
61 ··<section·id="Weighted-Least-Squares">61 ··<section·id="Weighted-Least-Squares">
62 <h1>Weighted·Least·Squares<a·class="headerlink"·href="#Weighted-Least-Squares"·title="Link·to·this·heading">¶</a></h1>62 <h1>Weighted·Least·Squares<a·class="headerlink"·href="#Weighted-Least-Squares"·title="Link·to·this·heading">¶</a></h1>
63 <div·class="nbinput·nblast·docutils·container">63 <div·class="nbinput·nblast·docutils·container">
64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[1]:64 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
65 </pre></div>65 </pre></div>
66 </div>66 </div>
67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline67 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="o">%</span><span·class="k">matplotlib</span>·inline
68 </pre></div>68 </pre></div>
69 </div>69 </div>
70 </div>70 </div>
71 <div·class="nbinput·nblast·docutils·container">71 <div·class="nbinput·nblast·docutils·container">
72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[2]:72 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
73 </pre></div>73 </pre></div>
74 </div>74 </div>
75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>75 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="kn">import</span>·<span·class="nn">matplotlib.pyplot</span>·<span·class="k">as</span>·<span·class="nn">plt</span>
76 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>76 <span·class="kn">import</span>·<span·class="nn">numpy</span>·<span·class="k">as</span>·<span·class="nn">np</span>
77 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>77 <span·class="kn">import</span>·<span·class="nn">statsmodels.api</span>·<span·class="k">as</span>·<span·class="nn">sm</span>
78 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>78 <span·class="kn">from</span>·<span·class="nn">scipy</span>·<span·class="kn">import</span>·<span·class="n">stats</span>
79 <span·class="kn">from</span>·<span·class="nn">statsmodels.iolib.table</span>·<span·class="kn">import</span>·<span·class="n">SimpleTable</span><span·class="p">,</span>·<span·class="n">default_txt_fmt</span>79 <span·class="kn">from</span>·<span·class="nn">statsmodels.iolib.table</span>·<span·class="kn">import</span>·<span·class="n">SimpleTable</span><span·class="p">,</span>·<span·class="n">default_txt_fmt</span>
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89 <p>Model·assumptions:</p>89 <p>Model·assumptions:</p>
90 <ul·class="simple">90 <ul·class="simple">
91 <li><p>Misspecification:·true·model·is·quadratic,·estimate·only·linear</p></li>91 <li><p>Misspecification:·true·model·is·quadratic,·estimate·only·linear</p></li>
92 <li><p>Independent·noise/error·term</p></li>92 <li><p>Independent·noise/error·term</p></li>
93 <li><p>Two·groups·for·error·variance,·low·and·high·variance·groups</p></li>93 <li><p>Two·groups·for·error·variance,·low·and·high·variance·groups</p></li>
94 </ul>94 </ul>
95 <div·class="nbinput·nblast·docutils·container">95 <div·class="nbinput·nblast·docutils·container">
96 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[3]:96 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
97 </pre></div>97 </pre></div>
98 </div>98 </div>
99 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">nsample</span>·<span·class="o">=</span>·<span·class="mi">50</span>99 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">nsample</span>·<span·class="o">=</span>·<span·class="mi">50</span>
100 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">20</span><span·class="p">,</span>·<span·class="n">nsample</span><span·class="p">)</span>100 <span·class="n">x</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">linspace</span><span·class="p">(</span><span·class="mi">0</span><span·class="p">,</span>·<span·class="mi">20</span><span·class="p">,</span>·<span·class="n">nsample</span><span·class="p">)</span>
101 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">column_stack</span><span·class="p">((</span><span·class="n">x</span><span·class="p">,</span>·<span·class="p">(</span><span·class="n">x</span>·<span·class="o">-</span>·<span·class="mi">5</span><span·class="p">)</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">))</span>101 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">column_stack</span><span·class="p">((</span><span·class="n">x</span><span·class="p">,</span>·<span·class="p">(</span><span·class="n">x</span>·<span·class="o">-</span>·<span·class="mi">5</span><span·class="p">)</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">))</span>
102 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">X</span><span·class="p">)</span>102 <span·class="n">X</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">add_constant</span><span·class="p">(</span><span·class="n">X</span><span·class="p">)</span>
103 <span·class="n">beta</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mf">5.0</span><span·class="p">,</span>·<span·class="mf">0.5</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mf">0.01</span><span·class="p">]</span>103 <span·class="n">beta</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="mf">5.0</span><span·class="p">,</span>·<span·class="mf">0.5</span><span·class="p">,</span>·<span·class="o">-</span><span·class="mf">0.01</span><span·class="p">]</span>
