PoissonRegression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x114c6d1d0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8J8fp/E0nOESnRpn+1uks/PhCZr5zJlOWqhyHyHCUMDKQi5IQY1nXrpYOwDi1\ntrogF+3GE3s28eair0ZrI94Tp/1X7cmjiJ8cp+PXHfiAY6XG1POnUr+2nhmXzKBmdQ2RkpGvRWQT\nb7JfOgHn1Nqa1y2X7QXrbBRy/w2TibhNQVPCGMV4SkJks65PfH8jR7v6AJhdXc4dV5+R19IG44k9\nm3hz0Vfp2rhw0Szaf9lO65OttD7ZSvuv2vFehwjUrK5h4c0Lmf626Uy7YNqYTjNlE++T25u55YGX\nONLZC8CsqjI+93tnnlzuRJuxvjhHOnuZVVVGVXlJXspYFHL/DZOJuE1hoLukRjCeUhZjLUfQFuvn\nqq88TWNrd3IEL8mBWadMr+Shm/JT2mA8sWcTby766kQblb2wZF+EuTsSLHgFFjca3p9MENXnVDP9\n4unJn9+aTsm07P5flE28yX55hsbW2JB+mcJDN10IwNV3PQPAgePdqcF2xsJRynrkK/6JWE5jIm5T\nPukuqRwZTymLsZYjaO7oIZ5wDDv5h8aBeCKRt9IG44k9m3izXZ+707Onh/ZftLPv8SOs+THUHQbz\nBPEIHFoAVWvqWHJZHdMunJZ1gshFvMl+SY68PtkvDgNxP9kecPK7kkiEeGL0sh75in8iltOYiNsU\nFkoYIxhPKYuxliOoq6kgGjEcJ5E66HN3opFI3kobjCf2bOLNdH3xnjidv+mk/VfttD3TRvsv2uk7\nlDztFamJ0jkPtp8Jh5dH2LMgQW8JPHDjspz/Mcimf5L98mp5DQDHKYnaa5Y78f1AIoFlUNYjX/FP\nxHIaE3GbwqLgI4/MbKGZ/czMtpjZZjP7SJp5LjazNjN7IfVzW6HjhPGVshjrH69plaWsvXIls6rK\nSLiTcGd2dTlrr8xfaYPxxJ5NvOnWd+u7TqP0YD9N9zex4y93sOHcDTw99Wl+8+bfsOtju+jc0Mn0\nt01n+VeWs/qF1fzW8QtZ9nADT14C2xYnk0W+yj9k0z/JfmlgdnX5yX6ZVVXG2itXnnym88myHqly\nHifKe+R6Owq5/4bJRNymsCj4NQwzmwfMc/fnzawG2AD8jrtvGTTPxcDN7n7FWNrO10hv3SU18rJj\nibf/aD+Hnz5O8zPHsY09xNZ3MHB0AIBIVYSpb5pKzXk1TD1vKlPPm0r5/PKcxzxWukuqOE3EbcqH\noioNYmYPAV9298cHTbuYECUMyU5/az+dz3fSsaGDjvUddDzXQc/u1Hl8g8qGymRiOD+ZHKpWVo36\njAgRya1698MqAAANS0lEQVSiuehtZvXAOcCv03z9ZjPbCDSSTB6bh2ljDbAGYNGiRfkJVEbVd6SP\nzt900vmbZILofL6T7p3dJ7+vqK+g5k01zL9hPjWra6hZXUPJVF1CEykmgf2LNbNq4PvAR929fcjX\nzwOL3L3TzC4HfgAsT9eOu98D3APJI4w8hiyAJ5zuV7rperGLzhc76XwhmSR6D/SenKeivoLqVdXM\nff9calbXUL2qmrLZ2Zf5FpFwCCRhmFkpyWRxv7s/MPT7wQnE3R81s6+a2Wx3P1LIOCe7gfYBOjd2\n0rWxK/n6YhedL3WS6EokZ4hA5YpKpr1lGtXnVFNzTg3V51RTOlPni0UmooInDEuW+/xXYKu7f2GY\neeYCTe7uZnYuybu5juY7tkJdJBu6nlxeMM+mnURvgti2GF2buk7+dGzspG/fq0cNJdNLqDqrinl/\nOo+qM6uoPquaqtOriE557ajptlg/zU0dBb3QGPbnOIz12R4iYRXEEcYFwHXAS2b2Qmra3wCLANz9\nbuA9wI1mNgB0A9d4nq/OF6qUwND1/M7Z8/nBCwfHvd5M4o93x+l+uZuuLV10be4itiVG1+au5LWG\n1EGDlRi+pIxNs3ppXglN8+Da65ZzwUXzRy3tHUQ5hsHr7OodwMyoLIsWbP2jGa5PVLpCilHgd0nl\nUrZ3SRWqlMDQ9cT6Bth3LMaimZVUlpWMq6zI4HatfYAZh+H2hmX4K710be0itjWWvEPpxK87ClOW\nTaFqZRVVDVVUrqyk6vQq+heU8p5//eWY+yKIcgyD11kSibCjuQOA5XU1DCQSgZeDGK5P7rv+XK6/\n71mVrpBQKJq7pMKiUKUEhq4nYgb+apmIsaw30Zug+5VuYttj7N/QyhU/hrojzoymASq7kvPsYydW\nblSuqKTmTTXMuW4OVadVUdlQSeUbKtM+MW5HU8drYsw0piDKMQxeZ09/HMPAoD+eoKI0+HIQw/XJ\n9qb2tNNVukLCTgmDwpUSGLqehDvYq2Uihq433hOnZ3cP3Tu66d7ZffI1tiNG777eV48WgOU1cKwW\ndp5pNNc6R2bDuv+1itrTasY0tiHbvgiiHMPgdZZGIzgODqXRSCjKQQzXJyvmTE07XaUrJOx0Sirl\nxDlldzDL/zWME+u5etlcfvHkYaYfgRnH4LerpjP9KHTv7H5dUiiZWcKUZVOYsnxK8nXZFCpXVDJl\n+RR+0XQ8Z/Fn2xeF6sPh1hnrS17DmFIaLdj6xxLf4JiC6CuRdIpqpHcujXekdz7uWol3xenZ20PP\nnp7k6+4eOnbG6NrVTeJAH/FjA6+Zv2RWCVNOTSaFyuWVr0kQo92umsv4s20riDt/dJeUSPaUMArE\n3RloG6B3X28yGeztoXdvbzI5pBJEf0v/a5axMqOivoKKJRVMWTrl1delyddcleYWEcmELnrnSDwW\np/dA78mfnn099O7vpXd/6v2+XuId8dcsY+VGxeIKKuormL1qdjI5pD5X1FdQNrcMi6hekogUHyWM\nQfZ8ag/tv2w/mSAGjg+8bp7S2aWULypnyrIpzHj7DCoWVVC+qPzka9kcJQQRmZiUMAaJbYvR19RH\nxZIKpv3WNMpPKad8YfmrrwvLiVZk/jxoEZGJRAljkFP+ZfmwFye3tXTSua+T6vLSrJ9TEVTpkXy1\nP9KzHMJ6QTdfcYVhe8MQg0xsShgpI5VwuOWBl2ju6E09exnmTK3gjqvPGNNtkEGVHsn1ek60H+uL\nc6Szl1lVZVSVl7xmPWEte5GvuMKwvWGIQSa+gj+iNYzaYv2se2QL0YhRWVZCNGKse2QL+4/GuP3h\nLRzp6CWRenC1O7R09HD7w1toi/WP0vLI7We6/Hi3I1frOdE+wLGu5DO2j6XaPrGeQm3rWOUrrjBs\nbxhikMlBCYP0JRzcYXtTO/FEAlLXsO3kqxFPJE4ul237mS6fqXyv50Q7J0qZlEQiJ0ubnFhPobZ1\nrPIVVxi2NwwxyOSghMFrSziceD1RwiGa+qMIyaOL5KsTjUQyLuUwXPv5LD2Sj/WcaOdEKZOBVDJN\nuJ9cT6G2dazyFVcYtjcMMcjkoIQBTKss5bYrGognnK7eAeIJ57YrGlg4q5K1VzYwu6acSOpWWTOo\nralg7ZUNGV9YHK79XF+YzPd6TrQPMKMy+QS9GVOSbZ9YT6G2dazyFVcYtjcMMcjkoJHeg4xUwmFX\nSyedvf26SwrdJVXIdostBik+Kg0iIiIZGUvC0CkpERHJiBKGiIhkJJCEYWaXmtl2M9tpZrek+d7M\n7Eup7zea2aog4hQRkVcVPGGYWRT4CnAZ0ABca2YNQ2a7DFie+lkD3FXQIEleQNzR1JF28NNI3413\nHZm2nW0M+4/GeGLLYfYfjWUVs4hMXkGUBjkX2OnurwCY2XeAq4Atg+a5CviGJ6/I/8rMppvZPHc/\nVIgARyqzkKsSDOnaATJqO9sY7vzJy3zppztPfv7w25bxl29/w5hjF5HJKYhTUqcA+wd9PpCaNtZ5\n8mKkMgu5KsGQrp3bH97M7Q+P3na2Mew/GjuZLEoiyV/7l366U0caIpKxor/obWZrzGy9ma1vaWkZ\nd3sjlVnIVQmGdO0MxJ14IjFq29nGsL2pHXg1WZREIifLn4iIZCKIhNEILBz0eUFq2ljnAcDd73H3\n1e6+ura2dtzBjVRmIVclGNK1UxI1opHIqG1nG8OKOVOBVDmP1OuJ8iciIpkIImE8Byw3syVmVgZc\nAzw8ZJ6HgT9O3S11PtBWqOsXI5VZyFUJhnTtrL1yJWuvHL3tbGNYOKuSD79tGQD98WTS+PDblrFw\nVuWYYheRySuQkd5mdjnwT0AUuNfdP2NmNwC4+91mZsCXgUuBGPB+dx91CHcuR3qPVGYhVyUY0rWT\nadvZxrD/aIztTe2smDNVyUJEVBpEREQyo9IgIiKSc0oYIiKSESUMERHJiBKGiIhkRAlDREQyooQh\nIiIZmVC31ZpZC7B3HE3MBo7kKJxcC2tsimtsFNfYKK6xySauxe6eUZmMCZUwxsvM1md6P3KhhTU2\nxTU2imtsFNfY5DsunZISEZGMKGGIiEhGlDBe656gAxhBWGNTXGOjuMZGcY1NXuPSNQwREcmIjjBE\nRCQjkzJhmNm9ZtZsZpuG+d7M7EtmttPMNprZqpDEdbGZtZnZC6mf2woQ00Iz+5mZbTGzzWb2kTTz\nBNVfmcQWRJ9VmNmzZvZiKq61aeYpeJ9lGFfB+2vQuqNm9hszeyTNd4HsYxnEFUh/mdkeM3sptc7X\nlejOW3+5+6T7Ad4CrAI2DfP95cCPAAPOB34dkrguBh4pcF/NA1al3tcALwMNIemvTGILos8MqE69\nLwV+DZwfdJ9lGFfB+2vQuj8GfCvd+oPaxzKIK5D+AvYAs0f4Pi/9NSmPMNz9KeDYCLNcBXzDk34F\nTDezeSGIq+Dc/ZC7P5963wFsBU4ZMltQ/ZVJbAWX6ofO1MfS1M/Qi4UF77MM4wqEmS0A3gV8bZhZ\nAtnHMogrrPLSX5MyYWTgFGD/oM8HCMEfopQ3pw4xf2RmKwu5YjOrB84h+T/TwQLvrxFigwD6LHUa\n4wWgGXjc3UPRZxnEBcHsY/8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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108fb9ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.random import uniform, normal, poisson, binomial\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(5)\n",
