notebooks/06_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. Compare logistic regression with other models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Predicting a Continuous Response"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "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['assorted'] = glass.glass_type.map({1:0, 2:0, 3:0, 4:0, 5:1, 6:1, 7:1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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>assorted</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>1</th>\n",
       "      <td>1.52101</td>\n",
       "      <td>13.64</td>\n",
       "      <td>4.49</td>\n",
       "      <td>1.10</td>\n",
       "      <td>71.78</td>\n",
       "      <td>0.06</td>\n",
       "      <td>8.75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.51761</td>\n",
       "      <td>13.89</td>\n",
       "      <td>3.60</td>\n",
       "      <td>1.36</td>\n",
       "      <td>72.73</td>\n",
       "      <td>0.48</td>\n",
       "      <td>7.83</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.51618</td>\n",
       "      <td>13.53</td>\n",
       "      <td>3.55</td>\n",
       "      <td>1.54</td>\n",
       "      <td>72.99</td>\n",
       "      <td>0.39</td>\n",
       "      <td>7.78</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.51766</td>\n",
       "      <td>13.21</td>\n",
       "      <td>3.69</td>\n",
       "      <td>1.29</td>\n",
       "      <td>72.61</td>\n",
       "      <td>0.57</td>\n",
       "      <td>8.22</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.51742</td>\n",
       "      <td>13.27</td>\n",
       "      <td>3.62</td>\n",
       "      <td>1.24</td>\n",
       "      <td>73.08</td>\n",
       "      <td>0.55</td>\n",
       "      <td>8.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</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",
       "1   1.52101  13.64  4.49  1.10  71.78  0.06  8.75  0.0  0.0           1   \n",
       "2   1.51761  13.89  3.60  1.36  72.73  0.48  7.83  0.0  0.0           1   \n",
       "3   1.51618  13.53  3.55  1.54  72.99  0.39  7.78  0.0  0.0           1   \n",
       "4   1.51766  13.21  3.69  1.29  72.61  0.57  8.22  0.0  0.0           1   \n",
       "5   1.51742  13.27  3.62  1.24  73.08  0.55  8.07  0.0  0.0           1   \n",
       "\n",
       "    assorted  \n",
       "id            \n",
       "1          0  \n",
       "2          0  \n",
       "3          0  \n",
       "4          0  \n",
       "5          0  "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "glass.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pretend that we want to predict **ri**, and our only feature is **al**. How would we do it using machine learning? We would 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",
    "How would we **visualize** this model? 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": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x12ec7a6d0>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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bvfeTN84yMBK6qkdyKj+mlWkqm8yFknCeTfdBnUt9Nxsf/NREfqlrkI6+Ua9+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\nCYuI+EhJWETER/8/CKsg8nZYJSAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12ec7acd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='al', y='ri', data=glass, ci=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we had an **al** value of 2, what would we predict for **ri**? Roughly 1.517.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x130c7e250>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GSE9JiW1KYhVwc2xh38f/991Mnb808b7DO17iPQunJ1aPR8priAxA49wlALz7+q+orm/m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\nwnqfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x130c8f150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Exercise: Draw the scatter plot using Pandas.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# scatter plot using Pandas\n",
