notebooks/12_logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Agenda\n",
    "\n",
    "1. Refresh your memory on how to do linear regression in scikit-learn\n",
    "2. Attempt to use linear regression for classification\n",
    "3. Show you why logistic regression is a better alternative for classification\n",
    "4. Brief overview of probability, odds, e, log, and log-odds\n",
    "5. Explain the form of logistic regression\n",
    "6. Explain how to interpret logistic regression coefficients\n",
    "7. Demonstrate how logistic regression works with categorical features\n",
    "8. Compare logistic regression with other models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Predicting a Continuous Response"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ri</th>\n",
       "      <th>na</th>\n",
       "      <th>mg</th>\n",
       "      <th>al</th>\n",
       "      <th>si</th>\n",
       "      <th>k</th>\n",
       "      <th>ca</th>\n",
       "      <th>ba</th>\n",
       "      <th>fe</th>\n",
       "      <th>glass_type</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.51966</td>\n",
       "      <td>14.77</td>\n",
       "      <td>3.75</td>\n",
       "      <td>0.29</td>\n",
       "      <td>72.02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>9.00</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>1.51115</td>\n",
       "      <td>17.38</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.34</td>\n",
       "      <td>75.41</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6.65</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>1.52213</td>\n",
       "      <td>14.21</td>\n",
       "      <td>3.82</td>\n",
       "      <td>0.47</td>\n",
       "      <td>71.77</td>\n",
       "      <td>0.11</td>\n",
       "      <td>9.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1.52213</td>\n",
       "      <td>14.21</td>\n",
       "      <td>3.82</td>\n",
       "      <td>0.47</td>\n",
       "      <td>71.77</td>\n",
       "      <td>0.11</td>\n",
       "      <td>9.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>1.52320</td>\n",
       "      <td>13.72</td>\n",
       "      <td>3.72</td>\n",
       "      <td>0.51</td>\n",
       "      <td>71.75</td>\n",
       "      <td>0.09</td>\n",
       "      <td>10.06</td>\n",
       "      <td>0</td>\n",
       "      <td>0.16</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          ri     na    mg    al     si     k     ca  ba    fe  glass_type\n",
       "id                                                                       \n",
       "22   1.51966  14.77  3.75  0.29  72.02  0.03   9.00   0  0.00           1\n",
       "185  1.51115  17.38  0.00  0.34  75.41  0.00   6.65   0  0.00           6\n",
       "40   1.52213  14.21  3.82  0.47  71.77  0.11   9.57   0  0.00           1\n",
       "39   1.52213  14.21  3.82  0.47  71.77  0.11   9.57   0  0.00           1\n",
       "51   1.52320  13.72  3.72  0.51  71.75  0.09  10.06   0  0.16           1"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# glass identification dataset\n",
    "import pandas as pd\n",
    "url = 'http://archive.ics.uci.edu/ml/machine-learning-databases/glass/glass.data'\n",
    "col_names = ['id','ri','na','mg','al','si','k','ca','ba','fe','glass_type']\n",
    "glass = pd.read_csv(url, names=col_names, index_col='id')\n",
    "glass.sort('al', inplace=True)\n",
    "glass.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question:** Pretend that we want to predict **ri**, and our only feature is **al**. How could we do it using machine learning?\n",
    "\n",
    "**Answer:** We could frame it as a regression problem, and use a linear regression model with **al** as the only feature and **ri** as the response.\n",
    "\n",
    "**Question:** How would we **visualize** this model?\n",
    "\n",
    "**Answer:** Create a scatter plot with **al** on the x-axis and **ri** on the y-axis, and draw the line of best fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "sns.set(font_scale=1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x4136358>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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59pIEr7c/vcpnicdTJXXIYR28PT5e2nky+vlLO0+ycn5twhbwxXwfplodCqUemYa/neHr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\n+P8B+BrrLF79BLIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x184006d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='al', y='ri', data=glass, ci=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question:** How would we draw this plot without using Seaborn?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x18395d30>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RRwHFxR2iq5k25zqrw6OItFQ6WyoCxDS1OOeKgR7AATOrwXvMscA5NwN4Fm+e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\n/AO8wGoeFgYWewAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x41362e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scatter plot using Pandas\n",
    "glass.plot(kind='scatter', x='al', y='ri')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x187b42b0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qxUknfT9KKLrGkP2+XLGuWLGehQsnMHnyHCZPnsMPfvAZFi1azXHH/ajL8M64\nejUK6Snpz3UudHKyXENXB6PHpljHEZH+KVlPhbt/Juv7R8lKctz9TuDOHt7/OeBzBRxnAbCgn6dZ\nVKUaDVCNQ/Dy9aS0tKxh06aGbu9rb9/W5X3Llv2A/fbbDJzard35598bTb2d4qGHbqC19W8JnWU9\nT8U9GLGk9eU697U3INfQ1ThiK9VxRKR/yrZQs1qVaihc3MftPgdDfDNExqGwm9PxwCIgjJwYNeo6\n4KCM96VYt24ooSOs62yYMCyj3QPRKqgPDGIs5+zc/9q1jbS0PJjzepbzUFIRSb6yLdSUZEv/VTx3\n7qpYZ4gslkmTjmLYsBsI69ndw9Ch32LlytOora3NaPUQcD6hTOc84B4mT57DXXdNzmqXdgIhScn9\n+KG/xZ7t7duAuwgz148HlkTbcst3nP48uirWozsVj4qUN/VUyKAppwmIUqkUixatZsOG5xgz5kOc\neeYxLFv2A9atez8AY8e+RGPjWTvbr1ixntbWbwKrAaet7XhWrtxAU9OJUQ9MI/A7wk08RUgwYMyY\nQ6irq6OxcRw//entPP74ucA71NVdTir1b8AZjBp1GRdc8FGamjoTrYH1DtQQkpt0IvN5IHvgVOfP\nYTB6IYr1CG0gx1GBp8jgU1IhFS8sp70kelRxKcuXw89+diswBAhzNtTU3N7Du98gPN6A+fOvpakJ\nFi6cwEkn3cKmTRcRBhLVAmcDD/ODH/ya9vbt1Nbuyvbt7wK3ANNIpSYwatQsLrjgYzQ1XdzlhpZK\npfjmN2/Nu/R5rrhaWtawYcOz3V5L95Rk30gLeexT6KOrXDfpYiSR/TmOHumIFIeSCgFK91dcMY7b\n0rKGdesOBE4mfTNdv34kIaEI3z/++Be73FwbG8dx881X8vzzV+9ss2nT1J1/IYdRITsIc6xdRFiW\n5kxeeGEzl1/eCNwD/HXGMWvZtGk2tbWruiUU4WZ3BKHHI1130fuad11vkuMZNmwOra3Tga7DV7Nv\npKecMizvz6uQ3oCk3aRV4ClSHKqpkJIN0yvNcVPA3cBTeVvmmsK+vb09Yz93Eta9e5gw+nkNnY8h\nsvP1FHAPa9c+3SXGzpvdccCNpOsihg27kUmTjurx3LoWZ66htfXCbiucdu57B/AAa9fuS3t7W0E1\nCfmGkiZhyLCIFJ+SCunTDSLOmSOLdWNqbBzH2LF/Ijyq+Anhxn0R9fXfJdxcWxk16jLa29tJpVI7\nH0e88MJfALG5AAAgAElEQVRYoPMGHEYmd9DYOI5Ro64iJBInAeuyjpiK2m/MOOZ3gIksX35pD8nT\nL4HppH8Wra3TWbFifY8xdS/OXMmYMYfkSALSyc94YCILF77CwoUTEltA218q8BQpDj3+kIIlrcs7\nra6ujqVLz+LrX/8+K1fOJH3j3rLly/zt336dl1/en02bvs3MmbBy5Q+oqRnC448fQbgB7QDujfaU\nYt26lwE47LBaNm2CsODtRcBsQu3F9wh1GLOBT7HbbvPYtm0IcCW5ut4nTTqK2bPn0No6uuB4UqkU\n69Y5kI4FchVnNjaO45ZbrmLTpm+T+QhnxYqBd/uX+5DhbNU4F4tIKSipkIJvEHE/ly7WjSldtzFk\nyJDMrcBKNm6cSGatRRgNMpGwFt0sQg/DasJadrWsXHkxK1f+O6FXIT03xS+AfwJWEJaluYWQjNzO\ntm3HZBzzTeBWYAdvvbUvCxY8wNq1T9Pa+i1CDcZVwL8AMGzYXCZNOr9bDO3t27jvvrf5+c+P7BZn\n9jDWuro6Lrjgo8yc2defWH5JvEmX02gkkUqlpEIqeibPngsa7yPUP2ROSPUm8CBhxvgF0eefEBKO\nIwjJx91Auk5hb+Bqdt/9j2zd+g/AeuAgQsKyFPibaL9HA1cQejVmACm+8515/OUvzYT/gnXAXxF6\nOh4EoLX1IlasCBNYdY3hHsLcGTvInJirp4SsqekE/uM/ek7cBlIoq5u0iGRTUiFAYTeIwehZGOwb\nU3bdRmvrRUyePAeA5csn0jkh1SnAD4BLgX8FbiIkEHsQkol08vFM9J6lhJqK7Wzduh+h1yLUZ8DV\nhMcdO4AfEda124OQUIQZNv/yl3+Nvj4peu8+hORiYnSczsmrusaQ/i9bR1j+5h4mT97IDTd8JWdC\nUFdXx8KFE5gxI8Q8Z07zgObGqMa5HqoxZpH+UlIhBUtil3d3dTQ0HEZj4zheeSWdIJ3BHntM4d13\n5xMed0yI2tYC26Ov08nHwXQmDbXAHwg9DDuAFwiPRWZnHG8IsDs910TXAWdx6qnXsHGjs2nTVKC3\nhO0EOh+77EJDw6s7E4pcN79UKpWxBgm88sodOUaHhCnH167dl29+89YeE5Suq7amuOWWq6JJvE6I\n5d9B+vzr6+uYOPGonPss9g0+qXVEIqVSk2vYnADQsXnzllKfw6AYMaKeSo0NusbXeVNoBsLNOn1T\nyLxB/eIXG1m5Ml2ncDyhJ+IMYDHhpvt5IMVBB11Oa2uKN964Idq+gs75Lu4mjLJ4B7iZsIjudELC\nMZ/weGU6kGLIkGvYsWNWl3MCct4ws2M49tg7+Oxn30NtbW2X5CHz5tfQcEeUAK5h+vRT6Szo3Mbc\nuaEOZsGCB6LXdhBGiDR1eW/2fBrHHfe9qOgzf/u+6un8c8/p0XObuHX+jLr//Pqrkv//VXJsUBXx\n1Qx0H+qpkIrWW+9K5qOXSZOO4v77v0Nb2xw6E4qH2WuvjXz1qx/n6afnMGbMh2hq+udoWfRro16F\n46mv/y5btswAjo2+/ibhccZ+6bMALgD+L+9//xf5+McP4aqrmrj33u7n1NPN6pRT6tl//3AO06ad\nz5Yt7V1ez1VEu2jRMjZseI7sFVTTOh9n7QucSW8LknVdtfUhQkIRT8FuKpXi61//PmvXdo5mybVP\nTWAlUv6UVEjFK6RuY/jw4WzYMJVPf3oer732T8DDjBr1OPff/88MHz682/4eeyzMwNnevo329oN4\n4ok50ZoizcyYcQPLl19K12LKXWhoeJe77rpuZ89CLtnd+0CXv85feeUOpk3rvpZJjj0xf/6LbNr0\nFUJNx1QgxahRV9Pe/lFSqdTOhOvrX7+JlSv/l1C4CrCQ9vY9u5zP2rVPA9+K4tmry3HgPtaufbpf\njyM6p1Bv69P7iiVpQ2dFSk2PP3qmxx8JNZD4ct3Uc9UppId3rlr1Fo8//iXCDTvUGADMnHk66VoF\nuK9LMWVP3fhAdIM9EICxY//EhAnDomm/O7vfb7zxbhYvfjlayyQkAkcddSu77FLL449/EYBRoy5j\n06aZpKcPh/vYddf/ZPv2K7scs66ujh/+8O6M8w3HuOqqn9LUdELGeaYYNuwGWlsvAu6jru4JUqkZ\nwJKd51DI44hca5FMn74rYYTMAuCb0flfx2OPfbGHxx/N0fEWFKW+Ie46jkr+/1fJsUFVxDfgxx9K\nKnqmpCKh4oov181/4cIJUeHjF4CVhBqK1YT5Kb4FwNix6Qm0vhi9bwELF07YOUNme3t7t5v43Lmh\n12PmzHfo7DGYz157Pc3rr1/bpe1ZZ81jyZLRZM6vERKBZdTW7pZxjN0z2qTrPXqrrej6GpC1vZXJ\nk2+goeEwJk06ihkzFkQ9Mp3vu/zyf+eJJ14EwkiTzF6eXD/PU04ZxsyZQ4C3SC/KBo9z+eWH8rWv\nnZbzmiR9JMZg//8r5c9Iv1uSTTUVIoMo1zP8GTPmRCMpdhCm534DGEFIKNITaE3hqquWcdpp4cY8\naVJmIgKjRv0rcHq344X6h8yb9Pt4/fXzCMNS9wTWsvvur/PrX4+kc1RKp/b29p1JxZlnHsP8+d9n\n06aT88bZUxd/9ynTw8iZ9KOkhobDWL488/U3+e53/5tUKhSgPvTQHDZsOH9nYpHr53nKKcv44AfX\nZyzc9g/ABGprcy/drrkxetfbaJVCk41KSNykdLT2h0gf7NixI/rqIeBjhF6F7rl5be1uOxfkWrr0\nl13myti06V8YNepasteh6KyNyF70LAU8D1zP1q2NbNr0r8BjwLfpXJfkcn70oxd3Ls52/vn3snLl\nlzKOcyzDhs3pdkzoLGbNXg8ke72MsWN/SHt7+851X7Jf33vvf44Sis71S2bMWNDrz7O2djemTPl4\nju21OVoPjjjXsynkWLfeevegHaun9XQKXbyvVIsLSuXQ44+e6fFHQsX/+KMZgLFjf0hHx19Yv353\nYBjwWzonubqTzNktM/867ByK2f1RRVgYrIba2lomTDiCiRP/nRdfPICQrKQYOnQGbW3vp3OxsfQQ\n1m8B3yWsjJpevOyfo3N5CGjnqqu2cuaZn9p5Y7/yykbuvfe/gML/As1dP9K1DqTrsNzM9Ui2ceqp\ns/nUpz4ChBE2ocemucvPCejycz7uuJ+waNHf9+n8+hJT9vv7Oky1v8csxpDYwh9l5R4aO9AhtPrd\nkmx6/CEyiLKHo7a37x3VQuwgLBz2L3SO7jiDvfa6mIsvPoamps4bRRiKOZPMKbVHjbqOpqZQb5FZ\nCDl79g20th5OGAJaC+ygre2vMs4oBfwJmEN45FJHmAzrTuAjdE4PHuaP+MEP5kSJQPeJr/LJVVAZ\nEoruwzkzh+U++mh6GnSor7+KV17ZP7pJha74UFvSfSht5s/5G984t9uQ2Z7OcaATU/V1mOpAjlmM\nIbGFP8oSGRx6/CHSi/Qz/K6/+OuAj9I5VfaDwMNcfPHRTJkyMccNJrPdPVxwwQdyzGi5htbWGVHb\ntIeASwj1E3MI65WMJIyQ+EvGtibgOMICaOn5I2p54YXRGYlA4UvL5+oCb2/Pf5MPw3LPZ/LkOUye\nPIeLLz6E9eundDn+ihXrd/48M39OmT/nQpOCnrr6B1MpjtkXhT7K6mnpdy0RLwNVsqTCzG41sx/m\nabPEzP6S9fFAjnY1ZnavmXVbj9HMXs2xj3+JMxapfKlUipUrX6NzjY8w0VX4L/R3NDS8SlPTid3e\n1/lLuvd2ndLTgW8jzMz5M2AaMIow5BJC4jEW+DIh8UgRlj2P55d/rhsndBR0sxk+fDi33fYtbrvt\nW+yxxx6xnM9gKuZNNF+NSl/1VAuSK0HrKdnIVmg7kZ4UvabCzGoISzbOAua7+4W9tH0auIPwmzyt\nzd3fymizG2Gt6S8As9z96ozX9gP+DBwLPJuxj7fd/d08p6qaioQajPi6TmkdahYuv/wt9tgjPJ7o\nTzV915qNFMOG3Rg9OgiTVB12WC13330ZmUM6P/CB66Oai7MIc0ScRVivpHttx9ixP+w2tLWQm0RP\nz9XTj0HyxZsZd3/mlSj0+sU1b0VfaiQGesxUKsXdd6/n9ddbc9aoFPIz7a3GpdQJgH63JFvi5qkw\ns4OB24HDgXeBB3pKKsxsKLAF+Dt3f6yHNh+L9jcMeC9wTVZScQJwL7C7u+/ItY9eKKlIqMFNKuJb\nAwK63tAmTTpq51wWnRNDdT3mVVcto76+jkceeZKPfOQgamt3Y926ZzIKJLtOtgW51xPJd05xTTLV\nn6LGvly/Ugx/HOgxR4yoZ968ZX3+99S1nuMesucpiePf40Dpd0uyJbFQs4GwlOPZwF152h5KOL9n\nemlzIvAocBnwXzleHw38oR8JhUgXgzVdc/a8C5lf5zpmU9NkRo4cQWNj5yOUpqYT2Lw53a7ryqXZ\n+yz0nOJajXaw55UYyP77mxzkOmYxkpuuj6VUY19MhaygK0FR/2W6+2LCso+YWb7mowkPH68wswnA\nVkJp+2x3b4v2NzfduIf9jQa2m9kqYAzwEnC9u/9kYJFItSnFsu+FHnMwzq3SJ5mKc0nz/uxr4Enq\nCYSnwp/v5/ulUKVYHTfJyjndPSz6/HvgJuAIwspII4HmPuzjvYT6jX8h9BfeYWa7uvuCOE9WKl8p\nbrSFHrPSk4C4xTm8sz/76k8i2DUR2YWxY9s49dSfUltbW5Qkt1ppddy+KeekYhYwx91bo++fMrMd\nQIuZTXX3NwrYx3HAbhlFmRvN7CBCOf2CfG8eMaK+H6edDJUcGyi+pBvs+Orru9+A6+vr+nXc/uwr\nvFbPJZd0n669lyPx8MOfZ8GCBwFobv5SWSYSlfZvM85/K9WgbJMKd+8AWrM2Pxl9HklYdCHfPrbT\nfZGEJ4FzCjmHSi3IqYJiI8WXYMWIb+LEo2ho6Pr4YeLEyf06bl/3NdD4Tj89DHndsqW9oEnCiqkS\n/23G+W+l3MWRKJVtUmFmS4Eh7p65VOEYoI2wJGS+9+9KWDDhe+5+XdY+nsz5JhGpCnEXoxa73kaK\nJ/P6hkJNXd/elDKpqIk+ADCzWmBv4DV3bwdagCVmNpWwxvSRwDxgXg9zTHQZCuPu281sOTDTzJ4j\n1GZMIgziz790o4hUtDjrUFTTUtnS17cSe2LiVsppujuij7RjgJcJw05x92WEOYebCaslzSWM3Lis\nl/1lmwbcDNwY7eNc4Ex3Xx3D+YtIkRVzRVER6TutUtozTX6VUIov2XqKr1KG9lXy9avk2KAq4hvw\n5FdaUExEEqHcF/MSESUVIiIiEhMlFSKSCFqWW6T8le2QUhGRTBq6KVL+lFSISGJo6Gb5y1yeHWqi\nacSLs4KslJ6SCpGEKsWy3yK96Ryhcw5hIerzgYEt2CbJopoKkQRK//KePv1Upk8/lbPPXq55G6Tk\nFix4KBqhs4aQUGikTrVRUiGSQBpeKSLlSEmFiIjEorn5hGiEzrHAQjRSp/qopkIkgRobx7F8edeV\nExsbJ5f2pKTqdY7QeZD29j2Bn0aFmqqnqBZKKkQSSMMrpVxphE51U1IhVS+poyj0y1tEyo2SCqlq\n2YtUaeibiEj/qVBTqppGUYiIxEdJhYiIiMRCSYVUNS1SJSISH9VUSFXTKAoRkfgoqZCqp1EUfZfU\nETMiMriUVCSEfolLudCIGRHpiWoqEkCLR0k50YgZEemJkooE0C9xERFJAiUVItInGjEjIj0pWU2F\nmd0KDHH3Kb20WQKckbV5tbuPz2pXA9wD/MLdr8p67XPAZcBI4AngG+6+IYYQikaLR0k50YgZEelJ\n0ZOKKAG4ArgQmJ+n+WhgBmEN3bS2rP3tBtwCnAT8POu1E4Hbga9Hr10MPGBmH3b3/x1AGEWlX+JS\nbjRiRkRyKWpSYWYHE27yhwMv5mk7FDgEWO/ur/bQ5mPR/oYBb+Zocglwp7vPj9p/GTgemAJ8p59h\nlIR+iYuISLkrdk1FA/ACoQdiU562hxKSnmd6aXMi8CjwUeCtzBfMbBfg6Oh1ANy9A1gDHNu30xYR\nEZF8itpT4e6LgcUAZpav+WhCJdgVZjYB2AosBWa7e1u0v7npxjn2NxzYE3gpa/ufgU/0LwIRERHp\nSTlPfnVY9Pn3wE3AEcC1hILL5gLev0f0OXtChzZABQkiIiIxK+ekYhYwx91bo++fMrMdQIuZTXX3\nN/K8f2v0eWjW9qHAOzGep4iIiFDGSUVU/9CatfnJ6PNIIF9S8ToheXhf1vYDgD8Vcg4jRtQX0iyR\nKjk2UHxJp/iSq5Jjg8qPb6DKNqkws6WEeSxOy9g8hvD44rl873f3DjP7FfBpOus4dgHGAbcVcg6b\nN2/p41knw4gR9RUbGyi+pFN8yVXJsUF1xDdQpUwqaqIPAMysFtgbeM3d24EWYImZTQVWAkcC84B5\n7v5uD/vLdi2wysx+CzwCTAPqyT8/hoiIiPRRKafp7og+0o4BXiYMO8XdlwFNhKLMjcBc4Hp3v6yX\n/XXh7vcTJtm6GPgNYZjqeHd/PZ4QREREJK2mo6PbvViCjkrt5qqGLjzFl1yKL7kqOTaoivhy9fj3\niRYUExERkVgoqRAREZFYKKkQERGRWCipEBERkVgoqRAREZFYKKkQERGRWCipEBERkVgoqRAREZFY\nKKkQERGRWCipEBERkVgoqRAREZFYKKkQERGRWCipEBERkVgoqRAREZFYKKkQERGRWCipEBERkVgo\nqRAREZFYKKkQERGRWCipEBERkVgoqRAREZFYKKkQERGRWCipEBERkVjsWqoDm9mtwBB3n9JLmyXA\nGVmbV7v7+Oj1PYDrgcmEWJYCU939nYx9vArsk7WPWe5+9cCjEBERkbSiJxVmVgNcAVwIzM/TfDQw\nA1iYsa0t4+vbgCOBicBuwI+ibedFx9qPkFAcCzyb8b63+x+BiIiI5FLUpMLMDgZuBw4HXszTdihw\nCLDe3V/N8fqBwDnA8e6+Ptp2AfCImV3i7n8mJCXbgcfdfUeswYiIiEgXxa6paABeINzsN+Vpeygh\n6Xmmh9ePBv4C/DJj26+AHcCnou9HA39QQiEiIjL4itpT4e6LgcUAZpav+WhgG3CFmU0AthJqJma7\nextwIPBqZsLg7tujGoqRGfvYbmargDHAS8D17v6T+KISERERKO/RH4dFn38PnEyow7iAUDMBsAeQ\nyvG+NqAuYx/vJdRujCckJXeYWfPgnLKIiEj1KtnojwLMAua4e2v0/VNmtgNoMbNphJ6LoTneNxRI\nj/44DtjN3d+Nvt9oZgcB04AFg3bmIiIiVahskwp37wBaszY/GX0+EPgjsK+Z1URtMbNdgX0Jjzlw\n9+2EQs3sfZxTyDmMGFHfv5NPgEqODRRf0im+5Krk2KDy4xuosk0qzGwpYR6L0zI2jyE83ngOeI1w\n/kfTWaz5KcIjnV9GCcbzwPfc/bqsfTxJATZv3jKQEMrWiBH1FRsbKL6kU3zJVcmxQXXEN1ClTCpq\nog8AzKwW2Bt4zd3bgRZgiZlNBVYS5qOYB8yLHme8G02OdbuZfZGQTPwQ+HE0nBQzWw7MNLPnCLUZ\nkwhzWJxcpBhFRESqRikLNTuij7RjgJcJw05x92VAE9AMbATmEkZuXJbxngsIw0jvAVYAq4GvZrw+\nDbgZuDHax7nAme6+Ov5wREREqltNR0dH/lbVqaNSu7mqoQtP8SWX4kuuSo4NqiK+mvytelfOQ0pF\nREQkQZRUiIiISCyUVIiIiEgslFSIiIhILJRUiIiISCyUVIiIiEgslFSIiIhILJRUiIiISCyUVIiI\niEgslFSIiIhILJRUiIiISCyUVIiIiEgslFSIiIhILJRUiIiISCyUVIiIiEgslFSIiIhILJRUiIiI\nSCyUVIiIiEgslFSIiIhILJRUiIiISCyUVIiIiEgslFSIiIhILHYt1YHN7FZgiLtP6aXNEuCMrM2r\n3X189PoewPXAZEIsS4Gp7v5Oxj4+B1wGjASeAL7h7hvijEVERERK0FNhZjVmdiVwIdCRp/loYAaw\nf8bHmRmv3wYcDUwE/h74dLQtfawTgduBecCRwEbgATPbJ45YREREpFNReyrM7GDCTf5w4MU8bYcC\nhwDr3f3VHK8fCJwDHO/u66NtFwCPmNkl7v5n4BLgTnefH73+ZeB4YArwndgCExERkaL3VDQALxB6\nIDblaXsoIel5pofXjwb+AvwyY9uvgB3Ap8xsl6jNo+kX3b0DWAMc249zFxERkV4UtafC3RcDiwHM\nLF/z0cA24AozmwBsJdRMzHb3NuBA4FV335Gx/+1m9iqhfmI4sCfwUtZ+/wx8YuDRiIiISKaSFWoW\n4LDo8++Bm4AjgGsJCUMzsAeQyvG+NqAuep0cbdKvi4iISIzKOamYBcxx99bo+6fMbAfQYmbTCD0X\nQ3O8byjwDvBuxve5XhcREZEYlW1SEdU/tGZtfjL6fCDwR2BfM6uJ2mJmuwL7Eh55vEFIHt6XtY8D\ngD8VcAo1I0bU9/Psy18lxwaKL+kUX3JVcmxQ+fENVNlOfmVmS83sp1mbxxAeXzxHKNDclVCMmfYp\nQky/jBKNXxGGmab3uQswjlCsKSIiIjEqZU9FTfQBgJnVAnsDr7l7O9ACLDGzqcBKwjwT84B57v4u\n8G40OdbtZvZFQjLxQ+DH0XBSCDUYq8zst8AjwDSgHphfjABFRESqSSl7KjroOvnVMcDLhGGnuPsy\noIlQlLkRmAtc7+6XZbznAkJvxD3ACmA18NX0i+5+P2GSrYuB3xCGqY5399cHJSIREZEqVtPRkW9S\nSxEREZH8yramQkRERJJFSYWIiIjEomyHlA4mMxsCzAbOJxRu3gf8Y641RqL2Y4AbgI8Shqt+290X\nFel0+6wf8fW6Gmy5KnCl20Rdu0xxrORbbsxsP0J91N8BuwPrgIvd/ake2ifq+vUjvqRdvwOB6whr\nKO1C+N0yLaM4Prt9Yq5fP2JL1LXLZGafBH5BWDsr52jI/l67au2puBz4PKEQdBxh3otluRqa2Qjg\nfmADYQTKjYQRJ39XlDPtn8spML5IvtVgy0qhK90m9NrFvZJv2YiGdC8nLBR4KmE4+FvAQ2a2V472\nibp+fY0vkqTrVwPcDbyHMFT/OMI8QKt6aJ+Y69fX2CKJuXaZzGxPYBEZoy9ztOn3tau6ngoz2w24\nCPiGuz8UbWsENplZg7uvzXrLBcAb7v7N6Pv/Z2YfA/4JeLBY512ovsaXbzXYctOXlW5J2LWDeFfy\nLUMfAT4J/I27O4CZNQGvAxMJv+gyJe369Sm+BF6/fYGngEvd/UUAM7sOWG5m73H3t7LaJ+n69Sm2\nBF67TNcSJo/8617a9PvaVWNPxUcJjwQeTW9w9xeA58m9eumxdJ8s6zHCENhy1Nf48q0GW276stJt\n0q4dxLuSb7l5gXBz/X8Z29I9McNztE/a9etrfIm6fu7+P+5+bsZN90Dgy4Qba3ZCAQm6fv2ILVHX\nLs3MTgYmEP7w7E2/r13V9VQQHgVA99VLX854LdP7CXNcZLfdw8z2KsM5L/oaX77VYMtKH1e6Tdq1\ni3sl37IS/bzvzdp8EaH24IEcb0nU9etHfIm6fpnMbAXhEc8bwGd6aJao65dWYGyJu3Zmtg9h4sdm\n4M08zft97aqxp2IP4C+ZS6ZHelq9NNdqqOl/NOW42mlf48tcDfZk4ApC19dtg3aGxZO0a9dXib52\nZnYqcDXwvfTjgiyJvn4FxJfk6zcLGEso9nvQzA7I0Sap16+Q2JJ47W4DfubuuRLcbP2+dtWYVGwF\ndomKqjL1tHpprtVQ09+X42qnfY1vFrCvu9/g7k+5+78D3wQ+b2bvHeRzHWxJu3Z9ldhrZ2bNwP8F\nWtx9eg/NEnv9CowvsdfP3Z90918DjcAQwkizbIm8fgXGlqhrZ2bnEx6N/1PWSz0Va/b72lVjUvHH\n6HP26qXvp/sjg3T77Ez1AODtHp61lVqf4nP3jozl5dPSq8GOjPncii1p165PknrtzGwm8CPgFnfP\n9Qs7LZHXr9D4knb9zGzfqOh7J3ffCvyB7tcJEnT9+hpb0q4dITE6EHjFzLbQWQtyr5ndnKN9v69d\nNSYVTwBb6Lp66QeBg8i9eukvCMMyM30m2l6O+hRfAavBJlnSrl2fJPHamdl04NvArIzK8p4k7vr1\nJb4EXr8PAnea2cfTG8zsPYABT+don6Tr90H6EFsCr915wN8QRih9BDgp2v4l4LIc7ft97aquUNPd\n26LM7Boz+19gM3Az8Ki7r8+xWurtwPRoIqIbgBOBc+i8KGWlH/HlWw22nOVb6TZR1y6Hga7kW1bM\n7AhCjcHthDHv+2e83Aq0k+Dr14/4EnX9gF8DPwfmm9mFwHbgu8CrwMKE///ra2yJunbu/nLm92a2\nLfryJXf/3zivXTX2VEB4HrYY+AnwMGHoXnpmtOzVUl8FPkv4R/OfwNeAJnd/tLin3Cd9ia+Q1WDL\nVb6VbpN47TLFsZJvOTmb8DvnS8CfCbGkP75FmCwqydevr/El6vq5ewdwGvA74D8Iw9bfBI6LbqSJ\n/f/Xj9gSde16MCi/O7VKqYiIiMSiWnsqREREJGZKKkRERCQWSipEREQkFkoqREREJBZKKkRERCQW\nSipEREQkFkoqREREJBZKKkSkbJnZo2b2YKnPQ0QKo6RCRMpZ9qyiIlLGlFSISDnraWlmESlDVbeg\nmIiUDzPbk7BK4mTgA4RVHtcCl7j7xlKem4j0nZIKESmlRYRFjC4F/hv4MHAlcCfwtyU8LxHpByUV\nIlISZlYH7A78o7v/NNr8czN7D3CNme1TurMTkf5QUiEiJeHuKWACgJm9n9BL8WHgFEJx5m6lOzsR\n6Q8lFSJSMmZ2EnA9YMAW4HfAO9HLKtIUSRiN/hCRkjCzvwZWABuAg939Pe5+HPAfKKEQSSQlFSJS\nKh8HhgJXu/vzGdsnEB5/6PeTSMLo8YeIlMpvgO3APDO7HqgDvgCMJfRU7Bm1U6+FSELoLwERKQl3\n/8jFdRQAAABlSURBVANwDnAQsAr4PuDAxwg9FceiGTVFEqWmo0P/X0VERGTg1FMhIiIisVBSISIi\nIrFQUiEiIiKxUFIhIiIisVBSISIiIrFQUiEiIiKxUFIhIiIisVBSISIiIrFQUiEiIiKx+P/RJ1D2\n1hZ/KQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18781390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# equivalent scatter plot using Matplotlib\n",
    "plt.scatter(glass.al, glass.ri)\n",
    "plt.xlabel('al')\n",
    "plt.ylabel('ri')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit a linear regression model\n",
    "from sklearn.linear_model import LinearRegression\n",
    "linreg = LinearRegression()\n",
    "feature_cols = ['al']\n",
    "X = glass[feature_cols]\n",
    "y = glass.ri\n",
    "linreg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ri</th>\n",
       "      <th>na</th>\n",
       "      <th>mg</th>\n",
       "      <th>al</th>\n",
       "      <th>si</th>\n",
       "      <th>k</th>\n",
       "      <th>ca</th>\n",
       "      <th>ba</th>\n",
       "      <th>fe</th>\n",
       "      <th>glass_type</th>\n",
       "      <th>ri_pred</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.51966</td>\n",
       "      <td>14.77</td>\n",
       "      <td>3.75</td>\n",
       "      <td>0.29</td>\n",
       "      <td>72.02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>9.00</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>1.521227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>1.51115</td>\n",
       "      <td>17.38</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.34</td>\n",
       "      <td>75.41</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6.65</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6</td>\n",
       "      <td>1.521103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>1.52213</td>\n",
       "      <td>14.21</td>\n",
       "      <td>3.82</td>\n",
       "      <td>0.47</td>\n",
       "      <td>71.77</td>\n",
       "      <td>0.11</td>\n",
       "      <td>9.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>1.520781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1.52213</td>\n",
       "      <td>14.21</td>\n",
       "      <td>3.82</td>\n",
       "      <td>0.47</td>\n",
       "      <td>71.77</td>\n",
       "      <td>0.11</td>\n",
       "      <td>9.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>1.520781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>1.52320</td>\n",
       "      <td>13.72</td>\n",
       "      <td>3.72</td>\n",
       "      <td>0.51</td>\n",
       "      <td>71.75</td>\n",
       "      <td>0.09</td>\n",
       "      <td>10.06</td>\n",
       "      <td>0</td>\n",
       "      <td>0.16</td>\n",
       "      <td>1</td>\n",
       "      <td>1.520682</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          ri     na    mg    al     si     k     ca  ba    fe  glass_type  \\\n",
       "id                                                                          \n",
       "22   1.51966  14.77  3.75  0.29  72.02  0.03   9.00   0  0.00           1   \n",
       "185  1.51115  17.38  0.00  0.34  75.41  0.00   6.65   0  0.00           6   \n",
       "40   1.52213  14.21  3.82  0.47  71.77  0.11   9.57   0  0.00           1   \n",
       "39   1.52213  14.21  3.82  0.47  71.77  0.11   9.57   0  0.00           1   \n",
       "51   1.52320  13.72  3.72  0.51  71.75  0.09  10.06   0  0.16           1   \n",
       "\n",
       "      ri_pred  \n",
       "id             \n",
       "22   1.521227  \n",
       "185  1.521103  \n",
       "40   1.520781  \n",
       "39   1.520781  \n",
       "51   1.520682  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make predictions for all values of X\n",
    "glass['ri_pred'] = linreg.predict(X)\n",
    "glass.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1a1fbda0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sTZ0BrLXWbjfGxALNgF+ttSXAbOBOY8wzOLMk3XCWkJ4dPN8OY8wbOM+uGIxT\nJp4DXg4uJwWYACwxxtyF82CsTsBgnOWqIhIOKSnkTZhEcZ/z8Y64kaQZ04hbtpicKTMobdXa7XQi\nUkdCnanYAbSqZt9pOA/HCtX9OMtRXwFWA9/iPEALnKWiPwFtAIJP2ewZfI+PgRuBgdbatRXONwRn\nGelinEsoK4Ghe3Zaa1cCF+CUkS+Au4CbrLWv7EdmEQlBSZt2ZK7dQv71NxL9zdek9T2b5Afuhvx8\nt6OJSB0I9bM/7gVG4TxIahFgcS5LHAQ8D0y11o6pxZxu0Wd/RCiNv+bjj9m2Fe+IocR88zWlRx9D\n7pSnKGnTbt8vrAci+c8/kscOGn9NP/sj1JmKR4CXcD4/wwa3rQcWAEuA8TUJISKNT2mr1vjXbCZ/\n6M1Ef/ctaef1IvnekZAXykIxEWmIQn2iZrm19nrgTziXIB7AecLmKdbay4M3RIqI/FZiInljxpO1\naDmlx/2RpFkzadqpDbGbNuz7tSLS4IS6pHQUMMta+xXwVaV9R+N8Kqgeey0iVSo9sxX+VRtJnvQw\niU9NJa1fbwquHkLuA2MhJcXteCISJqFe/hhN1Y/RBmgNXB+WNCLSeCUkkPfAGLIWr6TUHE/iC7Oc\nWYv1a91OJiJhUu1MhTFmI799/sNWY0x1h38QzlAi0niVnn4G/pUbSJr8KEnTnyCtf18KrhxM3oNj\nCXibuB1PRGpgb5c/ruV/D7UaC8zk9x/uVQZkAW+HP5qINFrx8eTfO4ri3n3wDh9K4svPE7dqOTmP\nT6ekc1e304nIAaq2VFhrvwQegv8++vo5a+1/S0XFR2OLiByI0lNOw79iPUmPTyRp2uOkXdKPgsuv\nJG/MeAJNUt2OJyL7KdTVH6OBvsaY1ypszjDG/NMYE9JnaIiIVCkujvy77ydr2RpK/3wSiXNfxteh\nNXGrlrudTET2U0ilIvgJpU/ifG7HHj/iPKvieWPMwFrIJiIRpPSkU/AvW0PenfcStfNnUgf0xzt8\nKJ4sv9vRRCREoa7+uBkYY629bs8Ga+031trBOJdIRtZGOBGJMHFx5N9xN/7l6yg56RQS5s11Zi2W\nL3E7mYiEINRScTj/+2TQytYDx4UnjogIlJ14EllLV5N3zwNE/foLqVdcgnfYdXj8mW5HE5G9CLVU\n/AvoUs2+9vx+VYiISM3ExpJ/60j8KzdQcuppJLw5D19GK+KWvO92MhGpRqgffT4TmBj8aPIFwE4g\nHeiLc+mx7KTsAAAgAElEQVTjgdqJJyKRruxPJ5C1eBWJM6aRPHECqYMGUHhBf3LHTyLQrJnb8USk\nglBXfzwBTAFuA7YAXwNbcQrFdGBSbQUUESEmhoLht+FftZGS0/9CwoK3aJpxFnGLFrqdTEQqCPXy\nB9bakTizE+cAA3FmKVpaa+/Q8ypEpC6UmePJWrSC3FHj8OTsJnXwFXivuwrPL7+4HU1ECP3yBwDW\n2ixgaS1lERHZt5gYCm4aQfHZvfCOuJGEdxYQt3E9OY9MprhvP7fTiUS0vX32xz+AC621fwv+HAA8\nwe97eILfA9baP9ZeTBGR3yo77o9kvbeMxGefJvnhsaQOGUTRuQvIeWQygYMPdjueSETa20zFJiC3\nws97o8sfIlL3oqMpGHoTxWf3xDtiGPGL3iV28wZyJ0yiqF9/8Hj2fQ4RCRtPIKA+sBeBXbty9n1U\nI5Se7iVSxw4af4Mcf3k5ibNnkvzQaDwFBRT1OpeciU8QOOSQ/T5Vgxx/mETy2EHjT0/31qiJh3yj\npohIvRYVRcG1Q8lcu4Xitu2JX7KIphlnEv/mPNA/nkTqxN7uqSjnf/dRwP8ucVRsMf+9z8JaG10r\nCUVE9kP50ceQvWARCS/MImXcgzQZdh1FC98md9IUyg89zO14Io3a3u6pGFvh5wScZ1R8BcwH/g00\nA/oAJ1U6VkTEXVFRFF5zHcXdeuC99Sbily0hdusWcsc9TNEll+leC5FaUm2pCH7cOQDGmNnA+8AF\nlZ5JMd4Y8wpwZq0lFBE5QOVHHkX2WwtJePkFksc8QJPhQyl6dwG5k6dR3ryF2/FEGp1Q76m4GHim\nmodczQF6hS+SiEgYRUVReNU1+NdvpbhDZ+JXrcCX0YqEuS/rXguRMAu1VORR/SeRngLoowNFpF4r\nP/wIst98h5zHp0MggPfWm0i9pB9RP/7gdjSRRiPUJ2q+CkwwxhQB7wK7gEOBS4ExwKO1E09EJIw8\nHgqvGERx5654bx9O3OqV+Dq0Jm/MeAqvGKR7LURqKNSZinuB5TifVvofoAzn484nAy+hGzVFpAEp\nb9GS7Nfms3vqDIiKwnv7cFIvOp+of33vdjSRBi2kmQprbSHQ3xjzZyADaAr8Aqy21v6zFvOJiNQO\nj4eiAVdQ0qkLKXeMIH7FMnwd25A3aizcMcLtdCIN0n49/Mpa+zkwG3gBeEGFQkQauvLDmrP7lTfY\nPf0ZiInBe9dt0K0bUd9963Y0kQYn5FJhjDnDGLMcyAF+BE42xrxojBlVa+lEROqCx0PRJZfh37CN\nop7nwJo1NO3UhoTZM6G83O10Ig1GSKXCGNMW2AD4gEf431M1vwFGG2NurJ14IiJ1p/zQw9j90msw\ndy6B+Hi894wktV9vor752u1oIg1CqDMVjwIrgLOAh4LbAtbascATwNBayCYiUvc8HrjsMjLXb6fo\nnD7EbdlE085tSXx2hmYtRPYh1FLxF6p/+NUi4NjwRRIRcV/gkEPY/cIr7H72BQKJiaTcfzdpfXsS\n/fU/3I4mUm+FWipygOo+P7hFcL+ISOPi8VB0/oVkbviAwr79iN2+FV/ndiTOmA5lZW6nE6l3Qi0V\nC4FxxpjT+d+nlWKMaY7zDIv3ayGbiEi9EEhPJ2fWS2TPeolASgopo+8j7dweRP/jK7ejidQroZaK\nu3GeS/EBsGed1RzgH0B0cL+ISKNW3Lcfmeu3U9jvQmI/+gBfl3YkTp8CpaVuRxOpF0IqFdbaX4HW\nwA3AZmAV8AVwF3C6tXZnrSUUEalHAgcdRM7MF8h+YS6BJqmkjBtFWu9uRP/fl25HE3FdSE/UNMY8\nCbxorX0OeK52I4mI1H/FvfuQ2aYtKffdRcL8N/B1yyBv5D0UDBsBMaF+rJJI4xLq5Y/BOM+oEBGR\noEDTZuQ8PYvsl+dRnuYjZfwY0np1JfqLz92OJuKKUEvFNqBDbQYREWmoinueg3/DNgovHkDsp5/g\n696BpMmPQkmJ29FE6lSoc3QfAXcZYy4E/grkVj7AWntdOIOJiDQkAV9Tcp6cSdF5/Ui5fQTJj44n\nbvEicqbOoOzEk9yOJ1InQp2p6A/8BCQBbYHuFb56BL+LiES84u498W/YRsFlA4n97FN8PTqSNHEC\nFBe7HU2k1oX60edH1XIOEZFGI5CaRu6Upyjqez7e24aT/NgjxC9eRM70pyk96RS344nUmn3OVBhj\nDjHGnGmMaVoXgUREGouSLt3xr99KwcCriPni76T16ETSI+OgqMjtaCK1otpSYYyJN8a8hnPZYxvw\nizFmnjFGq0BEREIUaJJK7uRpZL3xDuWHNSf58Un4enQk5q8fux1NJOz2NlMxFrgImA0MA6YCfYGZ\ndZBLRKRRKenUxZm1GHQNMV9+QVqvriSPHwOFhW5HEwmbvZWKC4Gx1trrrLVPW2tvxSkX/YwxCXUT\nT0Sk8QikeMmd9ARZ89+jvEVLkqZOxtctg5iPPnA7mkhY7K1UtATWVtq2BOezPo6qpTwiIo1eSUZH\nMtduoWDwtcR8ZUnr3Z3kMQ9AQYHb0URqZG+lIg6oPC/3S/B7Yu3EERGJECkp5D4ymay336f88CNI\nemoqvq7tiflgm9vJRA5YqM+pqMwT1hQiIhGqpF0GmWu3kH/dUKK//idp5/YgedS9kJ/vdjSR/ba/\npSJQKylERCJZcjJ5Dz1K1rtLKTv6GJKeeRJfl3bEbN3idjKR/bKvh19NM8bsrvD7nhLylDEmJ/iz\nBwhYa3uEPZ2ISAQpbd0G/+pNJD/yEIkznyLtvJ4UXHsDefeMguRkt+OJ7NPeZirWAwU491bs+YoJ\nbi+qsC02+CUiIjWVlETe2AlkvbecsmP/QNKzT9O0c1tiN290O5nIPlU7U2Gt7VSHOUREpILSs1rh\nX7WR5IkTSHx6Omnnn0PBNdeRe99oSElxO55IlQ70Rk0REaltiYnkPTiOrPdXUPpHQ+LsZ2naqS2x\nG9a5nUykSioVIiL1XOlfzsS/cgP5I24n6sd/kXZhH1LuvBVPbs6+XyxSh0L6lNJwMsZEAw8BgwAv\nsBQYZq3dWc3xZ+A8IvxUYAcwzlo7p8L+JGAK0A9nPG8Ct1pr86o4lw/4GzDLWjsmnOMSEalVCQnk\n3fcgRb374B1xI4kvziZu1QpyHp9OScfObqcTAdyZqRgNXAkMBDrgPLlzflUHGmPSgWXAh8BpwDRg\ntjGme4XDZgJtgd5AH6AT1X8+yQygBVoaKyINVOmpp+Nfvo6820YS9dMO0i46j5Tbh+PJ2b3vF4vU\nsjotFcaYOGA4cI+1dpW19hPgUqCdMaZNFS8ZAvittSOstV9Za58EXgHuCJ6vJTAAuNFau91auzH4\nmgHGmMMqvfcA4HSc2Q4RkYYrPp78ux8ga9kaSk84kcQ5L+Lr0JrY1SvdTiYRrq5nKk7FueSxds8G\na+33wHdARhXHZ+AsYa1oHdAu+HNboBzYVGH/ZqAMaL9ngzGmBc4llCv5/aPHRUQapNKTT8W/fC15\nd9xN1M//Ie3SC0i5ZRie7Cy3o0mEqutS0TL4vfJswU8V9lXUoppjk4wxzYKv2WmtLduz01pbCuwE\nDgcwxniAF3Duo9BD9UWkcYmLI//Oe/EvW0vJiSeT+OocfB1aE7diqdvJJALVdalIAsorloCgIqCq\nj1NP4vczC0XB7wnV7K98vpuBg4FRBxJYRKQhKDvpZLKWrSHvrvuI+mUXqZdfjPfmG/Bk+d2OJhGk\nrktFARBljKn8vvHA71ZrBI+Pr+JYgNxq9v/3fMaY44GxwKDgDMYe+kA0EWl8YmPJv/0u/CvWU3Ly\nqSS8/iq+jFbELV3sdjKJEHW9pPSH4PfD+O1ljRbAO9Uc37zStuZArrU22xjzA3CwMcZjrQ0AGGNi\ncGYmdgAXAynARmPMntcnAfcaY/pba0/aV+D0dG9IA2uMInnsoPFr/A14/B1bw4fbYdIkoseMIfXK\nS+Hyy2HqVGjWbJ8vb9BjD4NIH39N1HWp+BTIwVn2ORfAGHMUcCS/vyETYCNwdaVtnYPbwblBMwbn\nhs09N2u2x5mB2QSswlktsocnuO0dYHIogXftisyHy6SneyN27KDxa/yNZPzX3kx0Rje8I4YSO3cu\n5ctXkDNpCsXnnFvtSxrN2A+Qxl+zQlWnpcJaW2SMmQE8Zoz5BdiF8+yItdba7caYWKAZ8Ku1tgSY\nDdxpjHkGZ/VGN5wlpGcHz7fDGPMGzrMrBuOUieeAl621/w6+7W8uKBpjSoFMa+0PiIg0cmXH/4ms\n91eS+PSTJE8cT+pVl1HY70JyJzxGIIRZC5H94cbDr+7HmaV4BVgNfAv0D+5rh7O6ow1A8CmbPXEe\nfPUxcCMw0Fq7tsL5huAsI12MMwOxEhi6l/fXg69EJLLExFBw8y34V2+i5C9nkvD2fJpmnEnce1Vd\ndRY5cJ5AQH/H7kUgUqfBNAWo8Wv8jXT8ZWUkzpxB8iPj8BQWUti3H7kPP0YgPR1o5GMPgcbvrdFC\nBn2gmIhIJImOpuDGm/Gv2UTJWa1JWPg2TTucRfw780H/yJQaUqkQEYlAZcceR9a7S8gd9zCe/Hya\nXHc1TQYPhJ9/djuaNGAqFSIikSo6moLrh5G5ZjPFrdsS//5COOEE4ue/oVkLOSAqFSIiEa78mGPJ\nfmcxOQ9PgsJCmgwdQpNBA4j6+T9uR5MGRqVCREQgKorCa66Hzz6juF0G8UsX42t/FvFvvKZZCwmZ\nSoWIiPzPMceQPf89ch59HEpLaXLT9TS54mKi/v2T28mkAVCpEBGR34qKovDqIfjXbaE4oxPxK5bh\ny2hF/GuvaNZC9kqlQkREqlR+xJFkv/UuOY9NhfJymoy4kdQBFxK140e3o0k9pVIhIiLV83govPJq\n/Ou3UtypC3GrV+LLaEXCKy9p1kJ+R6VCRET2qbzl4WS//jY5U54CjwfvbTeTevH5RP2oj1GS/1Gp\nEBGR0Hg8FF42EP+GbRR17U7cujXOrMVLz2vWQgCVChER2U/lzVuw+9W32D3taYiOxjvyFlL79yXq\n++/cjiYuU6kQEZH95/FQdOnl+Ddup6hHT+I2rKNpxzYkzH4WysvdTicuUakQEZEDVn7oYeye8zq7\nn3qWQFws3nvuIPWCc4n69hu3o4kLVCpERKRmPB6KLroU/4btFPU6l7jNG2nauS2Jzz2tWYsIo1Ih\nIiJhUX7Ioex+cS67Zz5PICGBlPvuIvX8c4j+5p9uR5M6olIhIiLh4/FQ1K8/meu3U3TuecRt3Yyv\nczsSn3kSysrcTie1TKVCRETCLnDwwex+fg7Zs14ikJREyqh7SetzNtH//Ifb0aQWqVSIiEitKe7b\nj8wNH1B43gXEfrgdX5d2JD45VbMWjZRKhYiI1KrAQQeR89yLZM+eQyDFS8rYB0g7tzvRX1m3o0mY\nqVSIiEidKO5zHpkbtlN4wUXEfvQhvq7tSZz2BJSWuh1NwkSlQkRE6kygWTNynplN9kuvUZ6aRspD\nD5LWuxvRX37hdjQJA5UKERGpc8W9euPfsI3Ciy4l9pOP8XXvQNITk6CkxO1oUgMqFSIi4oqAryk5\nTz1L9iuvU960GckPjyOtV1eiP/+729HkAKlUiIiIq4p79MK/fiuFl15O7N/+iq9HR5Iee0SzFg2Q\nSoWIiLgukOYjZ9rTZL/2FuUHpZM8cQK+Hp2I/uxvbkeT/aBSISIi9UZx1x74N2yj4IpBxHz+Gb6z\nO5H06HgoLnY7moRApUJEROqVQJNUch+fTta8BZQfcijJkx/F170jMZ9+4nY02QeVChERqZdKunTD\nv34rBVcOJubLz0nr2YWkCWOhqMjtaFINlQoREam3At4m5D42hay3FlLevAXJUx7D170DMZ985HY0\nqYJKhYiI1HslHTrhX7eFgquHEPN/X5LWqyvJ4x6EwkK3o0kFKhUiItIgBFK85D76OFkLFlHe8giS\npj+Br2t7Yj7c7nY0CVKpEBGRBqWkfQcy120hf8j1xPzjK9LO7UHy6PuhoMDtaBFPpUJERBqe5GTy\nJkwi690llB9xJEkzpuHr0o6Y7dvcThbRVCpERKTBKmnTjsy1W8i/fhjR33xNWp8eJD9wD+Tnux0t\nIqlUiIhIw5aURN64h8lauIyyY44laeZT+Dq3JXbrZreTRRyVChERaRRKW7XGv3oT+TcOJ/r770g9\nrxfJ946EvDy3o0UMlQoREWk8EhPJG/0QWYuWU/aH40iaNZOmndoQu2mD28kigkqFiIg0OqVnnIV/\n1Ubyb76VqB/+RVq/3qTcdRvk5rodrVFTqRARkcYpIYG8B8aQtXglpeZ4El+Y5cxarF/rdrJGS6VC\nREQatdLTz8C/cgN5t95B1I4fSevfl5Q7bsGTs9vtaI2OSoWIiDR+8fHk3zOKrKWrKf3TCSS+/Dy+\nDq2JXbPK7WSNikqFiIhEjNJTTsO/Yj15t99F1M//Ie2SfqTcehOe3dluR2sUVCpERCSyxMWRf9d9\nZC1bQ+mfTyJx7sv4OrQmbtVyt5M1eCoVIiISkUpPOgX/sjXk3XkvUTt/JnVAf7j6ajxZfrejNVgq\nFSIiErni4si/4278K9ZTcvKp8OKLzqzF8iVuJ2uQVCpERCTilf35RLKWrIKHHiLq119IveISvMOu\nw+PPdDtag6JSISIiAhAbC/fdh3/lBkpOPY2EN+fhy2hF3JL33U7WYKhUiIiIVFD2pxPIWryK3PtH\nE5XlJ3XQALw3XIMn81e3o9V7KhUiIiKVxcRQMPw2/Ks2UvKXM0hY8CZN259F3KKFbier11QqRERE\nqlFmjidr0QpyH3wIT85uUgdfgfe6q/D88ovb0eollQoREZG9iY6mYNhw/Gs2U3JmKxLeWUDTDmcR\nt/Btt5PVOyoVIiIiISj7w3FkLVxK7tgJePLySB0yiCaDB+LZudPtaPWGSoWIiEiooqMpuOEm/Gs2\nUdKqDfGL3qVph7OIX/AmBAJup3OdSoWIiMh+KjvmD2S9u4Tc8Y/iKSykyQ3X0OSqy/H8/LPb0Vyl\nUiEiInIgoqIouHYomWs2U9y2PfFLFtE040zi35wXsbMWMXX9hsaYaOAhYBDgBZYCw6y1VV6UMsac\nAUwFTgV2AOOstXMq7E8CpgD9cMbzJnCrtTYvuD8WuBcYCBwKWGCMtVbrgkREpMbKjz6G7AWLSHhx\nNiljR9Fk2HUULXyb3ElTKD/0MLfj1Sk3ZipGA1fi/CXfAWgJzK/qQGNMOrAM+BA4DZgGzDbGdK9w\n2EygLdAb6AN0Cm7b4yHgemAEcDJO6VhgjMkI14BERCTCRUVROPhaMtdtoTijI/HLluDLaEX8vLkR\nNWvhCdThYI0xccAu4GZr7cvBbUcC3wLtrLVbKh1/D3CNtfYPFbY9D7Sw1p5tjGkJfAd0sdauD+7v\nAKzBKSs/B9/vXmvtzArnWAl8b629Zh+RA7t25dRkyA1WerqXSB07aPwaf+SOP5LHDmEafyBAwssv\nkDz6fqLycinq2p3cydMob94iPCFrUXq611OT19f1TMWpOJc81u7ZYK39HqcYVDVzkAGsr7RtHdAu\n+HNboBzYVGH/ZqAMaA94gIuAyouJA0DaAeQXERHZO4+HwkGD8a/fSnHHzsSvWoEvoxUJr85p9LMW\ndV0qWga/76i0/acK+ypqUc2xScaYZsHX7LTWlu3Zaa0tBXYCh1try6y1qyver2GMORPojHMvh4iI\nSK0oP/wIst94h5zHp0MggPeWYaReegFRP/7gdrRaU9elIgkor1gCgoqAhGqOL6ziWILHV7W/2vMZ\nY/6AM2uxDXg+9NgiIiIHwOOh8IpB+Ddso7hLN+LWrMLXoTUJc15slLMWdV0qCoAoY0zl940H8qo5\nPr6KYwFyq9lf5fmMMX8BNgK/AOdWUWxERERqRXmLlmS/Np/d056GqCi8tw8n9aLzifrX925HC6u6\nXlK6Z87nMH57WaMF8E41xzevtK05kGutzTbG/AAcbIzxWGsDAMaYGODgiuc3xvTAWWHyCdDHWpsd\nauD0dG+ohzY6kTx20Pg1/sgdfySPHWp5/DffABf0geuvJ+7992nWqQ1MnAjXXw9RDf/RUXVdKj4F\ncnCWfc4FMMYcBRzJ72/IBGdm4epK2zoHt4Nzg2YMzg2be27WbI8zA7MpeP4MYCHO0tSLrbVF7IdI\nvQtad4Br/Bp/ZI4/kscOdTT+uCbw/KvEvzmPlPvuIurGGyl+dR45j0+n/Kija/e996GmhapOl5QC\nGGMeBq4Kfu0CZgD51touwQdVNQN+tdaWGGMOxnlY1es4D8DqBjwGnG2tXRs832s4z7AYjFMmXgA2\nWGsHG2PigX8CmTjPsSitEKXIWuvfR1wtKY1QGr/GH6njj+SxQ92PP+rn/5Ay8hbily4mkJRE7gNj\nKLz6WtdmLRraklKA+3FmKV4BVuM8o6J/cF87nNUdbQCCqzZ64pSGj4EbgYF7CkXQEJxlpItxLqGs\nBIYG93XEubRyIvCv4Ln3fL1eG4MTEREJVfkhh7L7pdfY/fQsAvHxeO8ZSWq/3kR987Xb0Q5Inc9U\nNDCaqYhQGr/GH6njj+Sxg7vj9/z8M967byf+/YUEEhPJu+9BCobcUKezFg1xpkJEREQqCRxyCLuf\nn8Pu514kkJREyv13k9a3J9Ff/8PtaCFTqRAREakvPB6KzruAzPXbKezbj9jtW/F1bkfijOlQVv+f\nhKBSISIiUs8E0tPJmfUS2bNfJpCSQsro+0g7twfR//jK7Wh7pVIhIiJSTxX3OZ/MDR9Q2O9CYj/6\nAF+XdiROnwKlpft+sQtUKkREROqxQLNm5Mx8gewX5hJokkrKuFGkndudaPt/bkf7HZUKERGRBqC4\ndx8yN2yjsP8lxH78Eb6u7UmcOrlezVqoVIiIiDQQgabNyJnxHNkvz6Pc15SU8WNI69WV6C8+dzsa\noFIhIiLS4BT3PAf/hm0UXnIZsZ9+gq97B5ImPwolJa7mUqkQERFpgAJpPnKmP0P23DcoPyid5EfH\nk9azC9F//8y1TCoVIiIiDVhx957412+l4LKBxH72Kb4eHUmaOAGKi+s8i0qFiIhIAxdITSN3ylNk\nzZtP+cGHkPzYI/h6dCLms0/rNIdKhYiISCNR0qU7/g3bKBh4NTFf/J20Hp1IemQcFBXVyfurVIiI\niDQiAW8TcidPJeuNdyg/rDnJj0/C16MjMX/9uNbfW6VCRESkESrp1MW51+Kqa4j58gvSenUlefwY\nKCystfdUqRAREWmkAilecic+Qdb89yhvcThJUyfj65ZBzEcf1Mr7qVSIiIg0ciUZHclcu5mCa64j\n5itLWu/uJI8dFfZZC5UKERGRSJCSQu7Dj5H1zmLKjziSpCen4OvSjpgPtoXtLVQqREREIkhJ2/Zk\nrtlM/nVDif76n6Sd24PkUfdCfn6Nz61SISIiEmmSk8l76FGy3l1K2dHHkPTMk/i6tKvxaVUqRERE\nIlRp6zb4V28if+jNRH/7TY3Pp1IhIiISyZKSyBszHv+G7TU+lUqFiIiIUPZHU+NzqFSIiIhIWKhU\niIiISFioVIiIiEhYqFSIiIhIWKhUiIiISFioVIiIiEhYqFSIiIhIWHgCgYDbGURERKQR0EyFiIiI\nhIVKhYiIiISFSoWIiIiEhUqFiIiIhIVKhYiIiISFSoWIiIiERYzbAdxijIkGHgIGAV5gKTDMWruz\nmuPPAKYCpwI7gHHW2jl1FDfsDmD8bwD9K21eaa3tUatBa5kx5hkg2lp77V6OaVR/9hWFOP5G9Wdv\njDkEmAj/396dh8pZ3WEc/15rTYzQ61KDmmjc8NHWqlVBo8SoVGxUBBXRCpEUxYKikS4qGMQNW9Bi\nKsTiH7Z/aNS6JbjgEpS4QGirkhKj/tyjYBBpUpPGuF//OO/IOJnhzju+c2fmzPOBYbjnngvnlyd3\n5jfnXS4nANsC/wR+FxGrW8zPJv8Oas8t++nAzcDxpA/VjwO/jYi1LeZnkz10VH/p/Id5p+Jq4Fxg\nLnAMMB14oNlESTsDTwAvAD8HbgFul3TChKy0O66mzfoLBwKXA7vUPc7s7hK7R9KIpGuBC4CWN2vJ\nNPu26y9kk72krYAlwL7AqcBRwMfAU5J2bDI/m/zL1l7IKfsR4FFgFDgWmA3sCjzcYn422UP5+gul\n8x/KnQpJ2wCXABdHxFPF2NnAO5JmRsSKhh85H1gfEfOLr1+XdCjwe2DZRK27KmXrlzSJ9EL0r1Y7\nGYNE0t7A7cBPgffGmZ5V9lCu/tyyBw4GjgQOiIgAkDQXWAecDDR+Cs0p/1K1Z5j9VGA1cEVEvAcg\n6WZgiaTRiPi4YX5O2UPJ+jvNf1h3Kg4hbfkvrw1ExBrgXWBWk/mzgGcbxp4Bju7O8rqubP37kxrQ\n1yZgbRNhJrCG1IW/M87c3LKHcvXnlv0a0hvo63VjtZ2a7ZvMzyn/srVnlX1EfBgR59S9oU4HfkN6\n02xsKCCv7Dupv6P8h3KngrTVD+kYWb0P6r5XbxrwYpO5UyTtGBHrKl5ft5Wt/0Dgc+AaSXOAzcB9\nwPUR8VnXVtklEbEYWAwgabzpuWVftv7csl8HPNYwfAnp/IInm/xINvl3UHtW2deTtJR0CGg9cFyL\nadlk36jN+jvKf1h3KqYAX0fEVw3jnwGTW8z/tMlcWszvd2Xr/0nx/CpwEnANaWvwtq6tsH/kln1Z\nWWcv6VTgBuDPtUMCDbLNv43ac85+AXAE8DywTNJuTeZkmz3t1d9R/sPaVGwGtipOXKo3CdjUYv6k\nJnNpMb/fla1/ATA1Iv4SEasj4m5gPnCupB26vNZeyy37srLNXtI84H7gnoi4rMW0LPNvs/Zss4+I\nlyPi38DZwA9IV8E1yjJ7aLv+jvIf1qbi/eJ514bxaWx5SKA2v7GT2w34f4tjUf2uVP0RMRYRGxqG\nXy6ed694bf0mt+xLyTV7SVcCfwP+GhHNXlBrssu/3dpzy17S1OKE9G9FxGbgLbbMGDLLvmz9neY/\nrAJWaf4AAAMQSURBVE3Ff4CNpMtqAJC0JzCDLU/MgbRFdEzD2HHF+CAqVb+k+yQ92DB8OGkr8M2u\nrbI/5JZ9KTlmL+ky4DpgQd2Z/a1klX+Z2jPMfk/gLkmH1QYkjQICXmkyP6vsKVl/p/mPjI2Nd4l6\nniT9EZhXPD4CbgU+iYjjJf0Q2An4b0R8IWkqEMA/SDdC+QVwE3BiRCyf+NV/fyXrPwO4l3Qp1UOk\na7YXAbdFxFU9WH5lJC0H3qjd/GkYsq/XRv1ZZS/pIOAl4O+k7d2Rum9vAL4g0/w7qD237EdIV7z9\niHR/li+BPwF7ka6IyzZ76Kj+jvIf1p0KSL9Ui4E7gadJl9bV7hx2NOks35kAxTW6vyT9o74EXAjM\nHcT/WHXK1P8A6SZZ84BVpDvyLRzEF5YmxvjuzZ+GIft649WfW/ZnkV73zgPWkmqtPS4l3RAq1/zL\n1p5V9hExBpwOrAQeIb3B/g+YHRGfkPnvfgf1d5T/0O5UmJmZWbWGeafCzMzMKuSmwszMzCrhpsLM\nzMwq4abCzMzMKuGmwszMzCrhpsLMzMwq4abCzMzMKuGmwsz6mqTlkpb1eh1mNj43FWbW7xrv+mlm\nfcpNhZn1u5Hxp5hZP9i61wsws+EmaTvgKuA0YA/SX0FcAfwhIlb1cm1mVo6bCjPrtTtIf8ToCuBt\nYD/gWuAu4Gc9XJeZleSmwsx6RtJkYFvgooh4sBh+TtIocJOkH/dudWZWlpsKM+uZiPgUmAMgaRpp\nl2I/4BTSyZnb9G51ZlaWmwoz6ylJJwILAQEbgZXApuLbPknTbID46g8z6xlJ+wBLgReAvSNiNCJm\nA4/ghsJs4LipMLNeOgyYBNwQEe/Wjc8hHf7wa5TZAPHhDzPrpReBL4EbJS0EJgO/Bo4g7VRsV8zz\nroXZAPCnADPrmYh4C/gVMAN4GFgEBHAoaadiFr6jptnAGBkb8++qmZmZfX/eqTAzM7NKuKkwMzOz\nSripMDMzs0q4qTAzM7NKuKkwMzOzSripMDMzs0q4qTAzM7NKuKkwMzOzSripMDMzs0p8A7sOsm1A\nPLQVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1607b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot those predictions connected by a line\n",
    "plt.plot(glass.al, glass.ri_pred, color='red')\n",
    "plt.xlabel('al')\n",
    "plt.ylabel('Predicted ri')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1a21d7b8>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lIiKSmwLhcDh5qdwUztZurlzowlP7Mpfal7myuW2QE+0LJC/VunSeUioiIiIZREGFiIiI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a16b7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# put the plots together\n",
    "plt.scatter(glass.al, glass.ri)\n",
    "plt.plot(glass.al, glass.ri_pred, color='red')\n",
    "plt.xlabel('al')\n",
    "plt.ylabel('ri')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Refresher: interpreting linear regression coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear regression equation: $y = \\beta_0 + \\beta_1x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.51699012])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute prediction for al=2 using the equation\n",
    "linreg.intercept_ + linreg.coef_ * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.51699012])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute prediction for al=2 using the predict method\n",
    "linreg.predict(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('al', -0.002477606387469623)]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine coefficient for al\n",
    "zip(feature_cols, linreg.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation:** A 1 unit increase in 'al' is associated with a 0.0025 unit decrease in 'ri'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5145125136125304"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# increasing al by 1 (so that al=3) decreases ri by 0.0025\n",
    "1.51699012 - 0.0024776063874696243"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.51451251])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute prediction for al=3 using the predict method\n",
    "linreg.predict(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Predicting a Categorical Response"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    70\n",
       "2    76\n",
       "3    17\n",
       "5    13\n",
       "6     9\n",
       "7    29\n",
       "dtype: int64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine glass_type\n",