    "n_sample = 100\n",
    "a = 0.6\n",
    "b = -0.4\n",
    "\n",
    "x = uniform(1, 5, size=n_sample)\n",
    "mu = np.exp(a * x + b)\n",
    "y = poisson(mu)\n",
    "\n",
    "exog, endog = sm.add_constant(x), y\n",
    "\n",
    "import statsmodels.api as sm\n",
    "mod = sm.GLM(endog, exog, family=sm.families.Poisson(link=sm.families.links.log))\n",
    "res = mod.fit()\n",
    "\n",
    "y_pred = res.predict(exog)\n",
    "\n",
    "idx = x.argsort()\n",
    "x_ord, y_pred_ord = x[idx], y_pred[idx]\n",
    "plt.plot(x_ord, y_pred_ord, color='m')\n",
    "plt.scatter(x, y,  s=20, alpha=0.8)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/yuho/anaconda/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.random import uniform, normal, poisson, binomial\n",
    "from scipy import stats\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x12bbf7470>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(5)\n",
    "n_sample = 100\n",
    "a = 0.6\n",
    "b = -0.4\n",
    "sd = 0.3\n",
    "\n",
    "x = uniform(1, 5, size=n_sample)\n",
    "mu = a * x + b\n",
    "y = normal(mu, sd)\n",
    "\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "slope, intercept, r_value, p_value, std_err  = stats.linregress(x, y)\n",
    "xvals = np.array([0, 5.5])\n",
    "yvals = slope * xvals + intercept\n",
    "\n",
    "plt.scatter(x, y, s=20, alpha=0.8)\n",
    "plt.plot(xvals, yvals, color='magenta')\n",
    "plt.savefig('linear_regression.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.linspace(-3,3)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(3,1))\n",
    "ax.plot(xx, stats.norm.pdf(xx), color='k')\n",
    "\n",
    "ax.tick_params(labelbottom=\"off\",bottom=\"off\") # x軸の削除\n",
    "ax.tick_params(labelleft=\"off\",left=\"off\") # y軸の削除\n",
    "ax.set_xticklabels([]) \n",
    "plt.box(\"off\")\n",
    "\n",
    "plt.savefig(\"normal_dist.png\", transparent=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.arange(1, 20)\n",
    "\n",
    "for lam in [2, 4, 10]:\n",
    "    fig, ax = plt.subplots(figsize=(3,1))\n",
    "    ax.bar(xx, stats.poisson.pmf(xx, mu=lam), color='k', alpha=0.5)\n",
    "\n",
    "    ax.tick_params(labelbottom=\"off\",bottom=\"off\") # x軸の削除\n",
    "    ax.tick_params(labelleft=\"off\",left=\"off\") # y軸の削除\n",
    "    ax.set_xticklabels([]) \n",
    "    plt.box(\"off\")\n",
    "\n",
    "    plt.savefig(f\"poisson_dist_lam{lam}.png\", transparent=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(5)\n",
    "n_sample = 100\n",
    "a = 0.6\n",
    "b = -0.4\n",
    "\n",
    "x = uniform(1, 5, size=n_sample)\n",
    "mu = np.exp(a * x + b)\n",
    "y = poisson(mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2, 11,  7,  5,  3,  4,  8,  6,  3,  0,  1, 13,  3,  2,  6,  1,  7,\n",
       "        4,  3,  1,  3,  2,  5,  3,  4,  0,  1,  8,  8,  4,  1,  3,  5,  7,\n",
       "        3,  7,  2,  3,  4, 11,  3,  3, 10, 12,  1,  1, 13,  1,  9,  9, 12,\n",
       "        3,  1,  2,  3,  1, 13,  4, 16,  4, 10,  6, 18, 11, 11,  0,  2,  0,\n",
       "        4,  5,  3,  0,  4,  1,  4,  3,  5,  2,  7, 11,  6,  3, 14,  4,  2,\n",
       "        4,  3, 15,  2,  0,  9,  0,  4,  9,  2,  4, 11,  1,  4,  7])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OdEcnxjntNnvhWPAnfrM2TU7NsO/gGOWSGB4coFwS+w6O5fbTXq/qxDin3WavHAtO/GZtcsmB7ujEOKfdZq8cC078Zm1yyYHu6MQ4p91mrxwLTvxmbXLJge7oxDin3WavHAsu2WCWEpcc6I5OjHPabWZxLLhkg1kGXHKgOzoxzmm3mfdjwad6zMwKxonfzKxg2k78kp6X9LSkpyS94sS8qu6RdETSDyRd226fZmbWurTO8f9SRJxs8Nr7gTcmP28H7k9+W4/xxcvek+Z7lsX7n9djLq9xNasbF3dvBj4T1duHvi3pVZKuiIgXutC3paQXpqHbpdJ8z7J4//N6zOU1ruVI4xx/AF+T9ISk3XVefx1wdN7zY8ky6xG9Mg3dLkrzPcvi/c/rMZfXuJYrjcT/roi4luopnd+R9O5WGpG0W9IhSYcmJiZSCMvS0ivT0O2iNN+zLN7/vB5zeY1rudpO/BFxPPk9DjwCbF+wynFg87znVybLFrbzQESMRsToyMhIu2FZinplGrpdlOZ7lsX7n9djLq9xLVdbiV/SKklrao+B64FnFqx2APi15O6edwCTPr/fW3plGrpdlOZ7lsX7n9djLq9xLVdbJRsk/ROqn/KheqH4cxHxcUkfBoiIT0oScB9wAzAF/HpELFqPwSUb8qnX72QoIt/V0xl5jGs5JRtcq8fMrA8sJ/F75q6ZWcE48ZuZFYwTv5lZwbgscw/Kw4WlZmOot16jbZe7vNtxt2up/Vs5UObc7FzTfS4WY6tt5k0ejvV+5MTfY/IwXbzZGOqtB9TdtlGbWZQd6MQYL7V/Z6dnOXX2PBtWDzE8WF6yz8VirL02dX6Ok2emWb9qkFVDAz1XWiAPx3q/8l09PWRyaoZb7v8W5ZIYGigzPTvHXCXYf8d1Xb29rpkY6q13frYCiMGBS7d96Pbt3P7Qd1/RZqPlrexvO3G3O8aN2qztH8DRn79MRFCSuHLdZQAN+1wsRoBb7v8WAMd+/jKVCCSxeYk28yYPx3qv8V09fSoP08WbjaHeerNzwVyl8optD594qW6bjZZ3suxAJ8a4UZu1/StJEDBQKhHJ88X6XCzG2mslCai2SSzdZt7k4VjvZ078PSQP08WbjaHeegNlUS6VXrHt1k2X122z0fJOlh3oxBg3arO2f5UIEMxWKih5vlifi8VYe62S/E9+tlIBLd1m3uThWO9nTvw9JA/TxZuNod56e3ddw95dr9x28/rhum02Wt7JsgOdGONGbdb2D2DdZdX21w0PAiza52Ix1l6b31at7V4qLZCHY72f+Rx/D8rDnQ6+qye9vn1XT2N5ONZ7hUs2mJkVjC/umplZQ078ZmYF48RvZlYwhZm528xForQuJB09NcXhEy+xddPlbF4/3HI7y9FO7K1cCExjrLp94a6V/ianZvjJxBkgeMPImswvonbzOM6TftynLBUi8Tcz9Tut6eH3fv3H3PPYkQvP79x5NR9575taiLp57cTeSsmANMaq29PxW+nvm4fHuWv/05w8Mw3A+lWDfOIDb86sNEI3j+M86cd9ylrfn+qZnJph38ExyiUxPDhAuST2HRxjcmpmWes04+ipqQtJf6BUHdp7HjvC0VNT6e3QAu3EXtsW4MVk/RfPngdo2EYaY5XWeHeyv8mpGfYcGOPkmWlKEiWJU2fPs+fAs0xOzVw6dsmY1cawE/vSzeM4T/pxn/Kg7xN/M1O/05oeXpuCX0v6A6XSJVPzO6Gd2C+Z3t9kyYA0xqrb0/Fb6W/89DnmKpULSb8kIcTsXGRSGqGbx3Ge9OM+5UHfJ/5mpn6nNT28NgV/tlK58Hv+1PxOaCf2S6b3N1kyII2x6vZ0/Fb627hmJeVSiUrEhZ8gGCgrk9II3TyO86Qf9ykPWk78kjZL+oakMUnPSvq9OuvskDQp6ank5+72wl2+ZqZ+pzU9fPP6Ye7ceTUAM3PV5H/nzqs7eoG3ndgvmd7fZMmANMaq29PxW+lv7fAK9u7axobVQxcS//pVg+zddU0mpRG6eRznST/uUx60PHNX0hXAFRHxpKQ1wBPAv4yIsXnr7AD+ICJuWk7bnZi567t6lt7Wd/XU38Z39WSvH/cpbZmUbJD0d8B9EfHovGU7yEniNzPrZ10v2SBpC/A24Dt1Xn6npO9L+oqkaxZpY7ekQ5IOTUxMpBGWmZnV0Xbil7Qa+FvgoxGx8PaVJ4HXR8RbgHuBLzVqJyIeiIjRiBgdGRlpNywzM2ugrcQvaQXVpP/ZiNi/8PWIeCkiziSPvwyskLShnT7NzKw97dzVI+CvgB9GxJ81WOc1yXpI2p70d6rVPpcyOTXDcydOd3xyR71+0uo7zX1ota1ujWOjPrPovxmN4sprvGaNtFOy4TrgV4GnJT2VLPsYcBVARHwSuBW4Q9Is8DJwW3ToCwC6Na27Xj9AKn2nuQ+ttpXF9Pj5fZ6dnkUSw4PlrvXfjEbj4nIC1ov64otYJqdmuOX+b1EuiaGBMtOzc8xVgv13XJfqrV/1+jk/WwHE4EB7fae5D6221a1xbNTnQKnEc+OnAXjjxjXMViod73+5Mc4fl4du387tD323q+Nl1kjhvoilW9O66/UzOxfMVSpt953mPrTaVhbT4+f3OTNXQQhJzMxVcjM9v9G41EpxuJyA9Zq+SPzdmtZdr5+BsiiXSm33neY+tNpWFtPj5/e5olwiCCKCFeVSbqbnNxqXWikOlxOwXtMXib9b07rr9bN31zXs3dV+32nuQ6ttZTE9fn6f52bmWL9qkA2rhzg3M5eb6fmNxmXz+mGXE7Ce1Bfn+Gu6Na27Xj9p9Z3mPrTaVhbT4+f3CeRyen6jcXE5AcuDTEo2pMklG8zMlqdwF3fNzKx5TvxmZgXjxG9mVjB99WXri118q9VUH1m9sq266VleQO5E+4vVkc/zRctOxZaXfc5LHNaf+ibxLzal/q79T3PyzDSVgIhg0+UrGR4sL3t6fZZlIdLsp9b+1Pk5Tp6ZZv2qQVYNDVzST55LEXQqtrzsc17isP7VF6d6Jqdm2HdwjHJJDA8OUC6JfQfHOHpqij0Hxjh5ZpqSxFwlqAScOjMNVOvrNFtYq1EfaRfm6nQ/tfYBXjx7vvo7abvWT7f2tRWdii0v+5yXOKy/9UXiX2xK/VylQqlaIBQlPwGUpGVNr8+yLESa/dTaqY3JQKkEcel4ZFG6oVmdii0v+5yXOKy/9UXiX2xKfblUopLMVYjkR0AlYlnT67MsC5FmP7V2amMyW6mALh2PLEo3NKtTseVln/MSh/W3vkj8i02p37trGxtWD1GJoFwSJcGrVw0BLGt6fZZlIdLsp9Y+wLrhwervy6pt1/rJonRDszoVW172OS9xWH/rq5m7vqtn+e37rp7utNurcVjvcMkGM7OCcckGMzNryInfzKxg2kr8km6QdFjSEUl31Xl9SNIXkte/I2lLO/2ZmVn7Wk78ksrAXwLvB7YBH5S0bcFqvwn8PCKuBv4c+ESr/bVicmqG506crjv5ZbHX2u2j2bZbjeHoqSn+59g/cvTUVEsxm1mxtVOyYTtwJCJ+CiDp88DNwNi8dW4G/iR5/EXgPkmKLlxRXmzae1pT4uu1AzTVdqsx3Pv1H3PPY0cuPL9z59V85L1vWnbsZlZc7ZzqeR1wdN7zY8myuutExCwwCaxvo8+mLDbtPa0p8fXa2XPgWfYcWLrtVmM4emrqQtIfKFXfunseO+JP/ma2LLm5uCtpt6RDkg5NTEy01dZi097TmhJfr53ZuWCuUlmy7VZjOHziJeBi0h8olS6UpjAza1Y7if84sHne8yuTZXXXkTQArAVO1WssIh6IiNGIGB0ZGWkjrMWnvac1Jb5eOwNlUS6Vlmy71Ri2brocSMosJL9rpSnMzJrVTuL/HvBGSb8gaRC4DTiwYJ0DwIeSx7cCj3Xj/P5i097TmhJfr529u65h766l2241hs3rh7lz59UAzMxVk/+dO69m8/rhZcVuZsXW1sxdSTcCfwGUgQcj4uOS9gGHIuKApJXAXwNvA14EbqtdDF5MWjN3F5v2ntaU+HrtNNt2qzEcPTXF4RMvsXXT5U76Zga4ZIOZWeG4ZIOZmTXkxG9mVjBO/GZmBePEb2ZWME78ZmYFk8u7eiRNAD9rcfMNwMkUw0lLXuOC/MaW17ggv7HlNS5wbK1YTlyvj4imZr/mMvG3Q9KhZm9p6qa8xgX5jS2vcUF+Y8trXODYWtGpuHyqx8ysYJz4zcwKph8T/wNZB9BAXuOC/MaW17ggv7HlNS5wbK3oSFx9d47fzMwW14+f+M3MbBE9mfglPShpXNIzDV6XpHuSL3n/gaRrcxLXDkmTkp5Kfu7uRlxJ35slfUPSmKRnJf1enXW6Pm5NxpXJuElaKem7kr6fxLa3zjpDkr6QjNl3JG3JSVy3S5qYN2a/1em4FvRflvR/JB2s81rXx6zJuDIbM0nPS3o66fcVFSpT/9uMiJ77Ad4NXAs80+D1G4GvAALeAXwnJ3HtAA5mNGZXANcmj9cAPwa2ZT1uTcaVybgl47A6ebwC+A7wjgXr/Hvgk8nj24Av5CSu24H7sjjWkv5/H/hcvfctizFrMq7Mxgx4HtiwyOup/m325Cf+iHican3/Rm4GPhNV3wZeJemKHMSVmYh4ISKeTB6fBn7IK78juevj1mRcmUjG4UzydEXys/Ci2M3Ap5PHXwTeK0k5iCszkq4E/gXwqQardH3Mmowrz1L92+zJxN+EZr4IPivvTP6L/hVJ12QRQPJf67dR/aQ4X6bjtkhckNG4JacGngLGgUcjouGYRcQsMAmsz0FcAB9ITgt8UdLmOq93yl8AfwhUGryeyZg1ERdkN2YBfE3SE5J213k91b/Nfk38efUk1WnVbwHuBb7U7QAkrQb+FvhoROTmW9qXiCuzcYuIuYh4K9XvlN4u6Re71fdimojrvwNbIuLNwKNc/ITdUZJuAsYj4olu9NesJuPKZMwS74qIa4H3A78j6d2d7KxfE38zXwTfdRHxUu2/6BHxZWCFpA3d6l/SCqrJ9bMRsb/OKpmM21JxZT1uSb//D/gGcMOCly6MmaQBYC1wKuu4IuJUREwnTz8F/NMuhXQdsEvS88DngZ2S/uuCdbIYsyXjynDMiIjjye9x4BFg+4JVUv3b7NfEfwD4teRK+DuAyYh4IeugJL2mdi5T0naq49+VJJH0+1fADyPizxqs1vVxayaurMZN0oikVyWPLwPeB/xowWoHgA8lj28FHovkalyWcS04/7uL6rWTjouIP46IKyNiC9ULt49FxL9bsFrXx6yZuLIaM0mrJK2pPQauBxbeGZjq3+ZAy9FmSNLDVO/02CDpGLCH6gUuIuKTwJepXgU/AkwBv56TuG4F7pA0C7xM9cvnu3VR7jrgV4Gnk3PDAB8DrpoXXxbj1kxcWY3bFcCnJZWp/mPzNxFxUNI+4FBEHKD6j9ZfSzpC9cL+bTmJ605Ju4DZJK7buxBXQzkYs2biymrMNgGPJJ9tBoDPRcRXJX0YOvO36Zm7ZmYF06+neszMrAEnfjOzgnHiNzMrGCd+M7OCceI3MysYJ34zs4Jx4jczKxgnfjOzgvn/gDWWRitwaLcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y, s=20, alpha=0.8)\n",
    "plt.savefig('poisson_data.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x216 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_context('talk')\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(14, 3), sharey=True)\n",
    "\n",
    "xx = np.arange(20)\n",
    "lambdas = [1, 5, 10]\n",
    "\n",
    "for i, lam in enumerate(lambdas):\n",
    "    yy = stats.poisson.pmf(xx, lam)\n",
    "    axes[i].bar(xx, yy)\n",
    "    axes[i].set_title(r'$\\lambda={}$'.format(lam))\n",
    "\n",