Offset 111, 83 lines modifiedOffset 111, 42 lines modified
111 </pre></div>111 </pre></div>
112 </div>112 </div>
113 </div>113 </div>
114 </section>114 </section>
115 <section·id="WLS-knowing-the-true-variance-ratio-of-heteroscedasticity">115 <section·id="WLS-knowing-the-true-variance-ratio-of-heteroscedasticity">
116 <h3>WLS·knowing·the·true·variance·ratio·of·heteroscedasticity<a·class="headerlink"·href="#WLS-knowing-the-true-variance-ratio-of-heteroscedasticity"·title="Link·to·this·heading">¶</a></h3>116 <h3>WLS·knowing·the·true·variance·ratio·of·heteroscedasticity<a·class="headerlink"·href="#WLS-knowing-the-true-variance-ratio-of-heteroscedasticity"·title="Link·to·this·heading">¶</a></h3>
117 <p>In·this·example,·<code·class="docutils·literal·notranslate"><span·class="pre">w</span></code>·is·the·standard·deviation·of·the·error.·<code·class="docutils·literal·notranslate"><span·class="pre">WLS</span></code>·requires·that·the·weights·are·proportional·to·the·inverse·of·the·error·variance.</p>117 <p>In·this·example,·<code·class="docutils·literal·notranslate"><span·class="pre">w</span></code>·is·the·standard·deviation·of·the·error.·<code·class="docutils·literal·notranslate"><span·class="pre">WLS</span></code>·requires·that·the·weights·are·proportional·to·the·inverse·of·the·error·variance.</p>
118 <div·class="nbinput·docutils·container">118 <div·class="nbinput·nblast·docutils·container">
119 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[4]:119 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
120 </pre></div>120 </pre></div>
121 </div>121 </div>
122 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">mod_wls</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">WLS</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">X</span><span·class="p">,</span>·<span·class="n">weights</span><span·class="o">=</span><span·class="mf">1.0</span>·<span·class="o">/</span>·<span·class="p">(</span><span·class="n">w</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">))</span>122 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">mod_wls</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">WLS</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">X</span><span·class="p">,</span>·<span·class="n">weights</span><span·class="o">=</span><span·class="mf">1.0</span>·<span·class="o">/</span>·<span·class="p">(</span><span·class="n">w</span>·<span·class="o">**</span>·<span·class="mi">2</span><span·class="p">))</span>
123 <span·class="n">res_wls</span>·<span·class="o">=</span>·<span·class="n">mod_wls</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>123 <span·class="n">res_wls</span>·<span·class="o">=</span>·<span·class="n">mod_wls</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
124 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res_wls</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>124 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res_wls</span><span·class="o">.</span><span·class="n">summary</span><span·class="p">())</span>
125 </pre></div>125 </pre></div>
126 </div>126 </div>
127 </div>127 </div>
128 <div·class="nboutput·nblast·docutils·container"> 
129 <div·class="prompt·empty·docutils·container"> 
130 </div> 
131 <div·class="output_area·docutils·container"> 
132 <div·class="highlight"><pre> 
133 ····························WLS·Regression·Results 
134 ============================================================================== 
135 Dep.·Variable:······················y···R-squared:·······················0.927 
136 Model:····························WLS···Adj.·R-squared:··················0.926 
137 Method:·················Least·Squares···F-statistic:·····················613.2 
138 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········5.44e-29 
139 Time:························13:13:47···Log-Likelihood:················-51.136 
140 No.·Observations:··················50···AIC:·····························106.3 
141 Df·Residuals:······················48···BIC:·····························110.1 
142 Df·Model:···························1 
143 Covariance·Type:············nonrobust 
144 ============================================================================== 
145 ·················coef····std·err··········t······P&gt;|t|······[0.025······0.975] 
146 ------------------------------------------------------------------------------ 
147 const··········5.2469······0.143·····36.790······0.000·······4.960·······5.534 
148 x1·············0.4466······0.018·····24.764······0.000·······0.410·······0.483 
149 ============================================================================== 
150 Omnibus:························0.407···Durbin-Watson:···················2.317 
151 Prob(Omnibus):··················0.816···Jarque-Bera·(JB):················0.103 
152 Skew:··························-0.104···Prob(JB):························0.950 
153 Kurtosis:·······················3.075···Cond.·No.·························14.6 
154 ============================================================================== 
  
155 Notes: 
156 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is·correctly·specified. 