    "glass.plot(kind='scatter', x='al', y='ri')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit a linear regression model to predict ri from al\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": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.52194533024\n",
      "[-0.00247761]\n"
     ]
    }
   ],
   "source": [
    "# look at the coefficients to get the equation for the line, but then how do you plot the line?\n",
    "print linreg.intercept_\n",
    "print linreg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.51946772]\n",
      "[ 1.51699012]\n",
      "[ 1.51451251]\n"
     ]
    }
   ],
   "source": [
    "# you could make predictions for arbitrary points, and then plot a line connecting them\n",
    "print linreg.predict(1)\n",
    "print linreg.predict(2)\n",
    "print linreg.predict(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x130d3f510>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+HwePLqfl6HJarv1B+LquLnJr/xw4Kawl76+1vXdvb2foi6sY+uKqXuu6Ro+m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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x130d3fc90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# or you could make predictions for all values of X, and then plot those predictions connected by a line\n",
    "ri_pred = linreg.predict(X)\n",
    "\n",
    "# draw regression line with matplotlib and pandas\n",
    "plt.scatter(glass.al, glass.ri)\n",
    "plt.plot(glass.al, ri_pred, color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "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": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.51699012])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute prediction for al=2 using the predict method\n",
    "linreg.predict(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "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>feature</th>\n",
       "      <th>coef</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>al</td>\n",
       "      <td>-0.002478</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  feature      coef\n",
       "0      al -0.002478"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine coefficient for al\n",
    "pd.DataFrame(zip(feature_cols, linreg.coef_), columns=['feature', 'coef'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Note that we can't use a cross_val_score if we want to investigate variable relationships"
   ]
  },
  {
   "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": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.51451251])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute prediction for al=3 using the predict method\n",
    "linreg.predict(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Predicting a Categorical Response"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's change our task, so that we're predicting **assorted** using **al**. Let's visualize the relationship to figure out how to do this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1323058d0>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x130db5fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(glass.al, glass.assorted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's draw a **regression line**, like we did before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "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.assorted\n",
    "linreg.fit(X, y)\n",
    "assorted_pred = linreg.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x132156310>]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YAHy4wPUlDFQneItca4xZb4y5qdDFpdgBLM4wHqb1hOx1QnjW89/x0hN43xuH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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x132156390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scatter plot that includes the regression line\n",
    "plt.scatter(glass.al, glass.assorted)\n",