    "plt.savefig('Poisson_distribution.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x105c4c710>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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V4UlIu7JYxpOI1mpq3ybh0hx6Ghi0SAUIpfFQ1xssJ7VtG/gPfbCindZOHz97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\noYuIuIQSuoiIS/x/SXDjbsnBmQcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105c4c6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "slope, intercept, r_value, p_value, std_err  = stats.linregress(x, y)\n",
    "xvals = np.array([0, 5.5])\n",
    "yvals = slope * xvals + intercept\n",
    "\n",
    "plt.scatter(x, y, s=20, alpha=0.8)\n",
    "plt.plot(xvals, yvals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "exog = sm.add_constant(x)\n",
    "endog = y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Generalized Linear Model Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>y</td>        <th>  No. Observations:  </th>  <td>   100</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                  <td>GLM</td>       <th>  Df Residuals:      </th>  <td>    98</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>         <td>Poisson</td>     <th>  Df Model:          </th>  <td>     1</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Link Function:</th>          <td>log</td>       <th>  Scale:             </th> <td>  1.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                <td>IRLS</td>       <th>  Log-Likelihood:    </th> <td> -213.95</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 17 Sep 2019</td> <th>  Deviance:          </th> <td>  120.86</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>09:22:33</td>     <th>  Pearson chi2:      </th>  <td>  115.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Iterations:</th>          <td>5</td>        <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -0.2789</td> <td>    0.162</td> <td>   -1.720</td> <td> 0.085</td> <td>   -0.597</td> <td>    0.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.5646</td> <td>    0.042</td> <td>   13.508</td> <td> 0.000</td> <td>    0.483</td> <td>    0.647</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                 Generalized Linear Model Regression Results                  \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  100\n",
       "Model:                            GLM   Df Residuals:                       98\n",
       "Model Family:                 Poisson   Df Model:                            1\n",
       "Link Function:                    log   Scale:                          1.0000\n",
       "Method:                          IRLS   Log-Likelihood:                -213.95\n",
       "Date:                Tue, 17 Sep 2019   Deviance:                       120.86\n",
       "Time:                        09:22:33   Pearson chi2:                     115.\n",
       "No. Iterations:                     5                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -0.2789      0.162     -1.720      0.085      -0.597       0.039\n",
       "x1             0.5646      0.042     13.508      0.000       0.483       0.647\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod = sm.GLM(endog, exog, family=sm.families.Poisson())\n",
    "res = mod.fit()\n",
    "res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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saabpXzrZ/sLtDLYOEpkTYfWXV3Pl/zyL51+Re25vMkMiHiMRj9CTzF2S0/ifairzdI6RmyD6o5JVVQJ6T0fKkec5tuzrUDTNDI0ex4WHHPEPtNP/SB8AtetrWfPtNSRWJk557qLaKpw5DnenynL8i34jgZl9D3iLc+5YvhsIKjUdEZmMl/E4cMcB9n9kPy7jIApn/s2ZLHv/MiKx2Tn3pug3EjjnXp7vikVEwqrvsT52vnYnJx7MzYVPrE6w5ptrqL201ufKwi/wgZ8iIqXiZTye/uTTPPXhp3CDuatAS//fUlbcvoJoIhSzQQJPTUdEytJ00xl6H+ll5y076d3aC0BVSxXnfPUc6p+b95WkkvE8x+Y9x7h3d+6dkCvPms+GlfMD+X6Smo6IlJ3ppAp4KY/9f7+fA7cfwKUdGCx5+xJabm8hOif4Zzee5/j4T3fynQcO0D+YS0b49pb93HzZMt537ZrANZ7Z+W6YiJS1LXs72LQt96HDi2pz82Q2bWtjy76Ok57XfX83D657MHezQNqRWJXg4t9czKp/XhWKhgO5fd340EEGBjNELPc5RwODHhu3Hjplf4NAZzoiUnZOlyqQ6c6w96/30vpvreCACJzx7jM488Nnhu69m9y+ejigIhoBB2lzJNPZQKYhqOmISNmZKFVgUV0lR39wlF1v28VgWy5VoGZtDau/uJq56+b6XHV+cvsaYWAQMlkvl8PjCGwagi6viUjZGS9V4KZFC6l9ZzuP3vgog22DRKojrPyHlax9YG1oGw7k9vXGtUtJxGN4LvceTyIe4aZ1SwOZhjCtlOlyosmhIuVtJCng2AALftCL++xRvH4PgHkvnseqz68qm0/09DzH/Xs6+O3uoxjGFasa2dBS+LvXSpoyLSISJpGIsebpKLG/aKP/sX4A4s1xzvqns2h6RRNmwbqrayYiEeOKVfO5YlXwP0JBTUdEyk7yQJI979nD0f/KffwAEVjy1iWs+OgKYnX6b89PGn0RKRvZgSxPf/JpDtxxAG8gdymtdn0tqz63irlrw/u+TTlR0xGR0HPOcewHx9j9rt2k9qcAiC+K0/LxFha+aiEWsAmSs5majkzbdONFykWYokZOp5z2pfeRXnbfupuuu3M3BVmFsfSdS1n+geXE5j7zX9xsPW6DRnev6e61aZlOvEg5GS9qpDoeDWzUyGRy+/L40L5kAaiOx4b2JTx/j+mONE995CkOff4Q5HaDxusaWfmPK6leVX3Sc2frcVtohbh7TfN0ZFqmGi9SbsIWNTKZLXs72Lj1EAODHpGIETEYGMyw8aGDodiX7ECW/XfsZ8vKLRz6l1zDSZyd4IKfXMAFmy44peHA7D1ug0iX12RaThcvUq7CFjUymeG/QwxiZhAxBjMeybQX6H1xWUf719vZ96F9DB7KpQlE66Isv205S/9yKZH4xL9Dz9bjNojUdGRaJooXCWLcRiGFLWpkMsN/hwNpj4xz4DkMqKqIBHJfnHN03NXB3r/aOzLfxuLGkrctYfn7l1PRWHHadczW4zaIdHlNpmW8eJEbLlocyLiNQgpb1Mhk1rc0cuO6JSTiETzP4TlIxGPctDZ4+9K9pZuHn/swj9zwSK7hGCx81UIufeJSzvqHs6bUcGD2HrdBpBsJdCPBtI3Ei3Qlaa6vYv2K2XEXUKmiRkrB8xyb9x7jvl0dOBzPOauJy1cG5++x/8l+9r5/L8c2HhtZ1nBNAy13tDD34vzm28zW47aQCnEjgZqOmo5IYKTaU+z/yH5av9Q6ckdazdoaVn5iJQ3Pb/C3OFH2moiUh1Rbiqc/9TSt/9Y6EspZtaKKFR9bwYI/WaDJnWVETUdEfJM8kOTAJw7Q9uU2XCp31aVifgXLP7icxW9ePOkdaRJOajoiUnL9u/s5cMcBDn/jMC4z1GyaKjjjXWew+C2LidXqv6Zypb9ZkRAJe5RL32N97L99P0f+4wjkrqIRXxznjPecweI3LiZa7f9HRRdjjAu5zrAfA2o6IiER5iiXE78/wf6P7efYD47B0L1LlcsrWfZXy1h0yyKiVf43GyjOGBdynWE+BobpgqlISIQxyqXngR52XL+DrWu35m5/dpBYlWD111Zz2a7LWPLmJYFpOFCcMS7kOsN4DIylMx2RkAhTlEvXr7vY/9H9dP6yc2RZ9XnVLP/Acha8YgEWDeZv5cUY40KuM0zHwETUdERCIuhRLs45On/Ryf6P7qf7t90jy2vW1rD8tuXMf8n8wN/6XIwxLuQ6g34MTIUur4mERFCjXJznOPbjYzx02UNsv2b7SMOpvbyWC35yAeseXEfTy5oC33CgOGNcyHUG9RiYDiUSKJFAQiRIUS7ZZJbD3z7MwX88SP/j/SPL659Xz/LbllP/vHrMgt9oxirGGBdynX4eA4rBmQE1HZH8pNpTtP5rK63/2kr6aHpk+bxr57H8tuXUXVHnY3VSTLMmBsfMrgbumeDhNc65nSUsR2RW6nmwh0P/fIgj3z2CS+d+WbUKY8ErF7D0nUvzDuKU2SUUTWeUTwNbxyxr9aMQkdnAS3sc++ExDv7zQXo294wsjzXGWPymxSz5iyVULq70sUIJm7A1nV875+70uwiRcpdqS9H2xTZav9DKYNvgyPI5F8xh6a1LWfBnC4gmgjO/RsIjbE0HM5sLDDjnMn7XIoUX9oiPMHPO0XVPF63/1sqxHx4byUQjAo3XN7L01qXUX33yzQFhj3cJ6vEW1LoKIWxN51tADZAxs3uAdznndvhckxRIOUR8hFG6I037N9pp/UIrA08OjCyvmF9B8583s/jNi6lafuo8kLDHuwT1eAtqXYUSlnk6g8D3gVuBlwAfAS4F7jWzs8d7gZl1TfYF6BabgCmHiI+wcM7R9dsuHn/142xespk979oz0nBqr6jlnG+ew/qn19Py9y3jNhwIf7xLUI+3oNZVKKE403HObQY2j1r0YzPbBDwIfAi42ZfCpKDKIeIj6AYPD9L+zXbavtLGwBPPnNVE50ZZ+JqFLH7TYmouqJnSusIe7xLU4y2odRVKKJrOeJxz28zsl8DzJ3h80vvIdbYTPOUQ8RFEXtrj+E+O0/71djru6njmvRpg7iVzaX5DMwv+dAGxmun9dxD2eJegHm9BratQwnJ5bSJPA/P8LkIKoxwiPoKkd1svu9+xm/uX3M8jL32EY3fmbg6INcRY8vYlPPvhZ7Pu/9ax+A2Lp91wIPzxLkE93oJaV6GEOpFg6ExnjXNuSR6vVSJBAAUp5iWMUm0pjvznEQ5/8zC9D/c+84BBw4saWHTLIua/dH7BPk4g7PEuQT3eglrXrInBMbMm59zRMcuuBH4NfMM59/o81qmmI2Uh05Ph6A+OcuQ7R+i8u3PkEzkBEqsTLLplEQtftZCqpeVxeUb8M2ticIDvmlk/uZsJjgHnA28c+vnDPtYl4gtv0OP4/xzn8HcO07GpAy/5TKeJNcRoekUTi25ZRO1ltaEM3ZTyFZamcye5O9TeBdQCR4B/Bz7snDvgZ2EipeKyju57uzn874c5+r2jZDqfmR8dqYrQeEMjC29eyLxr5xGJh/3tWilXoWg6zrnPAJ/xuw6RUnOeo/u+bo5+7yhHv3/0pEgaItDw/AYW3ryQ+S+bT6w2FP+cZZbTUSoTCkIUx1RqmOg501kOFHRfZ1K3y45qNBvHNBpg7rPnsuDmBSz4kwVUNldOaZ3Dyw91DdDVP0hDdZzF9YnT7udUxnBhba6Gwz2p0EW2BOEYn23UdGRcQYjimEoNEz3n3S9czad+8cSUll934SLAuGt7YfY1n7qrI1H+NDKP5x+opuPOYwy2n9xoap5VQ9PLm1jwigUkViamtd3hff7xw60c7xsknXXEY8a8OZWT7udUxzaV8QBHPBohEY+FJrIlCMf4bKSmI+MaG8XRNZBm07Y2rjq7iQ0r5wemhome0zgnPuXlG7ceAoPKWLQg+zrVun/6uzbO3QUXPRGn5RGP6oEu2njmbsqadTUsePkCmm5qmrDRTGW7w/s8mPHIOgc40llHKpOddD+nMrY1VTG6jvcDxvyGStKeK/lxkq8gHOOzkZqOjCsIURxTqWGi5+w92jfl5fv7B8GMhXMLs6+T1Z1qT9FxVwe93zrEBzYbFRkDHJD7zTp9fiWrX7OEphubSLScvtFMZbvD+1wVi+A5iEWNjAfxWIRkOjvhfk5lbLuT6Vz1BhnnQhXZEoRjfDZS05FxBSGKYyo1TPSclqY501qOUbB9PammqhiJvRle/HiU+d8/xP3bdwMQB8DIRhwHzzK2nePx+LnwwT9fxbI8f8s+3Vik0lkiBpmswwwGM96k+zmVsY1FLdcuHcTMQhXZEoRjfDbSfZUyriBEcUylhome87oNK6a8/KZ1S7lx7dJJtzMdlyyq59XJedxwp/GGD2V5279EeMEvI7jtuYDN6Nwo829qYtd7arn9NsdnXpXmgcvh6qtmNr6nG4t4LELUDDAqolEqY9FJ93MqY9ubzJCIx0jEI/Qk0yPPCUNkSxCO8dkoFIkExaBEgtMLQhTHVGqY6DnTWQ7kva/OOfof7+f4T49z/KfH6fpNFy518r+rqhVVNF7fSOP1jdRfVU8kHinK+J5unw91DtA1MEhDIs7ihsRptzmVMVxUW4Uzx+HuVKAiW6YiCMd4mMyaGJxiUNORmch0Z+j8386RRpN6OnXyEyJQt6GOxutyjaZ6TbWSAST0ZlMMjoivvIzHid+doPOXnXT+vJPu+7she/Jz4ovjzLt2HvOunUfDCxqoaKjwp1iRAFPTERnH8CWzzrs76fxlJ133dJHtObnLWIVR95y6kUYz5/w5OpsROQ01HRFyTSa5N0nnPZ103d1F592dpA+nT3le9TnVNLyggYYXNVD/vPq8PodGZDbTv5gCm0n8ST7b2rznGPfuPgbAlWfNZ8PK+UV9I3QmtedTbyHGarx1mMHAngG6f91N16+66PpVF6mDqVNeG18Up/4P6ml4YQMNz2+g6ozJb6fNp97TjcvwOlu7BujsH6S+Os6SKUTY5KOUx2+QlOM+BZVuJCjgjQQziW2ZbvSG5zk+/tPH+c4DB+gfzF32qY7HuPmyZbzv2uLEeMyk9nzqLcRYDa/jrt+3UdeaZfXTUTZ0JVi82zHYOnjK82PzYtRfXU/DHzRQ/wf1VJ8z9RsA8qk3Ny47h8YlMzQu0aFxWQMwss7jfSkGM46KqDFvTpwbLl5c0MiWUh6/QVKO+1QshbiRQPN0CmhsrAbApm1tbNnXMa3nTHVbG7ceYmDQIxIxIgYDgxk2PnRw2uuazjbzrT2femeyvexAlq7fdnHf+3ZS/8523v9R4z2fq+CGH0eY/5vUSMOJzYvR+JJGzvr0WTx727O54ugVnL/xfJb8xRLmrJneezT51LtlbwcbHzrIwGCGiEEkYgwMemzceogt+zpG1pnKZElncxlnWecYzHh5HTczrb9Qx2+QlOM+BZkurxXQTGJbphu9MbweLDcTnIgxmPFIpr2ixXjMpPZ86p3O9lKHUvRs6aF7czfd93XT+1AvLp07iz+HZxpHby3sPsPjrD9awNU3n5l7879Av83mMz6513g4oCIaAQdpcyfF0yTTWSorIjiMWBQyHlSeJsKmWPWXY3RMOe5TkKnpFNBMYlumG70xvJ6BtEfGOfAcBlRVRIoW4zGT2vOpd6LtLaqM0/XbLnq29NDzQA8nHjgx7vsxALTEeXBeiqfOdHSujvHUnAwYfPLli6hZWTOD0Zh6vZONT+41EQYGIZP1ciFmjmdeN/RzKpPFcGSyubOh1GkibIpVfzlGx5TjPgWZLq8V0ExiW6YbvbG+pZEb1y0hMTSz3XOQiMe4ae3SosV4zKT2fOpd39LI9ecvoukInPHrFDfcabz/S3HSFz/Gw1c9zN737uXYxmMjDSdSFaHuOXUs+6tlnP/j89lwdANX7bqczN8u4vfrYGdlCqx4USf5jM/6lkZuXLuURDyG53LvLyTiEW5alxuX4XVWxqK5MyGMqBnxWKTg+1HK4zdIynGfgkw3EhQ4kWAmsS35bGvz3mPct6sDh+M5ZzVx+cri3nUzk9pPV69zjoE9A/Ru7eXEgyfo+V0PvVt7yfZmx11f4uwEtZfV5r7W1zJ+VOLDAAAPXklEQVTnwjlEKk79PaqUUSf5bMvzHPfv6eC3u49iGFesamRDy5i71/Z10No5QOfAIPWJOEumEGFTrPrLMTqmHPepGBSDMwOKwfGX8xwDuwY48dAJeh/qHfme6cqM+/zYvNhIg5l72VxqL62lYp5m/IuUkmJwJBSyA1n6Hu2j9+He3Nfve+nb3jfhGUy0JkrNs2qYe8lc5l4yl9pLaqlqqdJsf5EyoKYjBeOcI3UwRe+2XFPp3Z773v9EP3jjvyY6d6jBrJtLzdrc9+qzq7GoGoxIOVLTyVOpZjCP3c6lZ87j/546XpA0g5nUn+5K0/dIH307+ujd0Uf777rIPpEkcmKC7gLEm+PUXFRDzbNyX3MuquFh+th7IkVzXRUtJZgFPnq/F9ZWAnC4JxWYWegT/b1oxryUCzWdPJRqBvPY7VTGIiyoreToicEZpxlMtf50V5r+x/rpe7SPvkf7Rn4ebzb/8Fv4Xgzmnl9DzYVzqLmwhjlD3+ML43nVUCijtzkwmGEw6wFGZSwSiFnoE43Ju1+4mk/94gnNmJeyoKaTh7EzmLsG0mza1sZVZzexIc+PGp7Kdg73JNlxsIeGORUz2u4p9fen+fVv2rjyaIIzu2P0P96f+9rZz2D7qc3lJEsq2Dl3kMML4cQZEfY0ZjnWBB9/5ZmsmaSmUo3hRNucW1XBwc4BwNFYU00m64q+/enUN3pMGufESz5WIsWippOHUs1gHrudylgEzznisUhe2832Zel/sp+Onx7lOb9wLOuJMe9IloYjESpTkOEpdk/w2viSOHPOm8Occ+dQfV517ufz5vCjXe186SePj9ToeRH6p1CTH7PAR2+zO5kGA+cg67lAzEKfaEz2Hu3TjHkpG2o6eSjVDOax20llPCKWi4/xPDfudrN9WQZ2DzCwe4D+Xf25n3fl/jx8SWwucC1RYMzt8hFItCSoXlNN9TnVue9DP1fUj397cr5j4ccs8NHbjEVyM/8NiEYsELPQJxqTlqY5mjEvZUNNJw/DM5g3bWujvSdJVUW0KDOYx26nMhbhwqV1nDicIvZ4igt6IlwRr6XhY8f4/Z6nGdg1wGDbaS6HAdG6KN0Ljd3VadrmeXQtMs67oom33nIuserojGqc6liUagwn2uaJZJpEPDfDvzeZKcn2p1Pf6DF53YYVdPQNlnSsRIpFk0PznBxazBnM2b4syf1Jkk8lGdg7wN6HOxnYm6TqcJZIa4bsBBMoR4vWREmsSpA4K/HM97MSVK+upqKpAucoWP35joUfs8BHb3NhXSXmjPae4MxCn2hMNGNegkCJBDPgZyJBpjtD8kBypLGk9qdIPpUc+UofO/UTK8cTq49RtbKKRMtQYxlqLtWrqqlYUKHJlCJSUEokCCAv5ZE6lCL1dIrkgSSpgylSB1Ikn07mvh9Iku0efyb+WBY3qpZVUbUi95VoSeR+bsn9rBgYEQkbNZ08pdpTtH+lPddgDj7zlT46tbMUAKs0qpZXUXXm0Nfon8+sIr4oXrDPehERCQI1nTxle7Lsu23fpM+pWFhB1RlVVJ5RSeUZlVQtr6JyWWXu7GV5FRVNFWoqIjKrqOnkqaI5jl2YINkYIbG0kuXn1VG1tIqKJXEezfZzX283h/qSLK6v4jmrcpP4ppsa4EfMTqG3M7z+1q4BOvsHqa+Os6Q+cdJ2ghrxUqy6grC/QahBZic1nTx4nuMf7t3Fpj/teyaW5MIK3v3CM/jkz5/gOw8coC+VGZkF8+0tB3jV+uW879qpxZb4FbNT6O2MXv/xvhSDGUdF1Jg3J84NFy/mvdecA1DyOJzp1l7IuvyI/wliDTJ76ZND8zA2rgRg07Y2vrZ5HxsfOkj/YOakaZcDg1k2PnSQLfs6ZrT+qb5+qoq9neH1pzJZ0lkPcGSdYzDjjWynVPs6XcWqKwj7G4QaZPZS08nDcFxJfaJiJJYkmc4OxZV4jL0L3QHJtDfl2JKJ1l+smJ1ibWd4/fFYBIcRixqeg8pYZGQ7pdrXfGsvdF1B2N8g1CCzl5pOHkbHlYyOo8nFlUQYOz3GgKqKyJRjSyZafzFjdoqxneH1D2Y8DEcm64gYpDLeyHZKta/51l7ouoKwv0GoQWYvNZ08DMeVALT35H47HI4ruXHtUqrjMUb3nUQ8yk1rl045tmSi9RcrZqdY2xlef2UsSkU0FzkTNSMei4xsp1T7Ol3FqisI+xuEGmT2UiJBgWNwPM9x/54OfrP7KG2dSZrrK7lq1QIuXzm9u4NKFXtS7O0Mr7+1c4DOgUHqE3GWNCRO2k5QI16KVVcQ9jcINUj4KAZnBvyMwRERCaNCNJ3QXF4zs0oz+7iZtZrZgJltMbPn+12XiIhMXWiaDvB14B3At4FbAQ/4HzO73M+iRERk6kIxOdTMLgVeCbzDOffpoWXfBB4BPg5c5WN5IiIyRaFoOsBNQBr48vAC51zSzL4CfMzMmp1zbX4VN1mkSKHiRsZbDzCldedbQybj8bXN+9h7tI+Wpjm8bsMKYrEwnRyLSNCEpek8C9jpnOsds/z/yE2DuRjwpelMFikChYl4GW8b1124CDDu2j75uvONPMlkPG76wmZ2HOzBc46IGf+9o43vv2mDGo+I5C0s/3s0M35TGV62eOwDZtY12RdQV4jCJosUKVTcyHjr2bj1EBsfOnjadedbw9c272PHwR7AEY8Z4NhxsIev3T95sraIyGTC0nQSQGqc5clRj/tiskiRQsWNTLSeZNo77brzrWHv0T4854hFjYhFhiJsHHuP9E17jEREhoXl8toAUDnO8qpRj5/kdPeRF+psZ3SkSH2i4uRIEcfEjxVgGxinXfek9U2ipWkOETMyWUcs6g1F2BgtC+ZMe4xERIaF5UynjdwltrGGl7WWsJaTTBYpUqi4kfHWc9O6pdy4dulp151vDa/bsIILltYCxmDGAcaFS+t43eUrplW7iMhooUgkMLNPkpubM2/0zQRm9n7gY8AS59y0Gk8hEwkmixQpVNzIeOsBprTufGvIZDy+dv8+9h7po2XBHF53ue5eE5nNZk0MjpldBmzh5Hk6leTm6Rx2zl2ZxzoVgyMiMg2FaDqheE/HOfeAmX0P+ISZNQN7gNcCy4Fb/KxNRESmLhRNZ8hrgL8b+t4AbAf+0Dl3n69ViYjIlIWm6TjnksB7hr5ERCSE9K6wiIiUjJqOiIiUTCjuXisGM/MAq6srSBqOiEjZ6+7uBnDOubxPWGZz08mQO9PryXMVw92quzAVzQoas+nReE2Pxmt68hmvWsBzzuV9P8CsbTozNRSjc9q4HXmGxmx6NF7To/GaHr/GS+/piIhIyajpiIhIyajpiIhIyajpiIhIyajpiIhIyajpiIhIyajpiIhIyWiejoiIlIzOdEREpGTUdEREpGTUdEREpGTUdEREpGTUdKbJzJrN7A4zu8fMTpiZM7Or/a4rqMzsEjP7nJk9ZmZ9ZnbAzP7TzM7yu7YgMrNnm9kPzWy/mQ2YWbuZ/dTMNvhdW1iY2XuH/l0+7HctQWNmVw+NzXhf55SihtB8XHWArAbeB+wGtgP6z2By7wOuAL5HbrwWAW8Dfm9mlzrnHvezuABaSe7f5ZeANqAeuBn4jZm92Dn3Cz+LCzozWwTcBvT5XUvAfRrYOmZZayk2rFump8nM5gJx51yHmb0U+CHwPOfcr/ytLJiGfkN/0Dk3OGrZKmAH8J/OuVv8qi0szKwa2EtuHK/zu54gM7OvA8vIXcWpd85d7G9FwTJ0VeYe4GXOuTv9qEGX16bJOXfCOdfhdx1h4ZzbPLrhDC3bBTwKrPGnqnBxzvUDR8md9cgEzOxS4FXAO/2uJQzMbK6Zlfxql5qOlJyZGbAQOOZ3LUE19B/CfDNbbWa3A+cD/+t3XUE1dEz9C/AN55zeyzm9b5H71OQBM/u5mV1Qqg3rPR3xw83AEuADfhcSYF8Dbhz6eRD4N+B2/8oJvNcA5wIv9buQgBsEvg/8D7lf+i4E3g3ca2aXOOeeLHYBajpSUkN3yHwOuJfcb1syvo8AXwCWAq8GKoEKIOVnUUE09D7rHcAdzrk2v+sJMufcZmDzqEU/NrNNwIPAh8j9QlhUajpSMkN3Fv030Am83Dnn+VxSYDnndpC72QIz+za5/xS+DtzkY1lBdRu53+D/0e9Cwsg5t83Mfgk8vxTb03s6UhJmVkfulL4OuMY51+5zSaHhnEsDPwL+2MwSftcTJGbWDPw/cmfPC83sTDM7E6gC4kN/bvCxxLB4GphXig2p6UjRmVkVsAk4G7jOOfeEzyWFUQIwYK7fhQTMQiAOfBzYN+rrMnJ3R+4jN1dMJtdC7g7JotPlNSkqM4sC3wUuB17inNvic0mBZmZNzrmjY5bVAi8HnnbOHfGnssDaB7xsnOUfBeYA7wCK/uZ4WExwfF0JPA/4Rklq0OTQ6TOz24Z+XAP8GfBVcgd/l3Pus74VFkBm9mngVnJnOv815uFevyaoBZWZ3Q0kyb3Z2w6cAbyO3A0Fr3TOjR1DGYeZ/QpNDj3F0PHVT+74OkbuVvw3At3AJc65A0WvQU1n+sxsokHb75w7s5S1BN3QP/7nTvCwxmsMM3s9z9z+2wB0AVuATznnfu1nbWGipjM+M/tLcneonQXUAkeAnwEfLkXDATUdEREpId1IICIiJaOmIyIiJaOmIyIiJaOmIyIiJaOmIyIiJaOmIyIiJaOmIyIiJaOmIyIiJaOmI+IzM7vdzNxQGsHYx8zMfmVmKTM734/6RApJiQQiPjOzOLCVXM7a+c65g6Meewe5z4n5a+fcHT6VKFIwajoiAWBma4EHgLudc9cMLVsN/B7YDlzhnMv6WKJIQejymkgAOOceAv4eeJGZvXHoIyG+Se4zdF6rhiPlQmc6IgFhZhXA78h9oNa3gbcA73LO6WOYpWyo6YgEiJldRK7xVAD3As91znn+ViVSOLq8JhIs3UBq6OefqOFIudGZjkhAmJkBdwMbgD3AcuBC59weXwsTKSCd6YgEx9uBq4GPAC8HYsBXh5qRSFnQmY5IAJjZKuBh4FHgcudc1sz+GrgduNU59xlfCxQpEDUdEZ+ZWQT4LbAOeJZz7vGh5VFgC3AuuswmZUKX10T89y5y7+P8zXDDARiam3MLuswmZURnOiI+MrM15FIHfg9cOd4kUF1mk3KipiMiIiWjy2siIlIyajoiIlIyajoiIlIyajoiIlIyajoiIlIyajoiIlIyajoiIlIyajoiIlIyajoiIlIyajoiIlIy/x+MdurjJQ+1MAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred = res.predict(exog)\n",
    "\n",
    "idx = x.argsort()\n",