157 </pre></div></div> 
158 </div> 
159 </section>128 </section>
160 </section>129 </section>
161 <section·id="OLS-vs.-WLS">130 <section·id="OLS-vs.-WLS">
162 <h2>OLS·vs.·WLS<a·class="headerlink"·href="#OLS-vs.-WLS"·title="Link·to·this·heading">¶</a></h2>131 <h2>OLS·vs.·WLS<a·class="headerlink"·href="#OLS-vs.-WLS"·title="Link·to·this·heading">¶</a></h2>
163 <p>Estimate·an·OLS·model·for·comparison:</p>132 <p>Estimate·an·OLS·model·for·comparison:</p>
164 <div·class="nbinput·docutils·container">133 <div·class="nbinput·nblast·docutils·container">
165 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[5]:134 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
166 </pre></div>135 </pre></div>
167 </div>136 </div>
168 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res_ols</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">OLS</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">X</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>137 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">res_ols</span>·<span·class="o">=</span>·<span·class="n">sm</span><span·class="o">.</span><span·class="n">OLS</span><span·class="p">(</span><span·class="n">y</span><span·class="p">,</span>·<span·class="n">X</span><span·class="p">)</span><span·class="o">.</span><span·class="n">fit</span><span·class="p">()</span>
169 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res_ols</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>138 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res_ols</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>
170 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res_wls</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>139 <span·class="nb">print</span><span·class="p">(</span><span·class="n">res_wls</span><span·class="o">.</span><span·class="n">params</span><span·class="p">)</span>
171 </pre></div>140 </pre></div>
172 </div>141 </div>
173 </div>142 </div>
174 <div·class="nboutput·nblast·docutils·container"> 
175 <div·class="prompt·empty·docutils·container"> 
176 </div> 
177 <div·class="output_area·docutils·container"> 
178 <div·class="highlight"><pre> 
179 [5.24256099·0.43486879] 
180 [5.24685499·0.44658241] 
181 </pre></div></div> 
182 </div> 
183 <p>Compare·the·WLS·standard·errors·to·heteroscedasticity·corrected·OLS·standard·errors:</p>143 <p>Compare·the·WLS·standard·errors·to·heteroscedasticity·corrected·OLS·standard·errors:</p>
184 <div·class="nbinput·docutils·container">144 <div·class="nbinput·nblast·docutils·container">
185 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[6]:145 <div·class="prompt·highlight-none·notranslate"><div·class="highlight"><pre><span></span>[·]:
186 </pre></div>146 </pre></div>
187 </div>147 </div>
188 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">se</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">vstack</span><span·class="p">(</span>148 <div·class="input_area·highlight-ipython3·notranslate"><div·class="highlight"><pre><span></span><span·class="n">se</span>·<span·class="o">=</span>·<span·class="n">np</span><span·class="o">.</span><span·class="n">vstack</span><span·class="p">(</span>
189 ····<span·class="p">[</span>149 ····<span·class="p">[</span>
190 ········<span·class="p">[</span><span·class="n">res_wls</span><span·class="o">.</span><span·class="n">bse</span><span·class="p">],</span>150 ········<span·class="p">[</span><span·class="n">res_wls</span><span·class="o">.</span><span·class="n">bse</span><span·class="p">],</span>