    "plt.plot(glass.al, assorted_pred, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If **al=3**, what class do we predict for assorted? **1**\n",
    "\n",
    "If **al=1.5**, what class do we predict for assorted? **0**\n",
    "\n",
    "So, 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",
    "So, we'll say that if **assorted_pred >= 0.5**, we predict a class of **1**, else we predict a class of **0**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# understanding np.where\n",
    "import numpy as np\n",
    "nums = np.array([5, 15, 8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['small', 'big', 'small'], \n",
       "      dtype='|S5')"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 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": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.06545853,  0.19576455,  0.28597641,  0.16068216,  0.13562331,\n",
       "        0.32607057,  0.08550561,  0.04039968,  0.20077632,  0.19576455])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine the predictions\n",
    "assorted_pred[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,\n",
       "       0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0,\n",
       "       0, 1, 1, 1, 1, 0, 1])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# transform predictions to 1 or 0\n",
    "assorted_pred_class = np.where(assorted_pred >= 0.5, 1, 0)\n",
    "assorted_pred_class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x132413a10>]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yt9lsMtA1W/G+LPVTgClFmJdAUGC0v/6M+YN3CZYrj33m/Ex/+iwYFs3P4b/v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\nk7eEXkSWhfNjwjcUJHfcW/lK1Ocj6blnIykgAY7+8gfG334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4axfurj0IXtAwtjAYxDZu\nDKmtW6I7+C/OIcPJfvfDyIEnKcdB8pBYhey55z6C56ej37wJ42+/4mt+G6Ezz4ob1/Lu4sjBKlWS\n8N7fFgDTpx+jGo1IbjdSMBipn/PK6yUyhem3/kHKoCcj14Errowp1+3+O/LZ/XAnpMOHkXy+uH6i\nM3jF4XKR2ulB9Pv24hz0rLZXIRCcZAizzwkkedggjBu/x3PPfbgf71/h40v//Ydt7GhCaWm4Bg6J\nKdMd/JeUPj0xffuNlm5wyiwC114XU8f21htIoVDMPefwFwCwLtQ2ej0PJzjRq6oxvv3+G5sQOv0M\ndPv2YtyySfPlf25oTBPfbcV7Pkk5DuzdOiC53YRq1EB39GhcDH/rjPzkLaFzzi00k1fB3L35BSHs\nfXpi/PUXPA+2jySfFwhONsTK/wRhWTAX65yZBC68mJzxb58Q18CkV19Cl+PA+cyzqFHKzrT6c9Ka\n3YDp22/wtmhF5pr1cYpft38f1onjY+65u/YgVO9scLkwL32XYO3T8d16e9y4xu/XY9i5I3Ltaavt\nGZg++wQg4vqZR+D8dEJ16xX9MKpKSv/HtI3ox/oTrFMP1WSKOydhK5C5S/dP4s3ewlJjJr0wHPMn\nK/DdcCM5Y98SLp2Ckxah/E8Ahp9+IHnwU4TS0sieszAmPHGFybD5dywL5xG4oGF+chGfj6Tnh5Ha\nrg2Sw0HOy2NwzF0U88OQR9LLL8aYZQBcA7TE7uYVH6JzZGu2fkP8y6UlKsMXNhveVlpWLvOnmvI3\nbvwegFDNmppYheTqjcY6fTLmFR/iu+4GnM8MxfDnVgJyQzAaE9bPeXkMAPp/Yjd7vc21GEGhBGYf\ny+wZ2CZPIHB+Oo7ZC8BkKlYugaCyIpR/BaM7dBB71w5aHtdpcwjVP6fihVBVkp4dhKSq5I4cDQYD\nut1/U+2u27BNeovAuQ3I+nQ1nh6PJFzZGn7/FcvSd2Luufo8EdkLsIZ9+z3tO8a1lQ4fxrzyo/wb\nrVtDcjJSViamdV/H1M0L1haXtaugPD9sJOn5YYRqnUbOtNno9+xG8nrjcuRG2/s9Hbpo9wqs/CP7\nEAV+8EyrPyd5yNOap9PC9wp9MxAIThaE8q9Iwjlm9YcO4hzxEv6bm54QMcwfLcO04Tu8d9yJ/6Ym\nmD98n7RbbtTs2A+0I+vLbwhcUki8G1Ul6bnYFJKh5JTICV/9ju0YN36P76amCX/YLEsWIvn9+Tc6\naj8Q0QeyAHw3NcWwZTOq2YzvusL97aUjR7D37KxF0Jw2m1Dt0wtN2J40OurQVvgglvG7byO3/Fdd\nEzE5xdj8f/+dlB5dwGQie96SE/ODLRCUMUL5VyDJQwdi/OkHPPe1xf3oYydGCJeLpBeGo5pMOAcP\nI/mpJ7D36ooUDOKYMIWciVOLPGdg+uxTTFEKE8D9SN/I4aa8E72eDglO9IZCWOfPRtXrUXU6QrVO\ng+bNw/b6vjFV/Y1vxPDHZs2F0mZLLEwwiP3R7pq31NAR+G/QUjsWlrDd8v67cV0YN/+e313duhHl\nn+fto/v3ALRqhc6Zi+PtaQSuvDqxLALBSYZQ/hWEZe4srPPn4L/4f+SMm3DCNgptk95Cv38fvibN\nsPfqEpEpc/U3cYeh4vD7SXoxNmBZKC0t/4fM68Xy7iJC1avjvePOuObGb75Gv/tvVLsdKRTCc19b\nMBiwvZqfHzhwbgNUkwk1rPB9TZsX/ixjR2NauwbvbS1wP5bvLZVw5R/l358z/m0AdP/EhnUInVU3\nEqAuVC0NcnOxd3gQ/vmH3OEv4rvrmHITCQSVGqH8KwDDhu9JHjqQUI0aOOYuKnwlW87o/tkficFj\n/nwVBuVPXD16k/XJlyUKYGaZNzvGSwfA9diASMwc86qP0R09iueB9glDRFjnzQZAtWrP7237ICxZ\nQtIbrwNa0nbDX7vwNbs14oJZ2Gav8asvsY0dTbDe2eRMmBJzglj/xxaCZ9WJsdsb1+SnkfaFcwrY\nwuPmETzzrPyVf2oq9t5dtTeDnj1xP9avuOkRCE4qhPIvZ3QH/iG1e0fNJj19bvEui+VI8sD+kVg5\noWrVyJ67GOfLr5UoEJnkyCbp9djY+cHTauOOSqRimZ9n8on37dcdOohp1ccE69ZDd+QwAfkC8Hqh\nS