    "x_ord, y_pred_ord = x[idx], y_pred[idx]\n",
    "plt.plot(x_ord, y_pred_ord, color='m')\n",
    "plt.scatter(x, y,  s=20, alpha=0.8)\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.savefig('poisson_regression.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def logistic(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "\n",
    "np.random.seed(5)\n",
    "n_sample = 100\n",
    "a = 3.0\n",
    "b = -9.0\n",
    "\n",
    "x = uniform(1, 5, size=n_sample)\n",
    "q = logistic(a * x + b)\n",
    "y = binomial(n=1, p=q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12e969828>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.linspace(-8, 8)\n",
    "plt.plot(xx, logistic(xx))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom(n=1, p=0.8).pmf(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x12eb08e48>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sObKcuT8M7JJ0qaR+4EZgf2MDSVcBfwRMRsTR7pdpZmadaBvuEVEEbgHuB54A7o6IxyTdJmmy2uwPgWHgv0t6VNL+RbozM7NVkOWyDBFxH3Bf03N7G+6/tct1mZnZefBfqJqZJcjhbmaWIIe7mVmCHO5mZglyuJuZJcjhbmaWIIe7mVmCHO5mZglyuJuZJcjhbmaWIIe7mVmCHO5mZglyuJuZJcjhbmaWIIe7mVmCHO5mZglyuJuZJcjhbmaWIIe7mVmCHO5mZglyuJuZJcjhbmaWIIe7mVmCHO5mZglyuJuZJcjhbmaWIIe7mVmCHO5mZglyuJuZJShTuEu6TtIBSQcl3dpi+4Ckr1S3PyRpZ7cLNTOz7ArtGkjKA3cAbwMOAw9L2h8Rjzc0ez/wfERcJulG4BPAe1aiYIBDx2Y48MwJLt+6gQ3r+zj64iwXj6zjxOl5vvf08/QXxNYN6xkbHmC2WOLikXVsHOwD4PjMfL197blmtTbrCnlmi6VzbmuvffzIcaZ+9hwTr9jM+LaNi9bbPGZz/61qaZzjji2D9X6enD4JBK8cG1m0/k7nAtTra7yfpf9W81ts7Fr/T06/CGjB/mk17mLrlmXfdVJ/7XVPTp/k5Nw8wwN9vHJs+Jy5ZF37duvRyXxS8VKa61rRNtyB3cDBiHgKQNJdwB6gMdz3AL9Xvf9V4DOSFBHRxVoB+PQ3fsynHjgIQKkcbFzfx+ahfp47dYbjp+cpN4yYz4mLRwYY7M+z9/pxAG6792zZe68f582XX7yg/28dOMpt9z7Oqbkix06dYXigwMm5Yv12dLjS39aRAf7XU8/VX3fDVS/n9vdcdU69tf5q3vm6l/O1R39e77/WX2MtjXME+PC1l/Ga7Rdx6z0/4tmTcwBsGernE+96zTn1txp75kyJZ0/OnTOXLUP9SCIiGBoocGquiCQG+/OLrk+7+dVe0zx2bazTZ4qcOlOiVA6kyv4B6jXU+gBarlvzOFlqaedbB45y6z0/4pkTs5Tj7HHzBze8uj6XrGvfbj06mU8qlrtf7PyoXf5KejdwXUT8ZvXx+4A3RMQtDW3+rtrmcPXxk9U2zy7W78TERExNTXVU7KFjM1x7+zcByEvMFssAXDo6xE+ePdXyNf35HDs2r6dUDkD0F8RAIc9csRIw93zg6gVnijd89tuVsZ4/TblcplSGfA5KZSjkRU6VM87DL5yuzh1qS3jfh9604Ay+1l8+Vxlz5kyRp5+bYdtF6/n58VkigpzE9k3rAbjnA1dz4vR8fY6FXI5iuUxE8Esb1/PMiVlyEgDlCLZdtJ6//OCbWp4JNc7l8POnKUdQLEV9Lvkc5JSjHGUk8cujwzz17EkAdl08QrFcPmd9FhujNr/amn7hpt3c9IXvLhhbiHK5TDGgLwfFMgTQl89VFlBnxz1TDCDoL+QWrNslmwcZ7C8sue+aa1mq/trr9tzxbQ4/f4pStSYBhZzYtmmQL/7z3bzv89/lyAszbde+3Xo0HwdLzScVy90vtjhJj0TERLt2q/qGqqSbJU1Jmpqenu749QeeOQFUQq/2TQhwcnZ+0dcElQAtloJSucxAoXJWOlDIE1G5FFBTu5+TICBfG0ciqs8HMFcsVeZTn1fldupnZ8/kG/urjXk2HIA4O4+cVK+lcY71uQbMzpfISfUvUZlTY/2txq6NWbtV9bYyt8rZsxCn50sIIYn5Urnl+iw2RvOa1uZQG7NQHat5wUTljB2BODtuqfqDZcG6xdn+ltp3S+3fxeZQKpfr66J6jVAqlznwzAlK5XKmtW+3Hs3HwVLzScVy94udvyzhfgTY0fB4e/W5lm0kFYCNwLHmjiLizoiYiIiJsbGxjou9fOsGAIrlciUYqs8Pr1v8DECIcgSFvMjncvVgniuWkKhf74Wz98vVwCnVxolA1efF2QO1Nn7tzH3iFZsXjF3rrzZmudowJ0Bn51GOqNfSOMf6XAXr+vKUI+pfQWVOjfW3Grs2Zu229ptaZW6VSzJBsL4vTxBEBH35XMv1WWyM5jWtzaE2ZrE6VvOC1X5wEpUfwrVx87kc+ZwWrpvO9rfUvltq/y42h3wuV1+X+i+y1R/ul2/dQD6Xy7T27daj+ThYaj6pWO5+sfOXJdwfBnZJulRSP3AjsL+pzX7g16v33w08sBLX23dsGeTD114GQLEc5ASbBvsQlducFrbP58TmoX4A9k1ewb7JcUrl4NRckVI52Hv9+IJfDTcO9tWv925a34ckNjbcAmwa7GegL8c//OVKkNdmecNVLz/nTdVaf7UxoXL9PJ8Tmxr6A+q1NM5xvlQJ+I+8ZRcff+eVjA4P1ANmy1A/+yavWPRX2wVzqY6xsWlOmwb7GBtZx5ahfuZLZbYM9TM6PMDsfKnl+iw2RvOa7tgyeM7Ymwb7GNuwjovWF0BCquyfLUP9jI4MsGWovz7uvslx9k1ecc66AW333VL7d7E57JscZ2xkXf2sPZcToyMD7JuszGXf5HimtW+3Hp3MJxXL3S92/tpecweQ9A7gk0Ae+HxEfFzSbcBUROyXtA74InAV8BxwY+0N2MUs55p7jT8t40/L+NMyF5aX0lxXWtZr7pnCfSWcT7ibmb1Urck3VM3MbHU43M3MEuRwNzNLkMPdzCxBDnczswQ53M3MEuRwNzNLUM8+5y5pGvjZMl8+Ciz6j5L12Fqtba3WBWu3trVaF7i25VirdUFntb0iItr++y09C/fzIWkqy4f4e2Gt1rZW64K1W9tarQtc23Ks1bpgZWrzZRkzswQ53M3MEnShhvudvS5gCWu1trVaF6zd2tZqXeDalmOt1gUrUNsFec3dzMyWdqGeuZuZ2RLWbLhL+ryko9X/n7XVdkn6lKSDkn4o6fVrqLZrJB2X9Gj1a+8q1bVD0oOSHpf0mKSPtGjTk3XLWNuqr5ukdZK+K+kH1br2tWgzIOkr1TV7SNLOla6rg9pukjTdsGa/uRq1VcfOS/q+pHtbbOvJmmWsrSdrJumnkn5UHfOcf++869+bEbEmv4BfAV4P/N0i298BfJ3Kf8X5RuChNVTbNcC9PVizlwGvr94fAX4MjK+FdctY26qvW3Udhqv3+4CHgDc2tfmXwOeq928EvrKGarsJ+MxqH2vVsT8GfKnVPuvVmmWsrSdrBvwUGF1ie1e/N9fsmXtE/C2V/9VpMXuAP42K7wAXSXrZGqmtJyLiFxHxver9F4EngG1NzXqybhlrW3XVdThZfdhX/Wp+I2oP8CfV+18F3iKp6T917FltPSFpO/CrwB8v0qQna5axtrWqq9+bazbcM9gGHGp4fJg1EBYN/kH11+mvS7pitQev/hp8FZWzvUY9X7claoMerFv1V/hHgaPA30TEomsWEUXgOLBljdQG8K7qr/FflbSjxfaV8EngXwPlRbb3bM1oXxv0Zs0C+GtJj0i6ucX2rn5vXsjhvpZ9j8qfCL8W+DTwtdUcXNIw8OfARyPixGqO3U6b2nqybhFRiojXAduB3ZKuXI1xs8hQ218BOyPiNcDfcPZsecVIuh44GhGPrPRYncpY26qvWdWbIuL1wNuBD0r6lZUc7EIO9yNA40/c7dXnei4iTtR+nY6I+4A+SaOrMbakPirh+WcRcU+LJj1bt3a19XLdqmO+ADwIXNe0qb5mkgrARuDYatW1VG0RcSwi5qoP/xj4+6tQztXApKSfAncB10r6b01terVmbWvr0ZoREUeqt0eBvwB2NzXp6vfmhRzu+4F/Vn2H+Y3A8Yj4Ra+LApD0S7Xri5J2U1nnFT+wq2P+V+CJiLh9kWY9WbcstfVi3SSNSbqoen898Dbg/zQ12w/8evX+u4EHovoOWK9ra7omO0nlvYwVFRG/ExHbI2InlTdLH4iIX2tq1pM1y1JbL9ZM0pCkkdp94B8BzZ+26+r3ZmHZ1a4wSV+m8umJUUmHgd+l8oYSEfE54D4q7y4fBGaA31hDtb0b+ICkInAauHE1DmwqZy3vA35UvU4L8G+BSxpq69W6ZamtF+v2MuBPJOWp/DC5OyLulXQbMBUR+6n8UPqipINU3ki/cYVr6qS2D0uaBIrV2m5apdrOsUbWLEttvVizrcBfVM9dCsCXIuJ/SvoXsDLfm/4LVTOzBF3Il2XMzGwRDnczswQ53M3MEuRwNzNLkMPdzCxBDnczswQ53M3MEuRwNzNL0P8H4ddkrri3994AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y,  s=20, alpha=0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## custom GLM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "xとyは指数関数、誤差は正規分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.random.seed(5)\n",