191 ········<span·class="p">[</span><span·class="n">res_ols</span><span·class="o">.</span><span·class="n">bse</span><span·class="p">],</span>151 ········<span·class="p">[</span><span·class="n">res_ols</span><span·class="o">.</span><span·class="n">bse</span><span·class="p">],</span>
192 ········<span·class="p">[</span><span·class="n">res_ols</span><span·class="o">.</span><span·class="n">HC0_se</span><span·class="p">],</span>152 ········<span·class="p">[</span><span·class="n">res_ols</span><span·class="o">.</span><span·class="n">HC0_se</span><span·class="p">],</span>
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200 <span·class="n">colnames</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;x1&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;const&quot;</span><span·class="p">]</span>159 <span·class="n">colnames</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;x1&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;const&quot;</span><span·class="p">]</span>
201 <span·class="n">rownames</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;WLS&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS_HC0&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS_HC1&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS_HC3&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS_HC3&quot;</span><span·class="p">]</span>160 <span·class="n">rownames</span>·<span·class="o">=</span>·<span·class="p">[</span><span·class="s2">&quot;WLS&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS_HC0&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS_HC1&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS_HC3&quot;</span><span·class="p">,</span>·<span·class="s2">&quot;OLS_HC3&quot;</span><span·class="p">]</span>
202 <span·class="n">tabl</span>·<span·class="o">=</span>·<span·class="n">SimpleTable</span><span·class="p">(</span><span·class="n">se</span><span·class="p">,</span>·<span·class="n">colnames</span><span·class="p">,</span>·<span·class="n">rownames</span><span·class="p">,</span>·<span·class="n">txt_fmt</span><span·class="o">=</span><span·class="n">default_txt_fmt</span><span·class="p">)</span>161 <span·class="n">tabl</span>·<span·class="o">=</span>·<span·class="n">SimpleTable</span><span·class="p">(</span><span·class="n">se</span><span·class="p">,</span>·<span·class="n">colnames</span><span·class="p">,</span>·<span·class="n">rownames</span><span·class="p">,</span>·<span·class="n">txt_fmt</span><span·class="o">=</span><span·class="n">default_txt_fmt</span><span·class="p">)</span>
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3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|3 ····*·_\x8m_\x8o_\x8d_\x8u_\x8l_\x8e_\x8s·|
4 ····*·_\x8n_\x8e_\x8x_\x8t·|4 ····*·_\x8n_\x8e_\x8x_\x8t·|
5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|5 ····*·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|
6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»6 ····*·_\x8s_\x8t_\x8a_\x8t_\x8s_\x8m_\x8o_\x8d_\x8e_\x8l_\x8s_\x8·_\x80_\x8._\x81_\x84_\x8._\x85_\x8+_\x8d_\x8f_\x8s_\x8g·»
7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»7 ····*·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s·»
8 ····*·Weighted·Least·Squares8 ····*·Weighted·Least·Squares