5dIHTVZC6fgvedeTGvXEDzjzPiDZ2hupvY+PcBoxDFjboySl44cQX/oYJy9PzlqnyJU/xyk//6L\nCS8BaMHiwvNjGzcG8xef4WvSDN4+Ma64AkF5IpR/eeLxYO/WAd3h/3C+MAp/45tOmCjWqW9j/vJz\nAPxXXk3mV+vx3dGqxO1tb45DdzQ29LFrwNORtxjdnt2YvlmD/5rrCKbLce0ti+YjBQKE0qoj+Xz4\nr76O1M7tIHy6NlSjBvr9+1FtNkJnnInu6FFt1V9Q6fp82Ht2RpeRQe6oMQQuuyKmuLDNXoOiBZ9T\nzWaQJGxTJsbJqK38NbOP6dtvCDS8EMeMuYW6iwoEJzNC+ZcXqkryoCcx/vIzngfaRZKIVDihENYJ\n40kerp3g9d3YhKyPVpUoJHIeun17sU6bFHMvWKduxF0SwLJoHlBI6OZgEMuCuai2JAifCDYvW6rl\n5e2svSWETjsd/d7deFu0xLjhOyCxi2fSC8Mw/vwTnjYP4unUNa480WZvdNRO12P9kTIzsMyeEddW\nrVUrcmI5VL265tJpT41/HoHgFEAo/3LCMms61sUL8F92OTmvjT8hZgPp8GFS27ch+SUtK1fwtNpk\nv/9RwoNXRZE06oW4BOeupwfn2/UDASyLFxKyp+K9+9649qY1X6Lftxf/1ddg3LIJAF1uDq7efeCM\ncJwgt2Zr97Zug2nNalSdDl+B/Lfm5R/kh70uZE7zVv7RPv6W8F4DaO6c1ulT0DlzYw5yqTYb+m1b\nI9fZ7yw7ph9IgeBkQyj/csD43bckDx9MqGYtHLMXgtVa8UJ89ZUWouGr/I3OrM+/PuZuDL/+jOWD\n92LuBRqch+eBdpFr05efoz/4rxacLcFmdp7yjQ6R7L2thZYsZflyVLMZKSuTUGo1/FdejeGnHwhc\nfkWMLV+/YzvJ/R8jlJSMY+b8Qk9FG/7YgmqzEax/buRe0rgxkc/B89OxTp9CqHp1fAUC6VV7MP+H\nq6T5iwWCkxWh/MsY3f592Htopg/HzHmEzqpTsQIEAprrZPPm6I4eQQ2vjp2Dnk0YXbNIog50qVFv\nC65nhsa8PVgWzAHAHWUGykP3z35Mn6/Cf9nlmD/WTvYGz66PY8os9Hv+hq1bUS1WdFlZeO+8G+PG\n75GCwVgXT6cTe/eO6Jy55L4xgeD56Ynl9fnQ71AINLwwkttXcmTHVDEvex9ddhbu3n2RMjMi96Pj\nCfn/d1nxcyMQnOQI5V+WuN3Yu3ZAd+QIuSNH4w+7FFYUuv37qNa6JUnjXoOzwy6QBgPBOnVx9Xni\nmPszffoxpg3foUoSgQs1M0rgwovx3nNf/pj/HsD05ef4L7uc4CX/i+vDsnAeUiiE7tChyL2s5Z9C\ncjKmcCwfyaN52HjvbRN5U4m4eKoqKQP7Y/hzG64evfG2vr9QefXbFSS/n8CF+fb+6JwA3hatsE2Z\nQMieirt7L/QF/Pz9V12jDZkmQjcITn2E8i8rVJWUp57A+PuvuNt3xNO1R4UOb/pkJWnNbsD4wwY8\nd98Lv/2GefkyJL+f3OdHHrvpyeeLHOjytnkw4t/vHDwsxqfesniBdmArUejmQCBy4lcfTpjiHDgk\n8gaSl7hF8noJ1ToN//WNMX29mlBqtUiqRsv8OViWvoO/0ZXF5tRN5OmTNz6Afud2dEeO4O7RC9We\niq5A7l7nEO15EwV1EwhONUoVz1+WZQmYBFwKeIAeiqL8FVV+FzAc8AOzFUWJd604xbBOmxRRUrmv\njq24DV6Ph6QXh2ObMRXVYiFn7Ft4OnTG8sNGzKs+xnfdDaU6mWqZNwvDX7sI1qlL8JxzkVxO/Fc0\nik3zGAphWTQf1WbDe1+buD5MX3yG/uC/MffysnFJhw9j+GFD/mPccy/63X+j37cX712twWDA8Puv\n2uG4tDQc0+cWG0XTsCVP+YdX/j4fpnVr88t37kC12XD37IPkyEaXmxMpy3l5DJLXA8QHdRMITkVK\nu/JvDZgVRbkeGAKMyyuQZdkQvm4ONAF6ybJc6zjlrNQY160l6flhBE+rjWPWghIdmioL9Lt2UK1l\nc2wzphKQLyDzs6/xdOwCwSD0748qSVrUzmP8IZKys0h6/VUAckePxbJkIQDOISNi+jKuXYN+7x48\nre+PnPKNxhoduplwSsWwz7z5i1VIUSEXvPe2wbQm3+QjZWVi794J/H4ck2eUyPPGsFVz8wxepCVr\nN65fF1fH3bk7ao0aWKe8HXM/mH4BuPIOwAmzj+DUp7SZvBoDqwAURdkoy3J0rryGwA5FURwAsix/\nC9wEvH88gpaWjIwsBg1aw549ds4+O5sxY5qRllatRG137drD/fd/RGZmHdLS9jF7dlNmztzD9u1W\nzj47myFDGjFz+GeM/up5/EHokfwYjhEbGDOmGaoK/ft/xnffgdu9B6u1NjfcYKZfv4vo1u1rMjPr\nkJS0BZ0uBYejLl6vgqqmYTTmcO21ZsDEhg25BIP1qV59L6FQLhkZ5wA7gep0ZCdTdEswhny4O3bR\n8u/abOzatYcVLYYwKnsrC21XclpAYnznhaxbtw+nU0KSzkWn20IgoAMuCPeXC8jAHsDCaDbyDBnM\noyHLHv6MZexhDfVp1vZr4DegBvA377KStkDTRSobF40C6gIHgRzqU4NdfBkzn01mpPLjjOcACx+y\nkrxU7LtJ45xWX7CST2gFXPTkPt5+8hbuYg9z6t1Ot3Z/oaqjgPOQpJ1cc42Z3Nx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      "text/plain": [
       "<matplotlib.figure.Figure at 0x132413f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the class predictions\n",
    "plt.scatter(glass.al, glass.assorted)\n",
    "plt.plot(glass.al, assorted_pred_class, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What went wrong? This is a line plot, and it connects points in the order they are found. Let's sort the DataFrame by \"al\" to fix this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sinanozdemir/anaconda/envs/sfdat26-env/lib/python2.7/site-packages/ipykernel/__main__.py:5: FutureWarning: sort(columns=....) is deprecated, use sort_values(by=.....)\n"
     ]
    }
   ],
   "source": [
    "# add predicted class to DataFrame\n",
    "glass['assorted_pred_class'] = assorted_pred_class\n",
    "\n",
    "# sort DataFrame by al\n",
    "glass.sort('al', inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13270ea50>]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AeWa2wTn3DeAfCQJig5m9Xef6plrnOuApgjfLP5nZk+O0U08+QIP2Z1y1Ohul\nP9cBncCtzrn/ENa6nsbrz8nqbJT+/B/AA865/02QNTcAn3bONVJ/TlZjo/RlXE3+r+vePiIiOaSL\nvEREckjhLyKSQwp/EZEcUviLiOSQwl9EJIcU/iIiOaTwFxHJIYW/iEgO/X9iJWGiELd8wQAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13270e6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the class predictions again\n",