    "glass.glass_type.value_counts().sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ri</th>\n",
       "      <th>na</th>\n",
       "      <th>mg</th>\n",
       "      <th>al</th>\n",
       "      <th>si</th>\n",
       "      <th>k</th>\n",
       "      <th>ca</th>\n",
       "      <th>ba</th>\n",
       "      <th>fe</th>\n",
       "      <th>glass_type</th>\n",
       "      <th>ri_pred</th>\n",
       "      <th>household</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.51966</td>\n",
       "      <td>14.77</td>\n",
       "      <td>3.75</td>\n",
       "      <td>0.29</td>\n",
       "      <td>72.02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>9.00</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>1.521227</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>1.51115</td>\n",
       "      <td>17.38</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.34</td>\n",
       "      <td>75.41</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6.65</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6</td>\n",
       "      <td>1.521103</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>1.52213</td>\n",
       "      <td>14.21</td>\n",
       "      <td>3.82</td>\n",
       "      <td>0.47</td>\n",
       "      <td>71.77</td>\n",
       "      <td>0.11</td>\n",
       "      <td>9.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>1.520781</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1.52213</td>\n",
       "      <td>14.21</td>\n",
       "      <td>3.82</td>\n",
       "      <td>0.47</td>\n",
       "      <td>71.77</td>\n",
       "      <td>0.11</td>\n",
       "      <td>9.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>1.520781</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>1.52320</td>\n",
       "      <td>13.72</td>\n",
       "      <td>3.72</td>\n",
       "      <td>0.51</td>\n",
       "      <td>71.75</td>\n",
       "      <td>0.09</td>\n",
       "      <td>10.06</td>\n",
       "      <td>0</td>\n",
       "      <td>0.16</td>\n",
       "      <td>1</td>\n",
       "      <td>1.520682</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          ri     na    mg    al     si     k     ca  ba    fe  glass_type  \\\n",
       "id                                                                          \n",
       "22   1.51966  14.77  3.75  0.29  72.02  0.03   9.00   0  0.00           1   \n",
       "185  1.51115  17.38  0.00  0.34  75.41  0.00   6.65   0  0.00           6   \n",
       "40   1.52213  14.21  3.82  0.47  71.77  0.11   9.57   0  0.00           1   \n",
       "39   1.52213  14.21  3.82  0.47  71.77  0.11   9.57   0  0.00           1   \n",
       "51   1.52320  13.72  3.72  0.51  71.75  0.09  10.06   0  0.16           1   \n",
       "\n",
       "      ri_pred  household  \n",
       "id                        \n",
       "22   1.521227          0  \n",
       "185  1.521103          1  \n",
       "40   1.520781          0  \n",
       "39   1.520781          0  \n",
       "51   1.520682          0  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# types 1, 2, 3 are window glass\n",
    "# types 5, 6, 7 are household glass\n",
    "glass['household'] = glass.glass_type.map({1:0, 2:0, 3:0, 5:1, 6:1, 7:1})\n",
    "glass.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's change our task, so that we're predicting **household** using **al**. Let's visualize the relationship to figure out how to do this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1a570cf8>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zvtF21t/f16awO5Pt615TuW1g+7qd7Zu+ipKGiHg01TyDg4BfAXdRDQ28Gjg1Io7Y3gd0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\npCImDZIkqYhJgyRJKvL/AeawP24oEM1rAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a22b0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(glass.al, glass.household)\n",
    "plt.xlabel('al')\n",
    "plt.ylabel('household')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's draw a **regression line**, like we did before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# fit a linear regression model and store the predictions\n",
    "feature_cols = ['al']\n",
    "X = glass[feature_cols]\n",
    "y = glass.household\n",
    "linreg.fit(X, y)\n",
    "glass['household_pred'] = linreg.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1a87ddd8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XkYlIG3F798RmwLz4971xlpB+Of76V5y7KEQkTQX+9wUdBvYl48sviGy1NSWF\nU6jdr7vXYYlIG3Pb0/AbUDdYeRzwsbW2bkGnHqxekElE0kkkQs74MXQ6shcZX35BxTnns/Kd95Uw\niLRTbnsaHgPuMcacCewPDAIwxowFLsaZ8yAiacS/6Ec6DOpHcME8IhttTOmYQqoPO9LrsETEQy1Z\n3KkMOAjnGRT3xrfvjvN0y5sTH5qIeCIWI/vRh8i/6gp85WVUHncipbffTazzBl5HJiIec7u4UxS4\nJf6v/vaDWyMoEfGG748/CF06iKw3XyfasYDwvfdTddLJWqhJRACXSUN8WKLZVaCstY8nJCIR8UTm\ni88RGnEJ/pUrqT7oYMJjJxLdbHOvwxKRJOJ2eOKRZvZFgFpASYNICvKtKiZ/1HCyn36SWE4O4Vvu\npPK8C8Hvdp60iLQXbpOGbRvZlo8zKXIUcGLCIhKRNhOc9Q6hoQMILPmVmr33ITxhCpG/be91WCKS\npNzOaVjUxK4vjDGZwDjggEQFJSKtrLycvBuvIff+ycQyMigbNZryIZdChtu/I0SkPUrET4jPgdsS\ncB4RaQMZHy0kNKgfGd99S+0OhvCEKdTusZfXYYlIClivQct4L8P5OA+vEpFkVlND7m03UXDM4QS+\n/47y/oMoenO2EgYRcc3t3RPf4tw9Uf++qwCwEZALDE98aCKSKIFvLKGBfQl++jGRrlsQHj+Jmp4a\nURSRlnE7PDGnkW0xoAR40Vr7VuJCEpGEiUbJue9e8m68Fl9VFZWnnUnpjbcS66DHxYhIy7mdCNmn\nleMQkQTz//IzoSEXk/nebKIbbkjJ5Aep7v1Pr8MSkRTmeiKkMSYHOA9nKemOwHLgPeAha21F64Qn\nIi0Wi5H1xOPk/2ck/nAJVUf1JnzXeGJdungdmYikOFcTIY0xnYH5QCGwF84aDT2AicCHxphOrRah\niLjmW76cDuedRYchF0MsRsnYiZQ89F8lDCKSEG57Gm4FugDdrbUL6jYaY/YFnsd5YNXFiQ9PRNzK\nfO0VQpcOxr98GdX/2J/wuHuJbrmV12GJSBpxe8vl8cBV9RMGgPjrq4ATEh2YiLjjC5eQf8lAOp5z\nGr5wCaXX3cyqZ15SwiAiCee2pyEHWNzEvl8ADU+IeCA4dw6hwf0JLP6Jmt32cJaB3nEnr8MSkTTl\ntqfhC+CMJvadDnyZmHBExJXKSvKu+Q8dT+iN/5efKbt0BMWvzlDCICKtym1Pw43AS/EJkf8Ffgc2\nxUkYjok9QnF3AAAeHklEQVR/FZE2kPH5p4QG9iXj66+o3fZvhAsnU9ttX6/DEpF2wFVPg7X2FeAC\nYF/gMWAG8CjQDbjQWvtEq0UoIo7aWnLH3EnBUYeQ8fVXVJx/EUUz3lPCICJtxvU6DdbaB40x03Fu\nuczAWRFyERAxxmxmrV3SOiGKSOCH7wgN7Efwww+IbLIp4bETqTn4UK/DEpF2xu2zJ7YBHgf2a6JI\nDOdZFCKSSLEY2dOmkn/daHzl5VSedDKlt95JrEBzj0Wk7bntabgX2AFnbsMiINpaAYmIw//bEkKX\nDCTznRlECwoIj51I1fEneR2WiLRjbpOG/YEB1tqHWzMYEYmbPp1OF1+Mv7iYqkMPp/SeQqKbbOp1\nVCLSzrlNGkqB31ozEBEBX9FK8kdeCs89gy83l/AdY6g85zzw+dZ+sIhIK3O7TsNjwBBjjOYtiLSS\n4Ntv0unA7mQ/9wz06MHKt+dQee75ShhEJGk02dNgjLkPZ4IjQBZwNPCNMWYeUNawvLW2b6tEKJLu\nysrIv3Y0OQ9NJRYMUvqfa8i/7iqiK8u9jkxEZA3NDU8czuqkAZzlogNAzwbbfQ1ei4hLGR/MJzSo\nHxk//kDtTjtTUjiFyG67kx9Qp56IJJ8mkwZr7dZtGIdI+1JdTe6dt5I77m6IxSgfOJSyUaMhK8vr\nyEREmuR6cScRSYzAV18SGtiX4BefEdlya8KFk6jp/g+vwxIRWSu3EyFFZH1FIuRMGEenww8k+MVn\nVJx1LkUz5yhhEJGUoZ4GkTbg/2kRoSEXkzl3DtEuG1Fyz3iqjzja67BERFpEPQ0irSkWI/uxh+nU\n6x9kzp1D1THHsXLWPCUMIpKS1NMg0kp8S5cSumwwWa+/SrRDR0omTKHq36dq3QURSVlKGkRaQeZL\nLxAaMRT/ihVUH3AQ4XH3Et28q9dhiYisFyUNIgnkK1lF/pWXk/3kf4llZ1N6021UXNAP/BoJFJHU\np6RBJEGC784iNORiAr/+Qs2eexGecB+R7XfwOiwRkYTRnz8i66uigrzRIyn417H4f/+NshFXUPzy\nW0oYRCTtqKdBZD1kfPIRoYF9yfj2G2q334HwhCnU7rm312GJiLQK9TSIrIuaGnLvuIWCow8l49tv\nKO97MUVvvauEQUTSmnoaRFoo8O03hAb1JfjxR0Q225zwuHupObCX12GJiLQ69TSIuBWNkn3/JDod\nuj/Bjz+i8pTTKZo1VwmDiLQb6mkQccH/6y+Ehgwg892ZRDt3pmTCfVQfe7zXYYmItCklDSLNicXI\n+r8nyL9iBP6SVVQdcRThu8YT23hjryMTEWlzShpEmuBbsYLQiEvIeul5onn5hO8ppPKMs7UMtIi0\nW0oaRBqR+carhIYNxr9sKdXd/+EsA731Nl6HJSLiKSUNIvX4SsPkXX0lOY8+RCwzk9JrbqSi/0AI\nBLwOTUTEc0oaROKC894nNKg/gcWLqN1lN0omTCGy8y5ehyUikjR0y6VIVRV5119Nx+OPxv/LYsqH\nXkbR6+8oYRARaUA9DdKuBb74nA4D+5Lx1f+IbL0NJYVTqN13P6/DEhFJSuppkPYpEiFn3N10OrIX\nGV/9j4pzL2Dl23OUMIiINEM9DdLu+H/8gQ6D+hH8YD6RjTehdEwh1Yce4XVYIiJJTz0N0n7EYmQ/\n9ACdD+5J8IP5VB5/EkWz5iphEBFxST0N0i74//id/EsGkjXjTaIdCwhPfoCqE//tdVgiIilFSYOk\nvaznnyH/8mH4i4qo7nUI4bETiW66mddhiYikHCUNkrZ8xUXkjxpO9jNPEcvJIXzrXVSed6GWgRYR\nWUdKGiQtBWe+TWjoAAK/LaFmn26EJ0whsu12XoclIpLSNBFS0ktZGfmjLqPglBPwL1tK2RVXUfzi\nG0oYREQSQD0NkjYyPvyA0MC+ZPzwPbVmR8IT76N2tz28DktEJG0kZdJgjAkANwLnAiHgNWCgtXZp\nE+W7AWOBPYFfgRustY+0Ubjitepqcu++jdwxd0EsRvnFgym74irIzvY6MhGRtJKswxPXAucAZwMH\nAl2BpxsraIzpArwOLAT2AsYBU40xh7dJpOKpgP2agt6HkXf3HUQ378qqZ1+m7LqblDCIiLSCpOtp\nMMZkAkOAwdbaGfFtpwE/GmN6WGvnNjjkQqDIWjs0/vobY8zewHDgzbaKW9pYNErOpELybroOX1UV\nFWecTdkNtxALdfA6MhGRtJWMPQ174gxJzKzbYK39CVgEHNBI+QOA2Q22zQJ6tk544jX/z4vhkEPI\nv/pKYqEQqx76L6VjJihhEBFpZUnX04AzFAHO3IT6ltTbV9/mwIeNlM01xnS21q5McHzrrbKykunT\nnTzntNMOJHs9u9KLi4sZOXIaALfd1ofs7GwmTZpNOFy5xvnrrltTUw34CAaDjV6/srKSRx55i/nz\nvwL87Lffjpx99qFkZ2f/uW/hwu/o1m17jjtuH66+ejqRSA277bYVn3/+0xrHADzwwCs8++x8ttpq\nI+688wIARo6c9ucxn3zyPYsWLcXvz+Bf/+rJ+ecf1fh7EosRefB+8kZfCbVVlB52JJVjJ1IRCjF9\n2hvU1FRTU1PDRx99B/jZe+9tqago46GH3qKoqJrtttuEKVP6c/PNT/PRR98RjUaIxSKUlpZRWekn\nNzfAZpt1ISsrh0MO2YEnnnifFSuKCQYDVFdHiMVqiURqgSCBQDY9e25PRkaABQssVVURgsEIVVW1\nRCKZ5OVlsMUWm7LDDltw001n8vTT7/Pss/MpKPDz4Yc/UlFRy/bbd+WYY/bklVc+ZMmSMHvttTnL\nllXh98c49tg9mTbtXaqqlrNiBUCU7bbrynbbbQr4+O23VZx4Yg/OOKMXjz/+Nk88MYNffllFfn4u\nF154OBdddCzAGu1dU1PFRx/9SCAQ4PrrT+PVVz8D4IQT9uW55xas8X1zn5H6n4E99tiKYDCzyc9S\nS9X/v+EmFhFpW75YLOZ1DGswxpwFTLPWZjTYPgP43lrbt8H2b+Plb6q37UCcnoqu1tolTVwqtmxZ\nOKGxu1FZWcmppz7L3LnnAdCjx4M88cSJ6/yDsLi4mG7dHqKkZCQAodCN7LTTxixYcNEa5wfi1z0d\neAJnjulfr19ZWcnJJz/J/Pl+IPhnue7dp/Lww8dw9tkvMH9+Vnx7MYHAeCKREcCj8YhWH7PvvpOI\nRmtYuLAccOLLy7sGny+H0tJL4sfUACuALeoddx//938nr/Ge+JYtI3vIxeTPeIMSQgzmHp4LLWHO\n+6fRt+878XrVj+FUYApO7pkPXAUUA7cBWfFytUAFkAdsWi+Og+LH+uPx1ZWtiZctAPoBd8a3ZQAR\noDp+rU2BknidK/H5biAW6wCcAEyLn2ML4EhgPNAhXvf7gBHxa6+IXzcKbBY/Xz+gsN57VUlu7i2U\nl0eAALDtn+/h3nsXkpmZw7x5Z8bb+3hg8p8xBQJ3EIlcBVTSocPY+Oen7vuhNPUZWf35yIq/x01/\nlprTpUuIhv//1vy/sfZYklVjdUsnql9q69IltF6r2yXj8EQF4DfGNIwtCyhronxWI2Vporynpk+f\nHf+hGASCzJ3b58+/rNbFyJHT4j/wnfOFw3vFE4Y1z7/6urNxfgA3fv3p02czf35XnF9Uq8vNm3c+\nI0dOi++r2z41/otndrz8mscsWLAFCxdW4PyicraVleVRWjqq3jFhYO8Gx124RkyZr75M54P2I3/G\nG7xNL3bjcx7mAkrCIznrrHvq1at+DLOBH4AqnITBiRc6Abnxf6XASqB7gziux0kMSuPHV8XLLY0f\nPzJ+rrr9HYE/gKJ656qr82xisY7x19fGj6+7zu3xY0fGv697L38A9gM+AXrUO9/UBu/VbMrL8+Jx\n7LfGe/jRR9swb94F9dp76hoxOe3mfL/681P3fdOfkdWfj3ObLbcu1vy/sfZYRKTtJePwxM/xr5uy\n5hDF5sBzTZRv+CCBzYBSa+2q5i7UpUtoXWNcZ6HQX/9CCoWy1zmWrKzgOl2zqes7ZWvX+VqJEgpl\n0yUrBkOHwrRpkJXFw3sdQ5+PnyZWL0fMyAi0WUztWd1npLnPR/1ybjQst7bP6bpcwyvJHt/6Uv3a\nr2QcnsjC+ZNugLX2sfi2rXH+/OpurV3QoPwVwHnW2h3qbZsGbGSt7d3MpTwenugDQI8e0xI0PHE5\nAKHQTfHhiQvXOD/UDU+cBjyJc0frX6//1+EJp1z37g80GJ44B2d4opBIZDjwWDyi1cfsu+/kesMT\nTnx5edfGhyeGxo+pPzxRd9z9vHjZZmwwfCiBnxdTs/uehCdMYcXGm6xR1w4dbmfOnFPjwxOnNYjh\nFJzu/rrhidE4wxO3s/bhiQPjxzY3PNEXuIvmhycuxxmeuDE+PHE88BCrhyeOwBlu6BCv+/04N/3c\nR+PDE32BCfXeq0pyc29tMDzhvId77z0hPjxxRry9j8MZ9nBiCgTuJBIZjTMMMC7+ntZ9P6TJz8ia\nwxOnNFlubZofnujjKpZk1Q66t1W/FLa+wxNJlzQAGGNuAfrE/y0DJgLl1tpDjDFBYANghbW2xhiz\nEWBxBj7HAofhDDYfaa2d2cxlPEkaoG0mQr788oKUnAh5ynF/Z+gfHxC6fzKxQIDyoZdRftlICAbX\nqGtWVpDrrz+TgoKCNeqliZCpMRGyqR/M6TARsh380lH9Uli6Jg0BnBlrdYOZr+KsCLnSGNMLeBvo\nZa2dHS+/H86iTrvj3Jp5jbX2ybVcxrOkoS2k4gc/47NPnGWg7dfU/m07woWTqd3n742WTcX6tYTq\nl7rSuW6g+qW69U0aknFOA9baCE4/7fBG9s2kwQROa+18nJlgkopqa8kddze5d96Kr7aWigv6UnrV\n9ZCb63VkIiJST1ImDdJ+BL7/ltCgfgQ/XEhk080Ij51ITa9DvA5LREQakYy3XEp7EIuRPXUKnQ7Z\nn+CHC6n81ykUzZqrhEFEJImpp0HanH/Jr4SGDiBz1jtEO3WiZPwkqo870euwRERkLZQ0SNuJxch6\n5inyRw3Hv6qYqsOOoPSeQqIbb+J1ZCIi4oKSBmkTvpUryB95GdnPP0MsN4/wnWOpPLsP+NZrIq+I\niLQhJQ3S6jJnvEH+0IEElv5Bzb7dKRk/ieg223odloiItJAmQkrrKS0lf/gldDz93/iLVlI6+jqK\nn39VCYOISIpST4O0iowF8+kwqC+BRT9Su9MulEyYQmTX3bwOS0RE1oN6GiSxqqrIu/FaCo47Ev9P\niygfPIyiN2YqYRARSQPqaZCECXz5PzoMuIiML78gsuXWlBROprZ7D6/DEhGRBFFPg6y/SISc8WPo\ndMRBZHz5BRVn96Fo5hwlDCIiaUY9DbJe/It+pMPg/gTnzyXaZSNKxhRSffhRXoclIiKtQD0Nsm5i\nMbIffYhOB/ckOH8uVceewMrZ85UwiIikMfU0SIv5/viD0KWDyHrzdaIdOlIy8T6q/nWKFmoSEUlz\nShqkRTJffJ7QiKH4V66k+oBehMdNJLp5V6/DEhGRNqCkQVzxrSom/4oRZP/fE8RycgjfcgeV510E\nfo1wiYi0F0oaZK2Cs94hNHQAgSW/UrPX3oQn3Edku+29DktERNqY/kyUppWXk3flCApOPh7/0j8o\nu/xKil9+SwmDiEg7pZ4GaVTGxx8SGtiXjO++pXb7HQhPmELtnnt7HZaIiHhIPQ2yppoacm+/mYLe\nh5Hx3beU9xtA0VvvKmEQERH1NMhqgW8soYF9CX76MZHNuxIeP4ma/Q/0OiwREUkS6mkQiEbJmTKR\nTocdQPDTj6k89QyKZs1VwiAiImtQT0M75//lZ0JDB5D57iyiG2xAyb1TqT7mWK/DEhGRJKSehvYq\nFiPricfpdFAPMt+dRdWRR7Ny1nwlDCIi0iT1NLRDvuXLCY24hKyXXyCal094zAQqTz9Ly0CLiEiz\nlDS0M5mvv0po2CD8y5dR3aMn4XH3Et1qa6/DEhGRFKCkoZ3whUvIu/pKch57mFhmJqXX3kRF/4Fa\nBlpERFxT0tAOBOfOITS4P4HFP1Gz6+6EJ0whstPOXoclIiIpRn9mprPKSvKuHU3HE3rj/+VnyoYN\np/i1t5UwiIjIOlFPQ7r65BM6nXEmGV99Se022xIunEzt3/fzOioREUlh6mlIN7W15I65E/bdl4yv\nvqSizwUUvT1HCYOIiKw39TSkEf8P39NhUD+CCxfAZptRfHchNYcc5nVYIiKSJtTTkA5iMbKnTaXz\nIT0JLlxA5Yn/gs8/V8IgIiIJpZ6GFOf//TdnGeh3ZhAtKCB8TyFVJ/6b7M4hWBb2OjwREUkjShpS\nWNZzT5N/+TD8xcVUH3wo4bETiW6yqddhiYhImlLSkIJ8RSvJH3UZ2c8+TSw3l/Dt91B57vlaBlpE\nRFqVkoYUE3z7LUKXDCTw+2/U7PN3whMmE9l2O6/DEhGRdkATIVNFWRn5lw+j4LST8K9YTul/rqH4\nxdeVMIiISJtRT0MKyPhgPqFB/cj48Qdqd9yJkgn3Edltd6/DEhGRdkY9Dcmsuprcm6+n4NgjCSz6\nkfIBQyh6Y5YSBhER8YR6GpJU4KsvCQ3sS/CLz4hsuRXh8ZOo6dHT67BERKQdU09DsolEyJk4nk6H\nH0jwi8+oOPMcit6Zo4RBREQ8p56GJOJf/BOhwf3JnDuH6IZdKLmnkOojj/Y6LBEREUA9DckhFiP7\n8UfodFAPMufOoar3saycPV8Jg4iIJBX1NHjMt3QpoeFDyHrtFaKhDpSMn0TVKadroSYREUk6Sho8\nlPnyi4SGD8G/YgXVBxzkLAPddQuvwxIREWmUkgYvRKPkXzqYnMcfIZadTemNt1JxYX/wa7RIRESS\nl5IGD/iX/kH2E49Ts8dehCdMIbKD8TokERGRtVLS4IHoJpuy4lNLbIMNIBDwOhwRERFXlDR4JLbR\nRl6HICIi0iIaRBcRERFXlDSIiIiIK0oaRERExBUlDSIiIuKKkgYRERFxRUmDiIiIuKKkQURERFxR\n0iAiIiKuKGkQERERV5Q0iIiIiCtKGkRERMQVJQ0iIiLiipIGERERcUVJg4iIiLiipEFERERcyfA6\ngIaMMRsBhcDhQDXwIPAfa22kmWOWAhs22DzaWntzqwUqIiLSziRd0gA8DUSAA4GuwDSgFhjdWGFj\nzMY4CcMBwLf1dpW2apQiIiLtTFIlDcaYHkBPYBtr7U/A58aYEcB4Y8x11tqaRg7bFSepmNdcb4SI\niIisn2Sb03AAsCieMNSZBYSAPZs4ZlfgeyUMIiIirSupehpwhiN+bbBtSfzrFsAHjRyzK1BrjHkR\n6BY/foy19tFWi1JERKQdatOkwRizNfBDE7urgEfjX/9kra0xxsSA7CaO2xnohDPn4UqgN/CgMSbD\nWjstAWGLiIgIbd/T8AuwYxP7osAQIKv+RmNMEPABZU0cdxCQaa0tj7/+3BizFXApziRKERERSYA2\nTRqstbXAN03tN8b8gtNTUN9m8a8Nhy3qn7O2weYvgNPXEo6vS5fQWoqkNtUvtal+qSud6waqX3uW\nbBMh3wO2NcZ0rbftYKAE+KRhYWNMhjHmF2PMsAa7uuEkDiIiIpIgvlgs5nUMazDGvA/EgEHAJjhD\nDBOstdfH9+cBIWvt7/HX43F6Fc4DvgJOAG4Geltr32rzCoiIiKSpZLt7AuBE4F7gXSAM3FeXMMSN\nAK5mdS/JpUARMA4nyfgKOFkJg4iISGIlXU+DiIiIJKdkm9MgIiIiSUpJg4iIiLiSjHMaEsIYEwBu\nBM7FWYb6NWCgtXZpE+W7AWNxlqv+FbjBWvtIG4XbIutQtyeBfzfY/Ja19ohWDTQBjDGTgIC19qJm\nyqRM29Xnsm4p13bxh8jdjvOk2hxgPnCZtfZ/TZRPmfZbh7qlVPvF71y7BzgE54/K14BLrbW/NVE+\nZdoO1ql+KdV+9RljuuPckXiItXZ2E2Va3H7p3NNwLXAOcDarn5j5dGMFjTFdgNeBhcBeOJMqpxpj\nDm+TSFvuWlzWLW5XYCTORNG6fye3bojrxxjjM8ZcD/TFuZumqXKp1nau6xaXUm1njPEDzwLbAccB\n/wBWATOMMZ0bKZ8y7dfSusWlTPsZY3zAy0BHoBfOwnmbAi82UT5l2g5aXr+4lGm/+uJ3GT6CszBi\nU2XWqf3SsqfBGJOJs7rkYGvtjPi204AfjTE9rLVzGxxyIVBkrR0af/2NMWZvYDjwZlvF7UZL62aM\nycL5IbegqZ6IZGOM2RaYCuwCLF5L8ZRpO2hZ3VKx7YA9gO7ATtZaC2CMORtYCRyD84OsvlRqvxbV\nLQXbbyPgf8Aoa+1iAGPMPcCzxpiO1tpVDcqnUttBC+uXgu1X393Az8DfmimzTu2Xrj0Ne+J028+s\n2xB/cuYinCdpNnQA0LD7ZhbOY7qTTUvrtiNOcvh1G8SWKD2An3Cy/B/XUjaV2g5aVrdUbLufcH6B\n1l/5ta43paCR8qnUfi2tW0q1n7X2D2vtGfV+oXYF+uH80myYMEBqtd261C+l2q+OMaY3cDTOH5fN\nWaf2S8ueBpzuemj8iZld+avNgQ8bKZtrjOlsrV2Z4PjWR0vrtitQDVxnjDkaqACeAm601lY1Ut5z\n1trHgMcAjDFrK55KbdfSuqVi260EXm2weQjO+P8bjRySMu23DnVLufarY4x5DmcIpghnVd7GpEzb\nNeSyfinXfsaYDYH7gT5A8VqKr1P7pWtPQy4QtdZGGmyvovGnZeYClY2UpYnyXmpp3XaOf/0K57ke\n1+F0S01utQjbViq1XUulfNsZY47DWaH1rrou/QZStv1c1C2V2280sB/ORLo3jTGbNVImZdsOd/VL\nxfabDDxvrW0siW1ondovXZOGCsAfn7hUXxaNPy2zggZP16z3uqmna3qlpXUbDWxkrR1rrf2ftfa/\nwFDgHGNMp1aOtS2kUtu1VEq3nTGmD/B/wHRr7eVNFEvJ9nNZt5RtP2vtF9baD4DTgADOnVoNpWTb\ngev6pVT7GWPOxRm+Ht5gV1OTIdep/dI1afg5/nXTBts3p/GnZf7M6qdp1tkMKG1irMtLLaqbtTZm\nrS1psLnuYV5bJDg2L6RS27VIKredMeY/wAPAvdbaxn4g10m59nNbt1RrP2PMRvFJ1X+y1lYA3/PX\nNoIUa7uW1i/V2g8n8ekK/G6MCbN6LsarxpiJjZRfp/ZL16ThU5znVvSq22CM2RrYir9O/ACni+rA\nBtsOjm9PNi2qmzHmKWPMMw02d8Pphvqu1aJsO6nUdi2Sqm1njLkcuAEYXW9mdlNSqv1aUrcUbL+t\ngceNMfvUbTDGdAQM8GUj5VOq7Whh/VKw/c4CdsK5y2cP4Mj49gtwntfU0Dq1X1pOhLTWVsUzqzuN\nMcuBZcBEYKa1doExJghsAKyw1tbg3AJ3eXyxnbHAYThPzjyy8St4Zx3qNh14Mv748Bdw7se9A7jD\nWlvuTS1axEe97rVUbrtGrK1uKdd2xpjdccb5p+Lc871Jvd0lQA0p2n7rULdUa78PcB4UeL8xpi9Q\nC9wKLAUeSoP/ey2tX0q1n7V2Sf3Xxpjq+Le/WmuXJ6r90rWnAZzxqMeAR4G3cW5vq1vZqyfOLNEe\nAPF7cI/C+VB8BAwAzrbWzmzbkF1rSd2exlkEqg/wOc5qdmOstY1lnskoxpoLIKV629W3trqlYtud\nivNz5QLgN5z61P27BGdBpFRtv5bWLaXaz1obA04CPgFewrmtuxg4KP5LMqX/761D/VKq/ZqQ8J+d\nesqliIiIuJLOPQ0iIiKSQEoaRERExBUlDSIiIuKKkgYRERFxRUmDiIiIuKKkQURERFxR0iAiIiKu\nKGkQEU8ZY2YaY970Og4RWTslDSLitYYrY4pIklLSICJea+rRvSKSZNLygVUikjyMMXk4T9k7EdgS\n5ymBc4ER1trPvYxNRFpGSYOItLZHcB6SMwr4AdgBuB54HNjNw7hEpIWUNIhIqzHGZAM5wEBr7TPx\nze8aYzriPN59Q++iE5GWUtIgIq3GWlsJHA1gjNkcp5dhB+CfOJMfM72LTkRaSkmDiLQqY8yRwBjA\nAGHgE6AsvluTIEVSiO6eEJFWY4z5G/AcsBDY1lrb0Vp7EPASShhEUo6SBhFpTfsAWcDN1tpF9bYf\njTM8oZ9BIilEwxMi0po+BGqBO4wxY4Bs4DxgP5yehrx4OfU6iKQAZfki0mqstd8DpwNbAS8CEwAL\n7I3T03AAWhFSJGX4YjH9XxUREZG1U0+DiIiIuKKkQURERFxR0iAiIiKuKGkQERERV5Q0iIiIiCtK\nGkRERMQVJQ0iIiLiipIGERERcUVJg4iIiLjy/0h281Zt1ZIIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a86b2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scatter plot that includes the regression line\n",
    "plt.scatter(glass.al, glass.household)\n",
    "plt.plot(glass.al, glass.household_pred, color='red')\n",
    "plt.xlabel('al')\n",
    "plt.ylabel('household')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If **al=3**, what class do we predict for household? **1**\n",
    "\n",
    "If **al=1.5**, what class do we predict for household? **0**\n",
    "\n",
    "We predict the 0 class for **lower** values of al, and the 1 class for **higher** values of al. What's our cutoff value? Around **al=2**, because that's where the linear regression line crosses the midpoint between predicting class 0 and class 1.\n",
    "\n",
    "Therefore, we'll say that if **household_pred >= 0.5**, we predict a class of **1**, else we predict a class of **0**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['small', 'big', 'small'], \n",
       "      dtype='|S5')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# understanding np.where\n",
    "import numpy as np\n",
    "nums = np.array([5, 15, 8])\n",
    "\n",
    "# np.where returns the first value if the condition is True, and the second value if the condition is False\n",
    "np.where(nums > 10, 'big', 'small')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ri</th>\n",
       "      <th>na</th>\n",
       "      <th>mg</th>\n",
       "      <th>al</th>\n",
       "      <th>si</th>\n",
       "      <th>k</th>\n",
       "      <th>ca</th>\n",
       "      <th>ba</th>\n",
       "      <th>fe</th>\n",
       "      <th>glass_type</th>\n",
       "      <th>ri_pred</th>\n",
       "      <th>household</th>\n",
       "      <th>household_pred</th>\n",
       "      <th>household_pred_class</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>id</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.51966</td>\n",
       "      <td>14.77</td>\n",
       "      <td>3.75</td>\n",
       "      <td>0.29</td>\n",
       "      <td>72.02</td>\n",
       "      <td>0.03</td>\n",
       "      <td>9.00</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>1.521227</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.340495</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>1.51115</td>\n",
       "      <td>17.38</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.34</td>\n",
       "      <td>75.41</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6.65</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>6</td>\n",
       "      <td>1.521103</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.315436</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>1.52213</td>\n",
       "      <td>14.21</td>\n",
       "      <td>3.82</td>\n",
       "      <td>0.47</td>\n",
       "      <td>71.77</td>\n",
       "      <td>0.11</td>\n",
       "      <td>9.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>1.520781</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.250283</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1.52213</td>\n",
       "      <td>14.21</td>\n",
       "      <td>3.82</td>\n",
       "      <td>0.47</td>\n",
       "      <td>71.77</td>\n",
       "      <td>0.11</td>\n",
       "      <td>9.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1</td>\n",
       "      <td>1.520781</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.250283</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>1.52320</td>\n",
       "      <td>13.72</td>\n",
       "      <td>3.72</td>\n",
       "      <td>0.51</td>\n",
       "      <td>71.75</td>\n",
       "      <td>0.09</td>\n",
       "      <td>10.06</td>\n",
       "      <td>0</td>\n",
       "      <td>0.16</td>\n",
       "      <td>1</td>\n",
       "      <td>1.520682</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.230236</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          ri     na    mg    al     si     k     ca  ba    fe  glass_type  \\\n",
       "id                                                                          \n",
       "22   1.51966  14.77  3.75  0.29  72.02  0.03   9.00   0  0.00           1   \n",
       "185  1.51115  17.38  0.00  0.34  75.41  0.00   6.65   0  0.00           6   \n",
       "40   1.52213  14.21  3.82  0.47  71.77  0.11   9.57   0  0.00           1   \n",
       "39   1.52213  14.21  3.82  0.47  71.77  0.11   9.57   0  0.00           1   \n",
       "51   1.52320  13.72  3.72  0.51  71.75  0.09  10.06   0  0.16           1   \n",
       "\n",
       "      ri_pred  household  household_pred  household_pred_class  \n",
       "id                                                              \n",
       "22   1.521227          0       -0.340495                     0  \n",
       "185  1.521103          1       -0.315436                     0  \n",
       "40   1.520781          0       -0.250283                     0  \n",
       "39   1.520781          0       -0.250283                     0  \n",
       "51   1.520682          0       -0.230236                     0  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# transform household_pred to 1 or 0\n",
    "glass['household_pred_class'] = np.where(glass.household_pred >= 0.5, 1, 0)\n",
    "glass.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1a8af550>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UCiYNktqnNuVyhkmDVAYmDZLax5YGqVRMGiS1TaU25dIxDVIpNB3SnFJ60ngOFBF/3PJw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\nLAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a88fac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the class predictions\n",
    "plt.scatter(glass.al, glass.household)\n",
    "plt.plot(glass.al, glass.household_pred_class, color='red')\n",
    "plt.xlabel('al')\n",
    "plt.ylabel('household')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3: Using Logistic Regression Instead\n",
    "\n",
    "Logistic regression can do what we just did:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# fit a logistic regression model and store the class predictions\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "logreg = LogisticRegression(C=1e9)\n",
    "feature_cols = ['al']\n",
    "X = glass[feature_cols]\n",
    "y = glass.household\n",
    "logreg.fit(X, y)\n",
    "glass['household_pred_class'] = logreg.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1ace2080>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/kztJatOkIR85cVL+U79uMRt34GzLOkjjSn8/OLmTVHrtOHpCUjsZHKRrYIBB\nR09IpWfSIKm5Sj5lilcapNIzaZDUXH9/9mifBqn0TBokNZcnDTZPSDJpkNRUVyW/0mDzhFR6Jg2S\nmuvP+zR4pUEqPZMGSc2tb56wT4NUdiYNkpqyeUJSlUmDpOaqoyecRloqPZMGSc05ekJSzqRBUlNd\nTu4kKWfSIKk5J3eSlDNpkNRcfqXB5glJJg2SmnL0hKQqkwZJza1vnjBpkMrOpEFSc/02T0jKmDRI\nampD84QdIaWyM2mQ1JzNE5JyJg2SmnNGSEk5kwZJTVWbJwYdPSGVnkmDpOa8NbaknEmDpOacEVJS\nzqRBUlM2T0iqMmmQ1JyjJyTlTBokNVexT4OkjEmDpKaqt8YedMilVHomDZKas3lCUs6kQVJzJg2S\nciYNkppy9ISkKpMGSc1VJ3eyT4NUeiYNkppzcidJOZMGSU3ZPCGpqi0/BVJKE4EzgWOAHuA64N0R\n8XCD8rOBc4F9gPuAj0fEpaMUrjS+2RFSUq5drzScDhwNLAAOAmYCVw1VMKXUC/wXcDuwL3AecFFK\n6ZBRiVQa70waJOXa7lMgpTQJOBF4b0TcmC+bD9yZUpoXEbfWbXI88HhEvC9//seU0n7AScAPRytu\nabzaMLlT231cSBpl7XilYR+yJonF1QURcTdwF3DgEOUPBG6pW3YzcMDIhCeVzPpppO0IKZVdO/7r\nMDN/vK9u+f0162rtDvx8iLJTU0o7RcRjLY5vq/T19fHNb2Y5zvz5BzFlypSt3ueyZcs45ZSFAJx1\n1rFMmTKFCy64hRUr+jY6RvXY69atBbro7u4eMoa+vj4uvfQGbrvt98AE5s59DgsWvByASy+9gdtv\n/zOzZz+LBQteTl9fH6ecspBKZR1/+7d78pvf3L3JNl/96g+4+urb2HPPGZxzztsAOOmkC7nzzgfZ\nZZftefDBFTz1qU/hhS9MTJ06tenrUq3r5MndnHHGW9hhhx02iXe//Z5Od/ckYJDly5dxySU38Pjj\na5k1awdmzuzlD394mOc+d1cAfvObv7B8+XL6+iYwdepEdtutl8HBdTzwwBOsWzeBOXP25MEHl3HX\nXQ8yMNBPpdIPdNPVNYGdd57G6tVr6e/vZtasHZgxo4dbb/09/f3dTJu2DXvssSvPeMau7L33TK67\n7tfsuecM3vWul/CGN/wHTz65lmc9ayaHH74PP/jBz7nnnoeZMGESe+zxN3z/+6fyla/8kIsvvok1\nax7h0UcnK/b6AAAQo0lEQVQBBpg1awZr1gyw00478IY3vJi3vvVV61/fK664kXvvfYLttpvK8ccf\nwoIFh7Bo0RIAjjhiDosWLeHJJ1fyi1/cycSJEznjjPlce+2vN/lbADb5G/n/1vRlL37ePFF9vW+/\n/c+84AV70t09qeHf0nAN9TdajR9a956RtGW6BgcHxzqGjaSU/hFYGBHb1C2/Efi/iDihbvmf8vKf\nqFl2ENmVipkRcX+DQw0uXbqipbFvTl9fH0cddTW33nocAPPmXcwVVxy5VR+Cy5YtY/bsS1i+/BQA\nenrOZK+9/oYlS96+0TGA/NhvAq4g62O6aQx9fX284Q1XctttE4Du9eXmzLkAgCVLtl2/bPbszxGx\nihUr/gm4LI9o420GBtZx++1PAll806Z9FNiGVat2BdYBy4H3NY2pUV2nTz+LH//4KI4//vqaeI/K\n93UU8GWy3HM74L3AZ4FtgXfkv/cDq4FpwK7Ao/n6R4Ht83g+kx+9P493GjC55nl1358C1ubPd62p\n18X576cAASzM97EH8Ergc0BXvs8PA33AR/I4AAaA3YCHyHL8PWpe//OBCrff/hAwEXh6vq6P7bb7\nLCtXfgDoY/r0c1m+/B3Al/I4+pg48Wwqlfdv9LrPnftlurom8tOfvmWj5Vfs8ire+OBNPHbTj1n1\nzGflfx+Ta17r5uetXm9vD0O99za8P2r/RqvxnzKsY4ylRvUbL6xf5+rt7ena2n20Y9Lw/4BvAdtE\nxEDN8h8BP4uIf64r/2tgUUR8pGbZIWSdI3eMiCcaHGrUk4aFC6/n5JNfx4tYwjd4E9uymmnT1jJl\nSvcW73PFitWsXTu1ZslaYNJGZaZNWwvAqlWTGq6vxtDXt45Vq6prasutHWLZk8DUmnVDbdOfl6nd\nppoPVtc1j6lq07rCxIkrqVSq29bWb21NXNuRJQeD+fGqvw/kj9UkYBtgDdkX8FRgZc2RBvOfauzV\nP83qvvPOguv3Va1Xbf2X59tvk8e4kqyFcCDfDzVxT8r3u23NvqvbUVO2P99+Us26tUP8Xt1X7bL6\n133o5T2sYApreOzmn3LRbfdy8snbAK8GrgcOJUvWsu0//envceyxh9JMow/l6vtj4/1es0XHGEvj\n+UsHrF8na0XS0I7NE/fkj7uycRPF7sCiBuV3q1u2G7CyScIAZH8co6mnJ/vv6Emm8jAz2JYn2XX6\nKqbuuN1mtmxsxbpHeGLtzmT/rQKsIPsCqj4fZNfpWRbw8KppwCqy/3Q3Xl+Noe/xlTy8qppIble3\n3/pljwA75/tstM2avEztNpPz39fUbN84psZ1HWRK9wB9lWk1x67ua1VNzL1kVw/Ij1f9fR3ZF+70\nPJbJZF/sk/Ny1aSC/PcBNnzxrqvb95r8eXVf1Xr11dR/Tb795DzWAbK34Lp8P11kicSKmvXb1+y7\nul3961u94rFdzT6m1f3+aE0c1WX1r3v1uBsvf5hepu81hT3m7kPP7x5hQxKzqZ6eKYXeV0OVqb4/\nNqfoMcZSu8e3taxfebVj0vArsk+vg4HLAVJKs4A92bTDI8CPgOPqlr00X97UaGeThx8+h3nzLubW\nW4/lhfyEefMWcsUVR1LZikutq5ct40WzL2H58pMB6On5RN48cTzA+mMAvP2oq7n11vnAlWQjWtkk\nhr6+Pt62UfNEVm7OnC8B1eaJbNns2Z/PmyfeR36qNtlmQ/NEFt+0aaezafPEiU1jalTX6dM/PUTz\nxBvzfb0RuJANzRPvIZvKY1vghPz3zTVPHE3WjAHNmyfeA5zFps0TJ5I1RyzP6x/AJWxonjgU+Dwb\nmidOI0syPkrz5onq6/9FNm2eOJqseeJcVq7MmiKmTz+P5ctPIGuuOZmseeIcKpWTNnrd5869MG+e\nePOQ52Pp8rUcfvgc5s69kttuuyR/jS/ZqNzhhx+52fdVo//kNrw/5tfs90CmTz9r/TkveoyxNJ7/\nUwXr18lakQy1XfMEQErp34Bj85+lwPnAkxHxspRSN/m/ixGxLqU0g+zT+Aqyb4JXAOcAr4yIxU0O\nM+rNEzB6HSGvuWaJHSHtCAlsfUfI+vOxtR0hm30oj4eOkOP5SwesXycbl30aYP2MkGeR9YTqBq4l\nmxHysZTSwcBNwMERcUtefi7ZpE7PJxua+dGIuHIzhxmTpGG0jOc/fBjf9RvPdQPr1+msX+car30a\niIgK2eRMJw2xbjF180tExG3A3FEJTpKkkmrHyZ0kSVIbMmmQJEmFmDRIkqRCTBokSVIhJg2SJKkQ\nkwZJklSISYMkSSrEpEGSJBVi0iBJkgoxaZAkSYWYNEiSpEJMGiRJUiEmDZIkqRCTBkmSVIhJgyRJ\nKsSkQZIkFWLSIEmSCjFpkCRJhZg0SJKkQkwaJElSISYNkiSpEJMGSZJUiEmDJEkqxKRBkiQVYtIg\nSZIKMWmQJEmFmDRIkqRCTBokSVIhJg2SJKkQkwZJklSISYMkSSrEpEGSJBWyzVgHUC+lNAP4PHAI\nsBa4GPhQRFQalO8GPggsAHYBAvhYRHx3dCKWJKkc2vFKw1XADOAg4FjgOOBjTcqfCbwDeB/wfOBb\nwHdSSgeObJiSJJVLWyUNKaV5wAHAMRHxm4i4Fng/8N78ikJ9+QnA8WRXFq6JiL9ExKeAxWQJhyRJ\napG2ShqAA4G7IuLummU3Az3APkOU7wLeAFxdt3wQ2GFEIpQkqaTarU/DTOC+umX35497AD+rXZH3\nc7ipdllK6YXAS4F3jlCMkiSV0qgmDSmlWcBfGqxeA1yWP64XEetSSoPAlAL7fybZVYfbgK9uVbCS\nJGkjo32l4V7gOQ3WDQAnApNrF+Z9GbqAVc12nFL6O+Aa4EHgNY1GW0iSpC0zqklDRPQDf2y0PqV0\nL/DqusW75Y/1zRa12x1KNuriDuC1EfFEgXC6ent7ChTrXNavc43nuoH163TWr7zarSPkj4Cnp5Rm\n1ix7KbAc+OVQG+RDK79L1rfhkIIJgyRJGqauwcHBsY5hIymln5CNfngP2WRNC4EvRMQZ+fppQE9E\nPJhSmgz8GXgMOBzor9nVmoh4fDRjlyRpPGu3Kw0ARwIPAf9D1pnxwmrCkHs/G5oqXgLsDuwN/JVs\npEX154rRCliSpDJouysNkiSpPbXjlQZJktSGTBokSVIh7TYjZEuklCaS3cjqGLIpqK8D3h0RDzco\nPxs4l2yq6vuAj0fEpaMU7rBtQf2uBF5ft/iGiDh0RAPdSimlC4CJEfH2JmU66tzVKli/jjp3KaW/\nAT5NdpfabckmWvvXiPjfBuU76vxtQf067fzNBD4DvIzsn8rrgH+JiAcalO+08zfc+nXU+auVUtqf\nbETiyyLilgZlhn3+xuuVhtOBo8lul30Q2fTUVw1VMKXUC/wXcDuwL3AecFFK6ZBRiXTLnE7B+uX2\nBk4hG41S/XnDyIa45VJKXSmlM4ATyEbSNCrXieeucP1yHXPu8hvIXQ08E3gd8CLgCeDGlNJOQ5Tv\nqPM33PrlOun8dZFNkLc9cDBZR/Ndge81KN9p529Y9ct1zPmrlY8yvJRsYsRGZbbo/I27Kw0ppUlk\nM0u+NyJuzJfNB+5MKc2LiFvrNjkeeDwi3pc//2NKaT/gJOCHoxV3UcOtXz4s9ZnAkkZXItpJSunp\nwEXA88hGxDTTUecOhle/Tjt3wAuA/YG9IiIAUkoL2DAkuv4/mE47f8OqXweevxnA/wIfiIi/AqSU\nPgNcnVLafog5cDrt/A2rfh14/mr9B3AP8IwmZbbo/I3HKw37kF2yX1xdkN818y6yu2jWOxCov3Rz\nM9ktutvRcOv3HLLk8A+jEFsrzAPuJsvw79xM2U47dzC8+nXaubub7MuzdtbX6pWUoe4622nnb7j1\n66jzFxEPRcSba75QZwLvIPvSHGrSvI46f1tQv446f1UppVcDh5H9c9nMFp2/cXelgexSPQx9t8yZ\nbGp34OdDlJ2aUtopIh5rcXxba7j12xtYC3wspXQYsBr4FnBmRKwZovyYiojLgcsBUkqbK95p5264\n9eu0c/cYcG3d4hPJ2v6vH2KTjjp/W1C/jjp/tVJKi8iaYB4nm5V3KB11/moVrF/Hnb+U0lOArwDH\nAss2U3yLzt94vNIwFRgY4oZVaxj6TplTgb4hytKg/Fgbbv2emz/+nuy+Hh8juyz1pRGLcPR02rkb\nro4+dyml1wGfBP69ejm/TkefvwL16+Tzdxowl6wj3Q9TSrsNUaaTz1+R+nXi+fsS8J8RMVQSW2+L\nzt94TBpWAxPyTku1JjP0nTJXU3dnzZrnTe+sOUaGW7/TgBkRcW5E/G9EfAN4H3B0SmnHEY51pHXa\nuRuujj13KaVjgW8D34yIkxsU69jzV7B+HXv+IuK3EfEzYD4wkWykVr2OPX8F69dR5y+ldAxZ8/VJ\ndasadYbcovM3HpOGe/LHXeuW787Qd8q8hw130qzaDVjZpje/Glb9ImIwIpbXLf5t/rhHi2MbbZ12\n7oalU89dSulDZFPAfzEihvowrurI81e0fp12/lJKM/JO1etFxGrg/9j0PEGHnb/h1q/Tzh9Z4jMT\neDCltIINfTGuTSmdP0T5LTp/4zFp+BWwgmxIDQAppVnAnmza6QOyy1MH1S17ab68HQ2rfimlb6WU\nvlO3eDbZZag/j1iUo6PTzt2wdOK5SymdDHwcOK2mV3YjHXf+hlO/Djx/s4Cvp5T+rrogpbQ9kIDf\nDVG+087fLIZRvw48f/8I7EU2yucFwCvz5W8DPjJE+S06f+OuI2RErMmzqnNSSo8AS4HzgcURsSSl\n1A3sDDwaEevIhr+dnE+0cy7wCuBNbHjB28oW1O+bwJUppX8mu4X4vsDZwNkR8eTY1KKwLmourXX6\nuRvC5urXUecupfR8sjb+i8jGe+9Ss3o5sI4OPn9bUL+OOn/Az8huFPiVlNIJZHcN/hTwMHDJOHj/\nDbd+HXX+IuL+2ucppbX5r/dFxCOtOn/j8UoDZG1RlwOXATeRDW2rzup1AFkP0XkA+fjbV5H9QfwC\neBewICIWj27IwzKc+l1FNgnUscBvyGaz+2xEDJV5tptBNp78aDycu1qbq1+nnbujyD5T3gY8wMZ3\nnf0nssmQOvn8Dbd+HXX+ImIQ+Afgl8D3yYZ1LwNekn9JdvT7bwvq11Hnr4GWf356l0tJklTIeL3S\nIEmSWsykQZIkFWLSIEmSCjFpkCRJhZg0SJKkQkwaJElSISYNkiSpEJMGSWMqpbQ4pfTDsY5D0uaZ\nNEgaa/UzY0pqUyYNksZao1v3Smoz4+6GVZLaS0ppGtld9o4Enkp2l8BbgfdHxG/GMjZJw2PSIGmk\nXUp2k5wPAH8Bng2cAXwd+NsxjEvSMJk0SBoxKaUpwLbAuyPiO/ni/0kpbU92e/enjF10kobLpEHS\niImIPuAwgJTS7mRXGZ4NvIas8+OksYtO0nCZNEgaUSmlVwKfBRKwAvglsCpfbSdIqYM4ekLSiEkp\nPQNYBNwOPD0ito+IlwDfx4RB6jgmDZJG0t8Bk4FPRsRdNcsPI2ue8DNI6iA2T0gaST8H+oGzU0qf\nBaYAxwFzya40TMvLedVB6gBm+ZJGTET8H/AmYE/ge8AXgAD2I7vScCDOCCl1jK7BQd+rkiRp87zS\nIEmSCjFpkCRJhZg0SJKkQkwaJElSISYNkiSpEJMGSZJUiEmDJEkqxKRBkiQVYtIgSZIK+f8B9bZx\nqJnKRE0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a88fb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the class predictions\n",
    "plt.scatter(glass.al, glass.household)\n",
    "plt.plot(glass.al, glass.household_pred_class, color='red')\n",
    "plt.xlabel('al')\n",
    "plt.ylabel('household')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if we wanted the **predicted probabilities** instead of just the **class predictions**, to understand how confident we are in a given prediction?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# store the predicted probabilites of class 1\n",
    "glass['household_pred_prob'] = logreg.predict_proba(X)[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1accc550>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Sr8Se/4xzFYWIZIj8Rx7EX76G6nMugMJCr8MRkRThNmn4Bdgy9v1RwCfW2oYF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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b2eccc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the predicted probabilities\n",
    "plt.scatter(glass.al, glass.household)\n",
    "plt.plot(glass.al, glass.household_pred_prob, color='red')\n",
    "plt.xlabel('al')\n",
    "plt.ylabel('household')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.97161726  0.02838274]]\n",
      "[[ 0.34361555  0.65638445]]\n",
      "[[ 0.00794192  0.99205808]]\n"
     ]
    }
   ],
   "source": [
    "# examine some example predictions\n",
    "print logreg.predict_proba(1)\n",
    "print logreg.predict_proba(2)\n",
    "print logreg.predict_proba(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first column indicates the predicted probability of **class 0**, and the second column indicates the predicted probability of **class 1**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 4: Probability, odds, e, log, log-odds\n",
    "\n",
    "$$probability = \\frac {one\\ outcome} {all\\ outcomes}$$\n",
    "\n",
    "$$odds = \\frac {one\\ outcome} {all\\ other\\ outcomes}$$\n",
    "\n",
    "Examples:\n",
    "\n",
    "- Dice roll of 1: probability = 1/6, odds = 1/5\n",
    "- Even dice roll: probability = 3/6, odds = 3/3 = 1\n",
    "- Dice roll less than 5: probability = 4/6, odds = 4/2 = 2\n",
    "\n",
    "$$odds = \\frac {probability} {1 - probability}$$\n",
    "\n",
    "$$probability = \\frac {odds} {1 + odds}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probability</th>\n",
       "      <th>odds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.50</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.60</td>\n",
       "      <td>1.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.80</td>\n",
       "      <td>4.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.90</td>\n",
       "      <td>9.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   probability      odds\n",
       "0         0.10  0.111111\n",
       "1         0.20  0.250000\n",
       "2         0.25  0.333333\n",
       "3         0.50  1.000000\n",
       "4         0.60  1.500000\n",
       "5         0.80  4.000000\n",
       "6         0.90  9.000000"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a table of probability versus odds\n",
    "table = pd.DataFrame({'probability':[0.1, 0.2, 0.25, 0.5, 0.6, 0.8, 0.9]})\n",
    "table['odds'] = table.probability/(1 - table.probability)\n",
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is **e**? It is the base rate of growth shared by all continually growing processes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.7182818284590451"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# exponential function: e^1\n",
    "np.exp(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is a **(natural) log**? It gives you the time needed to reach a certain level of growth:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99989631572895199"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# time needed to grow 1 unit to 2.718 units\n",
    "np.log(2.718)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also the **inverse** of the exponential function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(np.exp(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probability</th>\n",
       "      <th>odds</th>\n",
       "      <th>logodds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.111111</td>\n",
       "      <td>-2.197225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>-1.386294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>-1.098612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.50</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.60</td>\n",
       "      <td>1.500000</td>\n",
       "      <td>0.405465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.80</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>1.386294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.90</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>2.197225</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   probability      odds   logodds\n",
       "0         0.10  0.111111 -2.197225\n",
       "1         0.20  0.250000 -1.386294\n",
       "2         0.25  0.333333 -1.098612\n",
       "3         0.50  1.000000  0.000000\n",
       "4         0.60  1.500000  0.405465\n",
       "5         0.80  4.000000  1.386294\n",
       "6         0.90  9.000000  2.197225"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add log-odds to the table\n",
    "table['logodds'] = np.log(table.odds)\n",
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 5: What is Logistic Regression?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Linear regression:** continuous response is modeled as a linear combination of the features:\n",
    "\n",
    "$$y = \\beta_0 + \\beta_1x$$\n",
    "\n",
    "**Logistic regression:** log-odds of a categorical response being \"true\" (1) is modeled as a linear combination of the features:\n",
    "\n",
    "$$\\log \\left({p\\over 1-p}\\right) = \\beta_0 + \\beta_1x$$\n",
    "\n",
    "This is called the **logit function**.\n",
    "\n",
    "Probability is sometimes written as pi:\n",
    "\n",
    "$$\\log \\left({\\pi\\over 1-\\pi}\\right) = \\beta_0 + \\beta_1x$$\n",
    "\n",
    "The equation can be rearranged into the **logistic function**:\n",
    "\n",
    "$$\\pi = \\frac{e^{\\beta_0 + \\beta_1x}} {1 + e^{\\beta_0 + \\beta_1x}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In other words:\n",
    "\n",
    "- Logistic regression outputs the **probabilities of a specific class**\n",
    "- Those probabilities can be converted into **class predictions**\n",
    "\n",
    "The **logistic function** has some nice properties:\n",
    "\n",
    "- Takes on an \"s\" shape\n",
    "- Output is bounded by 0 and 1\n",
    "\n",
    "We have covered how this works for **binary classification problems** (two response classes). But what about **multi-class classification problems** (more than two response classes)?\n",
    "\n",
    "- Most common solution for classification models is **\"one-vs-all\"** (also known as **\"one-vs-rest\"**): decompose the problem into multiple binary classification problems\n",
    "- **Multinomial logistic regression** can solve this as a single problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 6: Interpreting Logistic Regression Coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1b302a58>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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Sr8Se/4xzFYWIZIj8Rx7EX76G6nMugMJCr8MRkRThNmn4Bdgy9v1RwCfW2oYF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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b30cbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the predicted probabilities again\n",
    "plt.scatter(glass.al, glass.household)\n",
    "plt.plot(glass.al, glass.household_pred_prob, color='red')\n",
    "plt.xlabel('al')\n",
    "plt.ylabel('household')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.64722323])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute predicted log-odds for al=2 using the equation\n",
    "logodds = logreg.intercept_ + logreg.coef_[0] * 2\n",
    "logodds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.91022919])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert log-odds to odds\n",
    "odds = np.exp(logodds)\n",
    "odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.65638445])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert odds to probability\n",
    "prob = odds/(1 + odds)\n",
    "prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.65638445])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute predicted probability for al=2 using the predict_proba method\n",
    "logreg.predict_proba(2)[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('al', 4.1804038614510901)]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine the coefficient for al\n",
    "zip(feature_cols, logreg.coef_[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation:** A 1 unit increase in 'al' is associated with a 4.18 unit increase in the log-odds of 'household'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99205808391674566"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# increasing al by 1 (so that al=3) increases the log-odds by 4.18\n",
    "logodds = 0.64722323 + 4.1804038614510901\n",
    "odds = np.exp(logodds)\n",
    "prob = odds/(1 + odds)\n",
    "prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.99205808])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute predicted probability for al=3 using the predict_proba method\n",
    "logreg.predict_proba(3)[:, 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Bottom line:** Positive coefficients increase the log-odds of the response (and thus increase the probability), and negative coefficients decrease the log-odds of the response (and thus decrease the probability)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7.71358449])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine the intercept\n",
    "logreg.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation:** For an 'al' value of 0, the log-odds of 'household' is -7.71."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.00044652])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert log-odds to probability\n",
    "logodds = logreg.intercept_\n",
    "odds = np.exp(logodds)\n",
    "prob = odds/(1 + odds)\n",
    "prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That makes sense from the plot above, because the probability of household=1 should be very low for such a low 'al' value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Logistic regression beta values](images/logistic_betas.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Changing the $\\beta_0$ value shifts the curve **horizontally**, whereas changing the $\\beta_1$ value changes the **slope** of the curve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 7: Using Logistic Regression with Categorical Features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic regression can still be used with **categorical features**. Let's see what that looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create a categorical feature\n",
    "glass['high_ba'] = np.where(glass.ba > 0.5, 1, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use Seaborn to draw the logistic curve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1a16bda0>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KH+zY08gdT6wCYFBZERe9V80NMvDkW/JtAKJmlhxXGVDXRflvAoucc99wzi13zv0JuBr4\nuplpmYM89edHVtLU7L9fP7RwGsM1ik0GoHzrarY+eKyhc9PDOODOLspP4MCeEMuAEmAisLOnk1VX\nV/YuygwbSHEsX1nLC2/VAnDohOFceMYMipKWex9I1yMViqOzfImjr/It+S4H9gKnADcDmNlkYBKw\npIvyK4E5SdtmATHgnYOdrLZ2b+8jzZDq6soBE0csFueG217peH3RadPZsX1fzuNIheJQHAeLo6/y\nKvk655rM7Hrgh2a2DagFrgcWO+eWmVkJUAVsd8614Nt6l5jZN4E/A4cD/wtc55zb1/VZJCxPvLKJ\nDbX+f8uJs8YwpWZoyBGJhCff2nwBrsHXem8CFgGrgQuDffPxPR/mATjnngbeD5wLvAz8CPgl8OXc\nhiwHU9/Yyu1L/E220pIoH1o4LeSIRMKVVzVfgKCnw9XBT/K+xSR9YTjnHgEeyUlw0mv3PrOGvfUt\nAJx9wiRGVOommwxs+VjzlX5m594mHnneT5A+cmgZZ2pJIBElX8m+u59aTUurXwjz/JOmUFZSFHJE\nIuFT8pWs2rKjniXLNwNQU1XBibPGhByRSH5Q8pWsuuOJVR3TRf7DyVMpiuojJwJKvpJF67bsZdkb\nfhrmKTWVHHNYdcgRieQPJV/Jmr8/ubrj+YcWTtPy7yIJlHwlK9Zt2ctLK7cBcNiE4Rw+eWTIEYnk\nFyVfyYq7n17T8fz8+ZNDi0MkXyn5SsZtqN3HC85PnjN9/DBmTNIEcyLJlHwl4+5+ak3H8/PmT1Zb\nr0gXlHwlozZvr+P5N30Ph2ljh3KE2npFuqTkKxl1/7PrOtZlO/dE1XpFuqPkKxmzc28TS1e8C8D4\n6sFal02kB0q+kjEPP7eetpiv9551/CTVekV6oOQrGVHf2MLil/3KT1VDy3nPzFEhRySS35R8JSMe\ne2kjjcGimGceN4HiIn20RHqifyHSZy2tsY75eocMKmHB7LEhRySS/5R8pc+WvbGF3XXNAJx2zDjK\nSjVfr8jBKPlKn8TjcR56bj0AxUURTj1mfMgRiRQGJV/pE7duF+u3+hWJjz98NMMGl4YckUhhUPKV\nPmmv9QKcMXdCiJGIFJZuVy82s7RWOXTOret7OFJItuysZ/nbftrImZNGMHF0ZcgRiRSOnpaOX5P0\nOg5012s+DuguywDzyPMbOoYSn/Ee1XpF0tFT8v1kwvORwPeAR4C/AZuBKuADwLnAv2QrQMlPDU2t\nPPWqXxhz1IhBGkoskqZuk69z7vftz83sTuCPzrnLk4rdbGY/Bi4CfpOVCCUvLX3t3Y5BFe89ZjxR\nDSUWSUuqN9zOAG7pZt99wPzMhCOFIB6P8+gLflBFaUmU+UdqOXiRdKWafLcBx3ez71RgY2bCkULw\n5rpdbN5eD8CJR4yhorwk5IhECk9Pbb6JfgX8h5kNAv4O1AJj8M0NV6I23wFlUVDrBThNgypEeiXV\n5PvfwAjgX4GvJ2xvAK5xzv0804FJftq+u5EXV/r12Q6bMJzxo4aEHJFIYUop+TrnYsDVZnYtcAK+\n98M24Gnn3L5MBmRmRcC1wMeBSuAB4Ern3NZuyo8Hfgy8D/9lcCtwtXOuIZNxiff48k3Eg/5l7z1W\ntV6R3kq15guAc24XPhlm07eAS4FLgB3A9cBtwILkgmZWBjyMb3M+ETgE+AO+3/HnsxzngNPaFuOJ\n5ZsAGDaklKMPPSTkiEQKV08j3FbS9cCKeMLz9n1x59xhfQ3GzEqBq4AvOOceDbZdBKw2s3nOuaVJ\nh1yMb3s+wTm3Oyj/LeCzfY1FDvTyym0ds5ctmD1Wc/aK9EFPNd+n0nif+MGLpOQofFPD4vYNzrm1\nZrYGX/NNTr5nAg+1J96g/O+A32UoHknQvlJFJAIL52jOXpG+6GmQxSdyGEe79kbE5K5rmxL2JToU\nWGRm3wU+hv8SuB1/E7Apa1EOQFt21PP6mp0AzJ5aRdWw8pAjEilsKbf5Bt3MLgMWAsPwN9yeBP6Q\nwZtbFUDMOdeWtL0J6Opf+zDgU/iBHhfiE/TPgVH4G3aSIY+/vKnj+SlHjwsxEpH+IaVGOzMbCTyL\nT2xHA0OAefibYS+Y2YgMxdMARM0sOa4yoK6L8i3AduAS59yLzrm7gC8Bl2QwpgGvpbWNJ4N5HKqG\nlnHkVM3jINJXqdZ8vwdU429sLWvfaGbH4Qdd/BeZucnVPjlsDZ2bHsYBd3ZRfgPQ4JxLbHN+I3ic\nDOzs6WTV1fkxBWK+x7H4xQ3sa2gB4KwTpzB69NBQ4sg1xdGZ4sisVJPv+cA3ExMvgHNumZn9G/Bd\nMpN8lwN7gVOAmwHMbDIwCVjSRfkngCvMrNg51xpsmwW0ceCUmAeord3b54D7qrq6Mu/juPeJdwCI\nRiIcM70qq/EWwvVQHIojE18AqSbfQUB3k6VvwI9+6zPnXJOZXQ/80My24YcxXw8sDhJ9CX4qy+3O\nuRbgBuALwB/N7NvABOB/8O3QPdZ6JTVbdtTz5rpdAMyZXsXwIWUhRyTSP6TaUXMFvk9tVz4KvJ6Z\ncAC4Bl/rvQlYBKzG30wDP3vaJnx7M8Got5PxI+5eDI67FfXzzZgly/ffaFt4lLqXiWRKqjXfa4F7\nghtvfwbexQ9uuBg4B5+AMyLo6XB18JO8bzFJXxjOuTeA92fq/LJfa1us40bbyKFlzJqiG20imZLq\n3A73mdmn8BPsnJuwawtwuXOuu7l+pYC9vHIbe+v9jbaTjqwhGtWE6SKZkvL40GDk2FjgCPxos1nA\nOOfcjVmKTUL2eNDkEMEPJxaRzElrYh2gFN99q3047xgzA8A5t6m7g6TwbNvdwOurdwAwSyPaRDIu\npeRrZlOA/6P71Sy0enE/8+Qrmzsm7Dh5Tk2osYj0R6nWfH8BHIa/8bYGiGUrIAlfLBbvuNE2tKKE\nOdM1daRIpqWafE8CPuec+2M2g5H88PqaHezY4+clOnFWjaaOFMmCVP9V7QM2ZzMQyR9LXtn/v3qB\nmhxEsiLV5HszcFWwxI/0Y3vqm3npLb9G2/Txw6ipGhxyRCL9U08rWfya/ZOklwFnAW+Z2TN0McOY\nc+7TWYlQcuqZFe/SFvP/2xfMVq1XJFt6avM9g84rVGzA92iYz4FLCWVqJQsJUTwe54mgyaGstIj3\nzBgVckQi/VdPK1lMzmEckgdWb97Lxm3+j5rjZ46mvDTdbuAikqq0/3WZ2UT8SLcVQJuWaO8/nnhl\n/zgZNTmIZFc6ywidB/wAv25aHDgO+IaZ7Qau6GLpHykgjc2tPPv6FgDGHjKYqWOzO2G6yECX6jJC\nHwDuAF7Dr5nW3s77EH7hym9kK0DJjadf2Uxjs//+POnIGiIRTaIjkk2pdjX7Nn6C8n8A/tS+0Tn3\nS+A7wCVZiE1y6OFlawEoikY4cdaYkKMR6f9STb4zgb90s+9pYGJmwpEwbNlZz4p3tgMwZ/ohDB1c\nGnJEIv1fqsl3O2Dd7DsUv4y8FKgnE0a0naQbbSI5kWry/TPwXTP7IFDSvtHMjgb+DfhbFmKTHGiL\nxXgqmERn2JBSjpw6MuSIRAaGVHs7/Dt+8vTb8SsDAzwKDAOewidgKUArVu1g175mAObPqqEoqkl0\nRHIh1WWEGszsbOB04L34FYR3A48D9zjnNMKtQCU2Oahvr0jupNzPN0iwDwc/mFkxUKHEW7j21DXz\n8tu+uf6IqVWMHlkRckQiA0eq/XyLzezfzezi4PUp+MUzd5nZQ2Y2PIsxSpY8nTCJzhnHqcOKSC6l\n08/334D2JPszfA+ILwEzgO9lPjTJpnh8/2oV5aVFzNcCmSI5lWry/SjwDefc9WZ2OH4F4/90zv0E\n+DrwwWwFKNmxatMeNrVPonP4aMrLNImOSC6lmnzHAs8Ez8/GDy2+N3i9Ed/rQQrIkuX7J9FR316R\n3Es1+W4GpgTPzwNecs61D6yYB6zPdGCSPQ1NrSx7YysA46sHM7VGk+iI5Fo6ywj9yMwexC+meSOA\nmf2EYN6H7IQn2fDcm1tpavHdtRfMHqtJdERCkM4gizpgIfA1/FLyALOB7wL/lfnQJFva5+0tLoow\nT5PoiIQi1UEWMeC/g5/E7admIyjJno3b6nhn4x4AjjmsmiGDSg5yhIhkQ0rJ18w+xkHWaXPO/V9G\nIpKseiLhRtuCOepeJhKWVJsd/tTDvjagFchY8g2WqL8W+DhQCTwAXOmc25rCsfcAg1UrP1BLa4yn\nV7wLwCHDypk5aUTIEYkMXKnecJvaxc9s4HP4rmYnZjiubwGX4idpPxkYD9x2sIPM7DPs7wonSV5a\nWcu+hhbAdy+L6kabSGhSbfNd082uFWZWCvwUWJCJgIL3uwr4gnPu0WDbRcBqM5vnnFvazXHTgf8E\nluKXOZIkj7/smxyikQgLNKJNJFSZmD/wVWBuBt6n3VH4pobF7Rucc2uBNXST4INmij/ihzm/nsFY\n+o0tO+t5Y+1OAGZPq2JEZVnIEYkMbH1KvkEt9ZP4SXYyZXzwuDFp+6aEfcm+jm97/l9U6+1S4oi2\nhUep1isStlR7O6zEt6MmJrYiYBRQAVydwZgqgFgXS9E3AeVdxHYs8GVgrnMubmagNt9OWttiPBXM\n2zuisowjp1aFHJGIpNrb4akutsWBPcDdzrlHMhcSDUDUzKJB/+J2ZfiBHh3MrBzfE+Ma59yqhF2q\n/SZ4eeU29tT7G20nzxlLNKrLIxK2VG+4fSLLcSRqnyeihs5ND+OAO5PKHo+f0vL7Zvb9YFsZPnnv\nBWY65zZ0d6Lq6srMRNxH2Y7j6dtfBSAagfNPOZTqEYNCiSNViqMzxdFZvsTRVynPI2hmg4DL8EOM\nh+FXLH4S+INzriGDMS0H9gKn4OeUwMwmA5OAJUllnwWmJ7yO4Ic6TwQ+hp8QqFu1tXszEW+fVFdX\nZjWOLTvqefmtWgBmTa2C1tYuz5ftOFKlOBRHocTRV6m2+Y7E9z6YBbwNbMUvGX8xcJWZzXfO7exz\nNIBzrsnMrgd+aGbbgFrgemCxc26ZmZXg15Db7pxrBBKbGwhqvI1JzRAD1uKX9//xcOrR40KMREQS\npVrz/R5QDZzgnFvWvtHMjgP+jq9tfjaDcV2DX6L+puDxfuDKYN98YBG+ZpxcEwbfFq0bbkBLa1vH\nAplVQ8t1o00kj6SafM8HvpmYeAGCmui/4Wc2y1jyDXo6XE0XvSicc4vpoYucc+6KTMVR6J57cyt1\nja0AnHK0brSJ5JNU+/kOAtZ1s28DoEkC8tBjL/kmh6JohJM0ok0kr6SafFfg23e78lE0qizvrNuy\nt2PqyGOtmmGDS0OOSEQSpdrscC1wT3Dj7c/Au/iuYB8FzgkeJY+013oBTjlKN9pE8k2q/XzvM7NP\n4SdTPzdh1xbgcufcLdkITnqnrrGFpa/5qSPHHTIYmzg85IhEJFnKczs4536HX0TzJHxPg4XAccAD\nZqYGxTzyxPLNNLf4wYGnHTtea7SJ5KFU+/lOwU+Wfnw3ReL4uR4kZLFYnMde8oP6BpUVM++I0SFH\nJCJdSbXN9xfAYfi23zVArMfSEppXVm2ndlcjACcdWUN5acqDGEUkh1L9l3kS8Dnn3B+zGYz03aMv\n+FpvBDjtWN1oE8lXqbb57uMg8yRI+DZvr+O11TsAOHJaFaNHVIQckYh0J9XkezN+Dge16+axh5/f\nP4Hbe4/tbt55EckH3TY7mNmv2T9HQhlwFvCWmT1D0ry6AM65T2clQknJ3vpmnn7V/3Ey9pDBzJoy\nMuSIRKQnPbX5nkHnCWo24Hs0zE/aHkET2YRu8cubaG7190Hf954J6l4mkue6Tb7Ouck5jEP6oKU1\nxqLgRltlRQknHK7uZSL5LhOrF0vIlr2xhd11zYCfs7e0RE3zIvlOybfAxeNxHlzmV14qLopy6jG6\n0SZSCJR8C9yrq7azoXYfACccMVqzl4kUCCXfAnff0rWAv+t51vETww1GRFKm5FvAVm7YxVsbdgNw\nzGHV1FQNDjkiEUmVkm8Ba6/1Apw9b1KIkYhIupR8C9SGrftY/s52AGZOGsGUmqEhRyQi6VDyLVD3\nPbO/1nuOar0iBUfJtwBt3l7Hs29sAWBKTSUzJ2n9UpFCo+RbgO5+ag3xYED3efOnaCixSAFS8i0w\nm7fX8exaukH3AAAT6ElEQVTrvtY7eUwls6dVhRyRiPSGkm+BufupNR2zGJ1/kmq9IoVKybeAJNZ6\np9So1itSyJR8C8jtS1ap1ivSTyj5Foh3Nu3mBVcLwLRxQzlyqmq9IoVMybcAxONxbn3snY7XHz5l\numq9IgUuL9cVD9aKuxb4OFAJPABc6Zzb2k35jwBfB6bjF/r8DfAD51y/WOL+1VU7cOt3ATBnWhWH\nTRgeckQi0lf5WvP9FnApcAlwMjAeuK2rgmZ2FnAT8CvgSOBrwFeBb+Qi0GyLxePc9riv9UaAD50y\nLdyARCQj8q7ma2alwFXAF5xzjwbbLgJWm9k859zSpEM+A9zqnLs+eL3azGYCl+FrzwXtqVc2s36r\nn6/3xCPHML56SMgRiUgm5GPN9yh8U8Pi9g3OubXAGmBBF+WvBb6dtC0OFPyY2/rG1o5ab2lxlAsW\nTA05IhHJlLyr+eKbGAA2Jm3flLCvg3Pu+cTXZjYU+Cxwf1aiy6F7nl7DnvoWAM4+YRIjh5aHHJGI\nZEo+1nwrgJhzri1pexPQY/YxswrgTqAM3/ZbsN7dUc/Dz/u12aqGlnGmVqkQ6VfyMfk2AFEzS46t\nDKjr7iAzOwR4BN9s8X7n3PrshZhd8Xicvzy6kraYH1Lxj6cdSplWJBbpV/Kx2aE9adbQuelhHL5W\newAzmww8BAwGTnbOrUjlRNXVlb2PMoOS43hq+SZeCSZKnzWtirNOmpqTfr35ej3Cojg6UxyZlY/J\ndzmwFzgFuBk6kuskYElyYTMbBTwGtAAnBjfnUlJbu7fv0fZRdXVlpzjqG1v4xe3LASiKRvjHU6ax\nbdu+nMcRFsWhOAoljr7Ku+TrnGsys+uBH5rZNqAWuB5Y7JxbZmYlQBWw3TnXAlwXvD4NaDKzMcFb\nxZ1zW0L4Ffrk1sdXsXtfMwBnnTBRXctE+qm8S76Ba4AS/OCJEnzPhSuDffOBRcApZvYccAF+/MGy\npPdoBUpzEm2GrNywi8Uv+ZaW0SMG8YETJ4cbkIhkTV4m36Cnw9XBT/K+xXS+UZiXv0O6mlrauPG+\nNzteX3qmUVKsm2wi/VU+9nYYkG597B227KgH4KTZNcycPDLkiEQkm5R888Brq3fw6IsbAKgaWs5H\n33toyBGJSLYp+YZsX30zN973BuAbri8/dyaDyvpFS4qI9EDJN0TxeJyf/vVldu5tAuCM90zAJhb8\nlBQikgIl3xA9/PwGlr66GYDx1YP50EJNnCMyUCj5huTtjbv522NvA1BWWsRnPzhLvRtEBhAl3xDs\nqWvmhr+v6Ji74bKzZlBTNTjkqEQkl5R8c6ylNcbPb3+VHXt8O+/ZJ07muJmjQ45KRHJNyTeH4vE4\nv7//Td7euBuA6eOGcfn5s0KOSkTCoOSbQ/c9s5alr70L+P68n/+HI9XOKzJAKfnmyBPLN3Hb46sA\nf4PtixfOZujggpp6QkQySMk3B15wW/n9A37ehmgkwj+fdwTjR2m2MpGBTMk3y1as3s4v73qNuO/Y\nwKfOmcmc6YeEG5SIhE7jWLPolXe28fPbV9Da5jPvxacfyrxZYw5ylIgMBEq+WfLiW7X84s79fXkv\nOHkqp8+dEHJUIpIvlHyz4MlXNvP7+98kFrQ1fPjUaZx1/KSQoxKRfKLkm0HxeJw7nljNPU+v6dh2\n8emHqsYrIgdQ8s2QppY2/nD/mzzzul82riga4RNnzWD+kTUhRyYi+UjJNwO27Kzn+jtWsH6rX2V4\nUFkxn79gllajEJFuKfn20Quulhvve52GpjYAqoeXc9WFcxh3iCbKEZHuKfn2Un1jK39+5C2eWvFu\nx7ajph/C5efOpKK8JMTIRKQQKPn2wqurtvOHB97smJksGolwwclTOOuESUQjkZCjE5FCoOSbhh17\nGvnzoyt5wdV2bKupquDycw9nSs3QECMTkUKj5JuChqZWHly2jgeXraepxbftRoDT507gQwunUlqi\nmclEJD1Kvj1obmnj8eWbuOfpNeytb+nYPqWmkkvONCaPUW1XRHpHybcL9Y0tPPbSRh5+bj17EpLu\n0MGlfHDBFE6ePZZoVG27ItJ7Sr4JNmzdx6IXN7D0tS0dzQsA5aVFnHX8RN73nomUlaqJQUT6bsAn\n330NLTz3xhaeWvEuqzbt6bRvyKASTp87nvceO57B6j4mIhk0YJPvQ8+u5bHn1/HGmp0dM4+1q6mq\n4LRjxnPSkTWq6YpIVgzY5Puzv77c6XVJcZRjDqvm5Nk1zJg0goj664pIFuVl8jWzIuBa4ONAJfAA\ncKVzbms35ecCPwGOAjYC33XO/elg5ymKRpgxcTjvmTmauTaKivK8vBwi0g/la7b5FnApcAmwA7ge\nuA1YkFzQzKqBB4GbgMuA9wG/NbN3