9 *\x8**\x8**\x8**\x8**\x8**\x8*·W\x8We\x8ei\x8ig\x8gh\x8ht\x8te\x8ed\x8d·L\x8Le\x8ea\x8as\x8st\x8t·S\x8Sq\x8qu\x8ua\x8ar\x8re\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*9 *\x8**\x8**\x8**\x8**\x8**\x8*·W\x8We\x8ei\x8ig\x8gh\x8ht\x8te\x8ed\x8d·L\x8Le\x8ea\x8as\x8st\x8t·S\x8Sq\x8qu\x8ua\x8ar\x8re\x8es\x8s_\x8?\x8·*\x8**\x8**\x8**\x8**\x8**\x8*
10 [1]:10 [·]:
11 %matplotlib·inline11 %matplotlib·inline
12 [2]:12 [·]:
13 import·matplotlib.pyplot·as·plt13 import·matplotlib.pyplot·as·plt
14 import·numpy·as·np14 import·numpy·as·np
15 import·statsmodels.api·as·sm15 import·statsmodels.api·as·sm
16 from·scipy·import·stats16 from·scipy·import·stats
17 from·statsmodels.iolib.table·import·SimpleTable,·default_txt_fmt17 from·statsmodels.iolib.table·import·SimpleTable,·default_txt_fmt
  
18 np.random.seed(1024)18 np.random.seed(1024)
19 *\x8**\x8**\x8**\x8**\x8*·W\x8WL\x8LS\x8S·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*19 *\x8**\x8**\x8**\x8**\x8*·W\x8WL\x8LS\x8S·E\x8Es\x8st\x8ti\x8im\x8ma\x8at\x8ti\x8io\x8on\x8n_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
20 *\x8**\x8**\x8**\x8*·A\x8Ar\x8rt\x8ti\x8if\x8fi\x8ic\x8ci\x8ia\x8al\x8l·d\x8da\x8at\x8ta\x8a:\x8:·H\x8He\x8et\x8te\x8er\x8ro\x8os\x8sc\x8ce\x8ed\x8da\x8as\x8st\x8ti\x8ic\x8ci\x8it\x8ty\x8y·2\x82·g\x8gr\x8ro\x8ou\x8up\x8ps\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*20 *\x8**\x8**\x8**\x8*·A\x8Ar\x8rt\x8ti\x8if\x8fi\x8ic\x8ci\x8ia\x8al\x8l·d\x8da\x8at\x8ta\x8a:\x8:·H\x8He\x8et\x8te\x8er\x8ro\x8os\x8sc\x8ce\x8ed\x8da\x8as\x8st\x8ti\x8ic\x8ci\x8it\x8ty\x8y·2\x82·g\x8gr\x8ro\x8ou\x8up\x8ps\x8s_\x8?\x8·*\x8**\x8**\x8**\x8*
21 Model·assumptions:21 Model·assumptions:
22 ····*·Misspecification:·true·model·is·quadratic,·estimate·only·linear22 ····*·Misspecification:·true·model·is·quadratic,·estimate·only·linear
23 ····*·Independent·noise/error·term23 ····*·Independent·noise/error·term
24 ····*·Two·groups·for·error·variance,·low·and·high·variance·groups24 ····*·Two·groups·for·error·variance,·low·and·high·variance·groups
25 [3]:25 [·]:
26 nsample·=·5026 nsample·=·50
27 x·=·np.linspace(0,·20,·nsample)27 x·=·np.linspace(0,·20,·nsample)
28 X·=·np.column_stack((x,·(x·-·5)·**·2))28 X·=·np.column_stack((x,·(x·-·5)·**·2))
29 X·=·sm.add_constant(X)29 X·=·sm.add_constant(X)
30 beta·=·[5.0,·0.5,·-0.01]30 beta·=·[5.0,·0.5,·-0.01]
31 sig·=·0.531 sig·=·0.5
32 w·=·np.ones(nsample)32 w·=·np.ones(nsample)
Offset 35, 55 lines modifiedOffset 35, 27 lines modified
35 y_true·=·np.dot(X,·beta)35 y_true·=·np.dot(X,·beta)
36 e·=·np.random.normal(size=nsample)36 e·=·np.random.normal(size=nsample)
37 y·=·y_true·+·sig·*·w·*·e37 y·=·y_true·+·sig·*·w·*·e
38 X·=·X[:,·[0,·1]]38 X·=·X[:,·[0,·1]]
39 *\x8**\x8**\x8**\x8*·W\x8WL\x8LS\x8S·k\x8kn\x8no\x8ow\x8wi\x8in\x8ng\x8g·t\x8th\x8he\x8e·t\x8tr\x8ru\x8ue\x8e·v\x8va\x8ar\x8ri\x8ia\x8an\x8nc\x8ce\x8e·r\x8ra\x8at\x8ti\x8io\x8o·o\x8of\x8f·h\x8he\x8et\x8te\x8er\x8ro\x8os\x8sc\x8ce\x8ed\x8da\x8as\x8st\x8ti\x8ic\x8ci\x8it\x8ty\x8y_\x8?\x8·*\x8**\x8**\x8**\x8*39 *\x8**\x8**\x8**\x8*·W\x8WL\x8LS\x8S·k\x8kn\x8no\x8ow\x8wi\x8in\x8ng\x8g·t\x8th\x8he\x8e·t\x8tr\x8ru\x8ue\x8e·v\x8va\x8ar\x8ri\x8ia\x8an\x8nc\x8ce\x8e·r\x8ra\x8at\x8ti\x8io\x8o·o\x8of\x8f·h\x8he\x8et\x8te\x8er\x8ro\x8os\x8sc\x8ce\x8ed\x8da\x8as\x8st\x8ti\x8ic\x8ci\x8it\x8ty\x8y_\x8?\x8·*\x8**\x8**\x8**\x8*
40 In·this·example,·w·is·the·standard·deviation·of·the·error.·WLS·requires·that40 In·this·example,·w·is·the·standard·deviation·of·the·error.·WLS·requires·that
41 the·weights·are·proportional·to·the·inverse·of·the·error·variance.41 the·weights·are·proportional·to·the·inverse·of·the·error·variance.