    "n_sample = 100\n",
    "a = 0.6\n",
    "b = -0.4\n",
    "sd = 0.8\n",
    "\n",
    "x = uniform(1, 5, size=n_sample)\n",
    "mu = np.exp(a * x + b)\n",
    "y = normal(mu, sd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'endog' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-13-7fe8e615e949>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m  \u001b[0ms\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.8\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mmod\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mGLM\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mendog\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexog\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfamily\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfamilies\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mPoisson\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmod\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msummary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'endog' is not defined"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1197b57f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y,  s=20, alpha=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Generalized Linear Model Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>y</td>        <th>  No. Observations:  </th>    <td>   100</td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>GLM</td>       <th>  Df Residuals:      </th>    <td>    98</td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>       <td>Gaussian</td>     <th>  Df Model:          </th>    <td>     1</td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Link Function:</th>      <td>identity</td>     <th>  Scale:             </th> <td>1.51629275199</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>IRLS</td>       <th>  Log-Likelihood:    </th>   <td> -161.70</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>           <td>Sun, 22 Sep 2019</td> <th>  Deviance:          </th>   <td>  148.60</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>               <td>10:28:26</td>     <th>  Pearson chi2:      </th>    <td>  149.</td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Iterations:</th>         <td>2</td>        <th>                     </th>       <td> </td>      \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>   -3.0905</td> <td>    0.326</td> <td>   -9.479</td> <td> 0.000</td> <td>   -3.730</td> <td>   -2.452</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    2.7766</td> <td>    0.102</td> <td>   27.301</td> <td> 0.000</td> <td>    2.577</td> <td>    2.976</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                 Generalized Linear Model Regression Results                  \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   No. Observations:                  100\n",
       "Model:                            GLM   Df Residuals:                       98\n",
       "Model Family:                Gaussian   Df Model:                            1\n",
       "Link Function:               identity   Scale:                   1.51629275199\n",
       "Method:                          IRLS   Log-Likelihood:                -161.70\n",
       "Date:                Sun, 22 Sep 2019   Deviance:                       148.60\n",
       "Time:                        10:28:26   Pearson chi2:                     149.\n",
       "No. Iterations:                     2                                         \n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -3.0905      0.326     -9.479      0.000      -3.730      -2.452\n",
       "x1             2.7766      0.102     27.301      0.000       2.577       2.976\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exog = sm.add_constant(x)\n",
    "endog = y\n",
    "\n",
    "mod = sm.GLM(endog, exog, family=sm.families.Gaussian(sm.families.links.log))\n",
    "res = mod.fit()\n",
    "res.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 負の二項分布回帰\n",
    "np.random.seed(5)\n",
    "n_sample = 100\n",
    "a = 0.6\n",
    "b = -0.4\n",
    "sd = 0.8\n",
    "\n",
    "x = uniform(1, 5, size=n_sample)\n",
    "mu = np.exp(a * x + b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(5)\n",
    "n_sample = 100\n",
    "a = 0.6\n",
    "b = -0.4\n",
    "sd = 0.3\n",
    "\n",
    "x = uniform(1, 5, size=n_sample)\n",
    "mu = a * x + b\n",
    "y = normal(mu, sd)\n",
    "\n",
    "plt.scatter(x, y)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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