nXMPd3eCr146l3EjBjFkkNpyRST38i75mlkpcBXwBefco8G2\ni4DVZjbPObc06ZDLgZ3OuS8Gr98ys2OAq4Fuk+9Jc8ZRW7s387+AiEgK8i754psOKoHF7Rucc2vN\nbA2+5pucfBcAS5K2PQ5cl7UIM+ST31sEwI1fOw2A2l0NgB/G3BWbOKLb92o/tnr4oEyGmDfnE0lH\nIXw+8zH5jg8eNyZt35SwL9E44IUuylaY2Ujn3I4Mx5cR7Ym3/fmHFk7leVfLlh31tLTGOpYgaldS\nFOXQCcP4fx85+oD3unfpGp4P5puYa9WcM29yNkPP+flE0lEon898XDq+Aog559qStjcB5d2UT64q\nNgWPXZUPXWLibXfb46toam6lqbmNtliceJxOP7F4nJXrd+PW7ex0XO2uho4PGsDzrrbjWz8bcn0+\nkXQU0uczH2u+DUDUzKLOuVjC9jKgrpvyZUnb2l93Vb5DdXVlr4PMhqKiqJ+xJ37gvggQiUQYNryi\nU9xt0SglxZ2/Q0eOHEx1VfqTuadyPTJ5vr7EkQuKo7NCiCMXn89Mycfkuz54rKFz08M44M5uyo9N\n2jYW2Oec293TicK64Xbj1047oPbb3uxQVlLUZbNDJBJh+vihjBla1inuImDOtKpOf2YVxWJp/27V\n1ZUpHZOp8/U1jmxTHIUZR7Y/n4lx9FU+Jt/lwF7gFOBmADObDEziwBtrAE/iu5glOjXYnrcSE3D7\nDbfjZo4G0r/hds68yR3H5uIGQ67PJ5KOQvl85l3ydc41mdn1wA/NbBtQi+/nu9g5t8zMSoAqYLtz\nrgX4LfAVM7sBP9DidOCjwJnh/Aapu/Frp3X6Jm//oPTmA5PrD1k+f6hFCuHzmY833ACuwdd6bwIW\nAauBC4N98/G9GeYBBKPe3g8cDbwIfA64xDm3OLchi4ikLu9qvgBBT4erg5/kfYtJ+tJwzj0LHJ+T\n4EREMiBfa74iIv2akq+ISAiUfEVEQqDkKyISAiVfEZEQKPmKiIRAyVdEJARKviIiIVDyFREJgZKv\niEgIlHxFREKg5CsiEgIlXxGRECj5ioiEQMlXRCQESr4iIiFQ8hURCYGSr4hICJR8RURCoOQrIhIC\nJV8RkRAo+YqIhEDJV0QkBEq+IiIhUPIVEQmBkq+ISAiUfEVEQqDkKyISAiVfEZEQFIcdQDIzGwX8\nHDgDaAZ+B3zTOdfWTfkS4BvAJcAYwAHfds7dlZuIRUTSl48139uAUcDJwCeAy4Bv91D+WuAzwBeB\n2cDfgNvNbEF2wxQR6b28Sr5mNg+YD3zcOfeqc+5+4F+BLwQ13OTyUeByfE33XufcKufc94DF+MQt\nIpKX8ir5AguANc65tQnbHgcqgaO6KB8BPgzckbQ9DgzPSoQiIhmQb22+44GNSds2BY8TgOcSdwTt\nwIsSt5nZe4BTgc9mKUYRkT7LafI1s8nAqm52NwE3BY8dnHMtZhYHylN4/+n4WvCzwI19ClZEJIty\nXfPdAMzoZl8MuAooS9wYtPVGgLqe3tjMjgXuBd4Fzu2ud4SISD7IafJ1zrUCb3W338w2AGcnbR4b\nPCY3RyQe9z58L4mXgA8453anEE6kuroyhWLZpzg6UxydKY7O8iWOvsq3G25PAlPNbHzCtlOBPcDL\nXR0QdCm7C9/2e0aKiVdEJFSReDwedgydmNnT+N4Kn8cPmvg9cJ1z7jvB/sFApXPuXTMrA94GdgDn\nAK0Jb9XknNuZy9hFRFKVbzVfgAuALcAT+Jtmv25PvIF/ZX8TxEJgHDALWIfvGdH+c0uuAhYRSVfe\n1XxFRAaCfKz5ioj0e0q+IiIhyLcRblmR7kxpwTFbgUOSNl/jnPuvNM5bhJ/45+P4IdIPAFc657Z2\nU34u8BP8UOqNwHedc39K9XwZjOOvwIVJmx9xzr2vr7EknOMGoMg5d0UPZbJyPXoRR1auh5mNBv4H\n/7kchB8c9P+cc691Uz5bn49048ja5yPo6fQj4DR85fAB4MvOuc3dlM/WNUk3jrSvyUCp+aY1U1rw\nYTwEP9fEmISfH6d53m8Bl+KnuzwZP3z6tm7OWQ08CDwPHA38FPitmZ2R5jn7FEdgFvBVOv/uH85A\nHJhZxMy+A3wa36ulu3LZvB4pxxHI+PUIJoW6A5gOnAecCOwGHjWzkV2Uz8r1SDeOQFY+H2YWwQ+U\nGgacgr+hXgPc3U35bF2TtOIIpH1N+n3NN2GmtCnBhD2vmtm/Aj8zs28751q6OGwWvtvaM70dKWdm\npfgRe19wzj0abLsIWG1m85xzS5MOuRzY6Zz7YvD6LTM7BrgaeLg3MfQmjqD73nRgWXc14z7EMhX4\nLXAEvndKT7JyPdKNI4vXYw5wAjDTOeeCc13C/m6TybW3bF2PtOLI5ucDX0F6Dfiac25dcL4fAXeY\n2bAu+vBn65qkFUdvr8lAqPmmO1Ma+OT7Th+HKB8VnGNx+4YghjVBTF3FuSRp2+P4L46+SDeOGfgv\n5Tf7eN6uzAPW4q/v6oOUzdb1SDeObF2Ptfjkljjis70G3tWMfNm6HunGkbXPh3Nui3Pu4oSENx4/\nV/eybgZPZeWa9CKOXl2Tfl/zJc2Z0gKzgFYzuxuYGxz/Y+fcTWmel27OPZ4DjQNe6KJshZmNdM7t\nSOPcfYljFr5d/NtmdhbQgJ+g/lrnXFMX5VPmnLsZuBnAzA5WPFvXI904snI9gvjvT9p8Fb7N9aEu\nDsnK9ehFHFn7fCQyszvxzSA78aNcu5K1z0iacfTqmhR8zdfMJptZrJufBvyH6ICZ0vDf7t3NlHY4\nMAL4DfA+/IX8nZl9Io3QKoBYF7Xnpm7OWwE0dlGWHuLMRhyHB49v4OfZ+Db+z7tf9iGG3sjW9UhX\nTq6HmZ0H/Bfwv+1//ifJyfVIIY5cfT6uAY7HTznwsJmN7aJMLq5JKnH06pr0h5pvNmZKWwiUOufq\ng9evmtkk4Mv44c6paACiZhZ1zsUStpd1c96G5DgTXvc4o1uG47gG+L5zbk/w+jUzawP+YmZfyuGQ\n7Wxdj3Rl/XoEX+q/Av7snPtKN8Wyfj1SjCMnnw/n3IogpouA9fieOv+dVCzr1yTFOHp1TQo++WZj\nprTgPVuTNq8APppGaOuDx5qk84wD7uymfPK36lhgXx8nC0orDudcHD+RUaIVweME/J9fuZCt65GW\nbF8PM/sm8F3gZwk3jrqS1euRahzZvB5Bl9DTnHN/SThfg5m9w4G/O2TpmqQbR2+vScE3O6QgrZnS\nzKzYzDaY2ZeSds1l/wVNxXJgL76rSvt7TwYmceBNgvY4T07admqwvS/SisPM/mZmtydtnov/c+7t\nPsaSjmxdj7Rk83qY2VfwCe+agyReyOL1SCeOLH8+JgP/Z35u7vbzDQMMeL2L8tm6JmnF0dtrMiDm\ndrA0ZkoLXv8MX8u9DN+O80F8O9jZzrlH0jjvf+P7FX8CqAWuB+qdc6cFTR9VwPZgtY5R+GXvb8F3\nGj8d+CFwpnNucR9+/XTj+BDwV3x3nbvw/SevA37pnPv3vsSRFNNiYGX74IZcXo8048jK9TCz2cCL\n+AE/1+CbwdrtAVrIwfXoRRxZ+3wE/WsXA0Px/a9bge8BU/C9dnJ1TdKNo1fXZCDUfCG1mdI2Jbz+\nMj5B/RR4FbgY+HA6iTdwDf6u+k34+YZXs38UzPzgnPMAgv6B78f/j3sR+BxwSYYSTTpx3IYfjPEJ\n/O/+P/ieHhlLvIE4nQc35PJ6pBNHtq7HR/D//j4FbKbzjHz/gh/skIvrkW4cWft8BH++/wP+L9J7\n8AlwF7AwuP+Sk89IL+Lo1TUZEDVfEZF8M1BqviIieUXJV0QkBEq+IiIhUPIVEQmBkq+ISAiUfEVE\nQqDkKyISAiVfGZDMbI2Z/S7sOGTgUvKVgSp5ZJtITin5ioiEQMOLZUAys9XA0/jp/v4JP1nKX4Gv\nOuf2mV/x+SvAx4Cp+LmhX8LP/PV4OFFLf6KarwxUEeAf8asQXIxffeAS/AxZAD8AvoGfnepM4Ar8\nitZ/M7NBOY9W+p2Cn0xdpA+2Ame1r7NlZi3AL8xsDn7y+a85537RXtjMmoBb8Qk7ee0wkbQo+cpA\nFQfuTVrg8C7gF8B859xHAcysGj+J9qHAB4JypbkMVPonJV8ZyLYkva4NHoeZ2Vz8nM5zgXr8Kibt\nSzJFEOkjtfnKQDYy6fXo4LEOeAA/gfbhzrkhzrkT8Ks9iGSEkq8MVBHgdDNL/DfwYXxzxFJ8Yv6R\nc+7NhP1nBY/6dyN9pmYHGcjGA7eY2Q34tbm+i6/dOvz6Zf9uZuC7mV0InBccNyT3oUp/o29wGaji\n+DbdvcCd+HX8fgx8xjm3BzgfKML3bvg90AzMwjdFnBRCvNLPaJCFiEgIVPMVEQmBkq+ISAiUfEVE\nQqDkKyISAiVfEZEQKPmKiIRAyVdEJARKviIiIVDyFREJwf8HU/kYX6Gzs6YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1adcde80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# original (continuous) feature\n",
    "sns.lmplot(x='ba', y='household', data=glass, ci=None, logistic=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1b308e48>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jJ1FMOKoPpx/TJ+SqRNIn0TE8rYAVtTy3CuiYnHIkE+zYXcbdT81iy/ZSwE+i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\nSAj+PwPv3LvCTHQaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1b7bf780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# categorical feature\n",
    "sns.lmplot(x='high_ba', y='household', data=glass, ci=None, logistic=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x1bc03710>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rd5FYIk2+FYBq575xmG3khXDc1j1VPPG22UM1sOPwkEKpUiYST6TJ9+/Az5RS\nXwKCs9KVUscD/wG8EIPYhOiSfeW1/PHl9Xh9ZkrZ9ecrJhUXOByVEG2LdLbDf2KKp7+M2RkY4H0g\nH1iKScBCOKausYVfPrua2oYWAC44eSRnTB/qcFRCtC/SbYQalFIXAecAZ2N2EK4GPgTe1FrLCjfh\nGK/PbHxZWmZWvR8/bgBXzT3O4aiE6FjE83ztBPue/YVSKg3IkcQrnGRZFk+9o1ttfHnbJZNxy5Qy\nkeAineebppT6T6XUV+zbczGbZ1Yppd5VSslaTeGIt5bv4pN1ptrpgPws7r5yGpkZMqVMJL6uzPP9\nDyCQZP+AmQHxXWAC8MvohyZExz7bcoiXPvwCgMx0D/95yyn07ysbX4reIdLk+2XgR1rrBUqpSZgd\njH+utX4I+CHwpVgFKERbdpRW89ibmwBwueBbl01m9NB8h6MSInKRJt+hwHL73xdhlhYvtG+XYmY9\nCBEXZVUN/OGldbR4zVaCXzlnPNPHDnA4KiG6JtLkux8IbHJ1KfAvrXVgYcVsYE+0AxOiLXWNLfzu\nhbXU1JspZefMGs7Zs4Y7HJUQXdeVbYR+q5R6B7OZ5l8AlFIPYdd9iE14Qhzl9flZ8MoG9lfUAzBj\n7ACuO3ucw1EJ0T1dWWRRB5wJ/ACzlTzANOBnwH9HPzQhjrIsi6cWaTbvOgzAyEG53HbpJNxumVIm\neqdIF1n4gV/YX6Ht82IRlBDh3vy0hE/Wmyll/ftmcs9V08nK6PJeAEIkjIhevUqpr9LJPm1a679F\nJSIhwizbeIBXPt4JQFaGh3uumiZTykSvF2nX4ekO7vMBXiBqydfeov4B4OtAX2ARcIfW+lAEj30T\n6CO98uSgdx/mibdMlTK3y8XtX5rCyEF9HY5KiJ6L9ILbmDa+pgG3Y6aanRrluO4HbsAUaT8DGA68\n1NmDlFLf5OhUONHL7Suv4w8vhVYpG8+UMYUORyVEdEQ65lvSzl0blFIZwO+B06MRkP18dwN3aa3f\nt9uuA3YqpWZrrZe187ixwM+BZZhtjkQvVl3bxG+fX0u9vfHlRaeM4swZwxyOSojoibTn25H1wAlR\neJ6AGZihhiWBBq31LqCEdhK8PUzxFGaZ86YoxiIc0Njs5XcvrKOi5ujGl1ecOcbhqISIrh4lX7uX\nejOmyE60BGbMl4a17wu5L9wPMWPPDyK93l7N5/fzp1c3suvgEQDUiH7cdNFEqVImkk6ksx22YcZR\nQ88ADzACJ+a3AAAdmElEQVQQyAHujWJMOYC/ja3om4CsNmKbBXwPOEFrbSmlQMZ8e6XAXN71X1QA\nMKQwhzuvnEp6WjQ+oAmRWCKd7bC0jTYLqAHe0Fr/M3oh0QC4lVJue35xQCZmoUeQUioLMxPjPq31\nFyF3STepF3pjaQkf2+Uh83Mz+N41M+iTld7Jo4TonVyWlVidRKXUSZgiPiO01qUh7TuBh7XWvwlp\nOxP4gNZJORMznNIATNRa723nRyXWfzzFvbN8F398YQ1gdhz+1Z2nSZUykeh61MmLeImQUiobuAmz\nxDgfs2PxJ8CTWuuGngQRZi1wBJiLqSmBUqoYGAV8FHbsCmBsyG0XZqnzSOCrmIJA7SorOxKNeKOu\nqKhvSsW2Zls5D7+8DjA7Dt9++RRy091d/jmp9nuLFomte4qKejbfPNIx3wLM7IMpwHbgEGbL+K8A\ndyul5mitD/coEpvWukkptQD4jVKqHCgDFgBLtNYrlVLpmD3kKrTWjUDocANKqSNAY9gwhEhQ20ur\neeS1DQQ+gN08fyKTZcdhkQIi7fn+EigCTtFarww02kMEr2F6m9+OYlz3Ybaof8b+/jZwh33fHGAx\npmcc3hMGM5wgQwq9wL7yOh56YS3Ndl3ea+aNZfbkwQ5HJUR8RJp8LwN+HJp4Aeye6H9gKptFLfna\nMx3upY1ZFFrrJXQwRU5rfWu04hCxU1nTyIPPraGu0SyiOPeEEZx/0giHoxIifiKdw5MN7G7nvr1A\n/+iEI1JBbUMLDz63hsNHmgCziOLas8fikrm8IoVEmnw3YMZ32/JlZFWZiJBZvbY2WBB9yugCbp4v\niyhE6ol02OEB4E37wtvfgQPAEEzinW9/F6JDLV4/D7+8ni/21QAwekget18+hTSPLKIQqSfSwjpv\nKaW+gSmmfnHIXQeBW7TWz8UiOJE8/H6LP7+xkY0lZlLM0AF9+O41UhBdpK6Iuxxa6ycwm2iehplp\ncCZwErBIKTU0JtGJpGBZFk8u2sIqXQZAYV4W/3btDHKzZfWaSF2RzvMdjSmWfnI7h1iYWg9CtGJZ\nFv94f3tw2XBeTjr3XjdDdqIQKS/Sz3x/AsZjxn5LAH+HRwthe+2Tnby3ag8AOZlp/Nt1xzOoIMfh\nqIRwXqTJ9zTgdq31U7EMRiSXt1fs4vWlJQBkpnv47jXTGTEw19mghEgQkY751tJJnQQhQr3/+V5e\n+GAHAGkeN3ddOZXjhkmhHCECIk2+z2JqOMi4rujUR2v38ex7WwFTKOeOy6cwSeo1CNFKu8MOSqk/\nc7RGQiZwIbBVKbWcsLq6AFrr22ISoehVlq7fz5NvbwHMbsPfumwy08cOcDgqIRJPR2O+59K6QM1e\nzIyGOWHtLqSQjQCWbTjAXxZuNlueuOCWiycySw10OiwhElK7yVdrXRzHOEQvt2LTQR5buCm419TN\nF03kFKlQJkS7ZHmR6LHlGw/w5zc3BWvy3njRBOZMHeJsUEIkOEm+okeWbThgeryBxHvhBE6fJgse\nheiMJF/RbZ+s288Tb20ODjXceOEETp8uiVeISEjyFd3ywb9KefodDdiJ9yLp8QrRFZJ8RZe9+9ke\n/vH+NsDMavjG/ImcOkXGeIXoCkm+ImKWZfGP93Qw8XrcLm69ZBInTRzkcGRC9D6SfEVELMvi+Q+2\n885KUyQnzePi25dN4fjxRQ5HJkTvJMlXdMrn9/PUIh0sC5mR7uauK6YxebQsGRaiuyT5ig61eH08\n+vomVm81hdD7ZKdzz5XTGDtciuQI0ROSfEW76hu9/OGldeg9VQDk9cnggW+dSm667LkmRE/JWSTa\ndPhIE7/62+pg4i3ql8WPvjaT0UOlxytENEjPVxyjtLyO3z6/hsqaJgBGDMzle9dMJz9Xtv4RIlok\n+YpW9O7D/OGl9dQ3eQGYOKo/d14xlexMeakIEU1yRomgpev389e3t+Dzm0INsycP4qaLJpLmkdEp\nIaJNkq/Asixe+2RncL81gPmzR3HFGWNwuVzOBSZEEpPkm+KaWnz8ZeFmPttyCDCr1m44X0mBHCFi\nLCGTr71X3APA14G+wCLgDq31oXaOvxb4ITAWs9HnY8CvtdayxX0HDh9p4vcvrWPXgSMAZGemcfvl\nU5gs+60JEXMJmXyB+4EbgOuBSmAB8BJweviBSqkLgWeAe4C3gZnAn4F0TAIXbdi+t5qHX11PdW0z\nAAP7Z3PPVdMYUtjH4ciESA0Jl3yVUhnA3cBdWuv37bbrgJ1Kqdla62VhD/km8KLWeoF9e6dSaiJw\nE5J827RkTSnPvrs1eGFt4qj+fPtLU8jNTnc4MiFSR8IlX2AGZqhhSaBBa71LKVWC6fmGJ98HgNqw\nNgvoH7MIe6kWr49n39vGR2v3BdvOOWE418wbKzMahIizREy+w+3vpWHt+0LuC9Jarwq9rZTKA76N\nGYIQtvKqBh5+dUNwfDfN4+bGC5XU4RXCIYmYfHMAv9baF9beBGR19EClVA7wKpAJ/CA24fU+a7eX\n89ibm6hrNAsnCvOyuP3yKYwekudwZEKkrkRMvg2AWynlDputkAnUtfcgpdQA4HVgAnCu1npPbMNM\nfF6fn5c+3BGswQswZUwBt10yWcZ3hXBYIibfQKYYQuuhh2GYXu0xlFLFwLtAH+AMrfWGSH5QUVHf\n7kcZYz2N7UBFHQ/+7V/o3YcBcLvguvMmcO0543G7e7ZwIpl/b7EksXVPIsfWE4mYfNcCR4C5wLMQ\nTK6jgI/CD1ZKDQQ+AFqAU7XWuyL9QWVlR3oebQwUFfXtUWzLNhzg6Xc1jc1m5Ca/TwbfvHQyE0b1\np6Ii/NpkfGOLJYmteyS27unpm0LCJV+tdZNSagHwG6VUOVCGmee7RGu9UimVDhQCFVrrFuBh+/ZZ\nQJNSarD9VJbW+qAD/wXH1De28My7W1m+6eh/e/LoAm65eBL5fTIcjEwIES7hkq/tPswiiWfs728D\nd9j3zQEWA3OVUp8Bl2N2L18Z9hxeIGUyzsaSSv6ycDOHj5gykGkeF1edeRznnDgCt9RnECLhJGTy\ntWc63Gt/hd+3hNZF4BPy/xAvjc1eXlyyg8Wrjw6PDx3Qh9sumcTIQck5ViZEMkjpxNXbbSqp5K9v\nb6G8uhEw3f9zTxzBlWeOIT3N42xwQogOSfLtheoaW3jhg+18tHZ/sG1AfhY3XzSRCaNkYZ8QvYEk\n317Esiw+23KIv/1zGzV1zcH2s2cN58ozx5CVIX9OIXoLOVt7iYOV9Tzz3lY27qwMtg0uyOHGCycw\nfkQ/ByMTQnSHJN8E19Ti461lu3h7xS68PlOFzON2MX/2KObPHiVju0L0UpJ8E5RlWazcfIjnP9ge\nnD4GMGFkP756nmLYAKm7K0RvJsk3AeldlTzy8jq2760OtuX3yeDas8Zy8qRBsq+aEElAkm8COXS4\nnpc/+oKVm4/ulpTmcXHuiSO4eHaxbN8uRBKRszkBVNU28canJXy0Zl9wdwmAmeOLuHrucQwqyHEw\nOiFELEjydVBNfTOLVuxm8ed7afYerZ45dkQ/rjx9NGqkzNkVIllJ8nVATV0z73y2m8Wfl9LUcrRm\n/KCCHK48YwwXnDaG8vKeVR8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nP7BvnhrDxNvV2FZg5lpOt79mYIaNPrNv73cwNjCzZY5X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\nkOQrhBAO+P/4F1lHt8eV0wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bc03be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# categorical feature, with jitter added\n",
    "sns.lmplot(x='high_ba', y='household', data=glass, ci=None, logistic=True, x_jitter=0.05, y_jitter=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1000000000.0, class_weight=None, dual=False,\n",
       "          fit_intercept=True, intercept_scaling=1, max_iter=100,\n",
       "          multi_class='ovr', penalty='l2', random_state=None,\n",
       "          solver='liblinear', tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit a logistic regression model\n",
    "feature_cols = ['high_ba']\n",
    "X = glass[feature_cols]\n",
    "y = glass.household\n",
    "logreg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('high_ba', 4.4273153450187195)]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine the coefficient for high_ba\n",
    "zip(feature_cols, logreg.coef_[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation:** Having a high 'ba' value is associated with a 4.43 unit increase in the log-odds of 'household' (as compared to a low 'ba' value)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 8: Comparing Logistic Regression with Other Models\n",
    "\n",
    "Advantages of logistic regression:\n",
    "\n",
    "- Highly interpretable (if you remember how)\n",
    "- Model training and prediction are fast\n",
    "- No tuning is required (excluding regularization)\n",
    "- Features don't need scaling\n",
    "- Can perform well with a small number of observations\n",
    "- Outputs well-calibrated predicted probabilities\n",
    "\n",
    "Disadvantages of logistic regression:\n",
    "\n",
    "- Presumes a linear relationship between the features and the log-odds of the response\n",
    "- Performance is (generally) not competitive with the best supervised learning methods\n",
    "- Can't automatically learn feature interactions"
   ]
  }
 ],
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