42 [4]:42 [·]:
43 mod_wls·=·sm.WLS(y,·X,·weights=1.0·/·(w·**·2))43 mod_wls·=·sm.WLS(y,·X,·weights=1.0·/·(w·**·2))
44 res_wls·=·mod_wls.fit()44 res_wls·=·mod_wls.fit()
45 print(res_wls.summary())45 print(res_wls.summary())
46 ····························WLS·Regression·Results 
47 ============================================================================== 
48 Dep.·Variable:······················y···R-squared:·······················0.927 
49 Model:····························WLS···Adj.·R-squared:··················0.926 
50 Method:·················Least·Squares···F-statistic:·····················613.2 
51 Date:················Sun,·10·Aug·2025···Prob·(F-statistic):···········5.44e-29 
52 Time:························13:13:47···Log-Likelihood:················-51.136 
53 No.·Observations:··················50···AIC:·····························106.3 
54 Df·Residuals:······················48···BIC:·····························110.1 
55 Df·Model:···························1 
56 Covariance·Type:············nonrobust 
57 ============================================================================== 
58 ·················coef····std·err··········t······P>|t|······[0.025······0.975] 
59 ------------------------------------------------------------------------------ 
60 const··········5.2469······0.143·····36.790······0.000·······4.960·······5.534 
61 x1·············0.4466······0.018·····24.764······0.000·······0.410·······0.483 
62 ============================================================================== 
63 Omnibus:························0.407···Durbin-Watson:···················2.317 
64 Prob(Omnibus):··················0.816···Jarque-Bera·(JB):················0.103 
65 Skew:··························-0.104···Prob(JB):························0.950 
66 Kurtosis:·······················3.075···Cond.·No.·························14.6 
67 ============================================================================== 
  
68 Notes: 
69 [1]·Standard·Errors·assume·that·the·covariance·matrix·of·the·errors·is 
70 correctly·specified. 
71 *\x8**\x8**\x8**\x8**\x8*·O\x8OL\x8LS\x8S·v\x8vs\x8s.\x8.·W\x8WL\x8LS\x8S_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*46 *\x8**\x8**\x8**\x8**\x8*·O\x8OL\x8LS\x8S·v\x8vs\x8s.\x8.·W\x8WL\x8LS\x8S_\x8?\x8·*\x8**\x8**\x8**\x8**\x8*
72 Estimate·an·OLS·model·for·comparison:47 Estimate·an·OLS·model·for·comparison:
73 [5]:48 [·]:
74 res_ols·=·sm.OLS(y,·X).fit()49 res_ols·=·sm.OLS(y,·X).fit()
75 print(res_ols.params)50 print(res_ols.params)
76 print(res_wls.params)51 print(res_wls.params)
77 [5.24256099·0.43486879] 
78 [5.24685499·0.44658241] 
79 Compare·the·WLS·standard·errors·to·heteroscedasticity·corrected·OLS·standard52 Compare·the·WLS·standard·errors·to·heteroscedasticity·corrected·OLS·standard
80 errors:53 errors:
81 [6]:54 [·]:
82 se·=·np.vstack(55 se·=·np.vstack(
83 ····[56 ····[
84 ········[res_wls.bse],57 ········[res_wls.bse],
85 ········[res_ols.bse],58 ········[res_ols.bse],
86 ········[res_ols.HC0_se],59 ········[res_ols.HC0_se],
87 ········[res_ols.HC1_se],60 ········[res_ols.HC1_se],
88 ········[res_ols.HC2_se],61 ········[res_ols.HC2_se],
Offset 91, 36 lines modifiedOffset 63, 26 lines modified
91 ····]63 ····]
92 )64 )
93 se·=·np.round(se,·4)65 se·=·np.round(se,·4)
94 colnames·=·["x1",·"const"]66 colnames·=·["x1",·"const"]
95 rownames·=·["WLS",·"OLS",·"OLS_HC0",·"OLS_HC1",·"OLS_HC3",·"OLS_HC3"]67 rownames·=·["WLS",·"OLS",·"OLS_HC0",·"OLS_HC1",·"OLS_HC3",·"OLS_HC3"]
96 tabl·=·SimpleTable(se,·colnames,·rownames,·txt_fmt=default_txt_fmt)68 tabl·=·SimpleTable(se,·colnames,·rownames,·txt_fmt=default_txt_fmt)
97 print(tabl)69 print(tabl)
98 ===================== 
99 ··········x1···const 
100 --------------------- 
101 WLS·····0.1426··0.018 
102 OLS·····0.2707·0.0233 
103 OLS_HC0··0.194·0.0281 
104 OLS_HC1··0.198·0.0287 
105 OLS_HC3·0.2003··0.029 
106 OLS_HC3··0.207···0.03 
107 --------------------- 
108 Calculate·OLS·prediction·interval:70 Calculate·OLS·prediction·interval:
109 [7]:71 [·]:
110 covb·=·res_ols.cov_params()72 covb·=·res_ols.cov_params()
111 prediction_var·=·res_ols.mse_resid·+·(X·*·np.dot(covb,·X.T).T).sum(1)73 prediction_var·=·res_ols.mse_resid·+·(X·*·np.dot(covb,·X.T).T).sum(1)
112 prediction_std·=·np.sqrt(prediction_var)74 prediction_std·=·np.sqrt(prediction_var)
113 tppf·=·stats.t.ppf(0.975,·res_ols.df_resid)75 tppf·=·stats.t.ppf(0.975,·res_ols.df_resid)
114 [8]:76 [·]:
115 pred_ols·=·res_ols.get_prediction()77 pred_ols·=·res_ols.get_prediction()
116 iv_l_ols·=·pred_ols.summary_frame()["obs_ci_lower"]78 iv_l_ols·=·pred_ols.summary_frame()["obs_ci_lower"]
117 iv_u_ols·=·pred_ols.summary_frame()["obs_ci_upper"]79 iv_u_ols·=·pred_ols.summary_frame()["obs_ci_upper"]
118 Draw·a·plot·to·compare·predicted·values·in·WLS·and·OLS:80 Draw·a·plot·to·compare·predicted·values·in·WLS·and·OLS:
119 [9]:81 [·]:
120 pred_wls·=·res_wls.get_prediction()82 pred_wls·=·res_wls.get_prediction()
121 iv_l·=·pred_wls.summary_frame()["obs_ci_lower"]83 iv_l·=·pred_wls.summary_frame()["obs_ci_lower"]
122 iv_u·=·pred_wls.summary_frame()["obs_ci_upper"]84 iv_u·=·pred_wls.summary_frame()["obs_ci_upper"]
  
123 fig,·ax·=·plt.subplots(figsize=(8,·6))85 fig,·ax·=·plt.subplots(figsize=(8,·6))
124 ax.plot(x,·y,·"o",·label="Data")86 ax.plot(x,·y,·"o",·label="Data")
125 ax.plot(x,·y_true,·"b-",·label="True")87 ax.plot(x,·y_true,·"b-",·label="True")
Offset 129, 55 lines modifiedOffset 91, 26 lines modified
129 ax.plot(x,·iv_u_ols,·"r--",·label="OLS")91 ax.plot(x,·iv_u_ols,·"r--",·label="OLS")
130 ax.plot(x,·iv_l_ols,·"r--")92 ax.plot(x,·iv_l_ols,·"r--")
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51578 ········"3":·"py:attribute",51578 ········"3":·"py:attribute",
51579 ········"4":·"py:method",51579 ········"4":·"py:method",
51580 ········"5":·"py:property",51580 ········"5":·"py:property",
51581 ········"6":·"py:data",51581 ········"6":·"py:data",
51582 ········"7":·"py:exception"51582 ········"7":·"py:exception"
51583 ····},51583 ····},
51584 ····"terms":·{51584 ····"terms":·{
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51587 ········"00":·[13,·197,·199,·201,·202,·203,·206,·209,·210,·216,·217,·219,·229,·233,·243,·246,·247,·250,·254,·257,·259,·261,·263,·2235,·3736,·4671,·6460],51587 ········"00":·[13,·199,·201,·206,·210,·216,·217,·219,·229,·247,·254,·257,·261,·263,·2235,·3736,·4671,·6460],
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51589 ········"0000":·[197,·198,·207,·208,·209,·211,·219,·246,·252,·267,·2235,·3058,·3059,·3074,·4566,·4567,·4581,·5016,·5017,·5029,·5227,·5228,·5239,·5537,·5538,·5549,·5697,·5698,·5712,·5917,·5918,·5931,·6033,·6034,·6045],51589 ········"0000":·[198,·208,·211,·219,·252,·267,·2235,·3058,·3059,·3074,·4566,·4567,·4581,·5016,·5017,·5029,·5227,·5228,·5239,·5537,·5538,·5549,·5697,·5698,·5712,·5917,·5918,·5931,·6033,·6034,·6045],
51590 ········"00000":·6466,51590 ········"00000":·6466,
51591 ········"000000":·[197,·198,·202,·207,·209,·219,·234,·254,·257,·258,·4692,·6466],51591 ········"000000":·[198,·219,·254,·258,·4692,·6466],
51592 ········"0000000000000002":·[3261,·3286,·3311,·3336,·3367,·3392,·3423,·3448],51592 ········"0000000000000002":·[3261,·3286,·3311,·3336,·3367,·3392,·3423,·3448],
51593 ········"00000000e":·219,51593 ········"00000000e":·219,
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51651 ········"000778":·260, 
51652 ········"000787":·226, 
51653 ········"0008":·[198,·208],51625 ········"0008":·[198,·208],
51654 ········"000827":·196,51626 ········"000827":·196,
51655 ········"0008399438093390379":·255, 
51656 ········"000863":·243, 
51657 ········"00090255":·196,51627 ········"00090255":·196,
51658 ········"00091369":·226, 
51659 ········"000943":·226, 
51660 ········"00095571e":·196,51628 ········"00095571e":·196,
51661 ········"000969":·6466,51629 ········"000969":·6466,
51662 ········"000e":·203, 
51663 ········"001":·[198,·199,·201,·207,·208,·210,·214,·217,·220,·222,·227,·229,·232,·239,·259,·267,·268,·1468,·1476,·1929,·2027,·2056,·2633,·3913,·3914,·3915,·3916,·6414],51630 ········"001":·[198,·199,·201,·207,·208,·210,·214,·220,·239,·267,·268,·1468,·1476,·1929,·2027,·2056,·2633,·3913,·3914,·3915,·3916,·6414],
51664 ········"00100017":·219,51631 ········"00100017":·219,
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51666 ········"001043":·196,51632 ········"001043":·196,
51667 ········"001059":·259, 
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51669 ········"001105e":·236, 
51670 ········"001119":·6466,51634 ········"001119":·6466,
51671 ········"00118179":·231, 
51672 ········"001185":·196,51635 ········"001185":·196,
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51676 ········"001327":·196,51638 ········"001327":·196,
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51678 ········"001342":·236, 
51679 ········"001375":·196,51639 ········"001375":·196,
51680 ········"0014148605045516088":·256, 
51681 ········"0014148605045516095":·256, 
51682 ········"001428":·222, 
51683 ········"0014626434089526352":·4,51640 ········"0014626434089526352":·4,
51684 ········"0015":·6466,51641 ········"0015":·6466,
51685 ········"001502":·[183,·199],51642 ········"001502":·[183,·199],
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51687 ········"001527":·6466,51644 ········"001527":·6466,
51688 ········"00154646":·196,51645 ········"00154646":·196,
51689 ········"00156519":·226, 
51690 ········"00157":·6431,51646 ········"00157":·6431,
51691 ········"0015750750324668":·[3262,·3287,·3312,·3337,·3368,·3393,·3424,·3449],51647 ········"0015750750324668":·[3262,·3287,·3312,·3337,·3368,·3393,·3424,·3449],
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51698 ········"001813":·220,51650 ········"001813":·220,
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51703 ········"001990":·226, 
51704 ········"001991":·196,51654 ········"001991":·196,
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Files identical despite different names