    "plt.scatter(glass.al, glass.assorted)\n",
    "plt.plot(glass.al, glass.assorted_pred_class, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3: Using Logistic Regression Instead\n",
    "\n",
    "Logistic regression can do what we just did, but better.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# fit a linear regression model and store the class predictions\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "logreg = LogisticRegression()\n",
    "feature_cols = ['al']\n",
    "X = glass[feature_cols]\n",
    "y = glass.assorted\n",
    "logreg.fit(X, y)\n",
    "assorted_pred_class = logreg.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the class predictions\n",
    "assorted_pred_class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x130ad3f90>]"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HueiTvKQI0k5eDgM9sccdZjYafv+7wALg+8CJwGzn3D+b2TcmarRU6plok0xQna2VhzpL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\naUMKfxGRNvT/AUbpkYIOEufSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1324b8d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the class predictions\n",
    "plt.scatter(glass.al, glass.assorted)\n",
    "plt.plot(glass.al, assorted_pred_class, color='red')"
   ]
  },
  {
   "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": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# store the predicted probabilites of class 1\n",
    "assorted_pred_prob = logreg.predict_proba(X)[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1331ca9d0>]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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H4j8k/G/wtzVfLyJJKb2Lf11dqLBv+ATvJ+tDBT5c6L0bP201it8mK4vA3vvi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\nSMVfRCQNqfiLiKSh/wfOtFi4ctYpUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1331caa50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the predicted probabilities\n",
    "plt.scatter(glass.al, glass.assorted)\n",
    "plt.plot(glass.al, assorted_pred_prob, color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.89253652  0.10746348]]\n",
      "[[ 0.52645662  0.47354338]]\n",
      "[[ 0.12953623  0.87046377]]\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": [
    "What is this? 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",
    "$$odds = \\frac {probability} {1 - probability}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "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": 79,
     "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": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.7182818284590451"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# exponential function: e^1\n",
    "e = np.exp(1)\n",
    "e"
   ]
  },
  {
   "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": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# time needed to grow 1 unit to 2.718 units\n",
    "np.log(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also the **inverse** of the exponential function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(np.exp(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "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": 85,
     "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",
    "Notes:\n",
    "\n",
    "- **Multinomial logistic regression** is used when there are more than 2 classes.\n",
    "- Coefficients are estimated using **maximum likelihood estimation**, meaning that we choose parameters that maximize the likelihood of the observed data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 6: Interpreting Logistic Regression Coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1334d3d10>]"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CxV8kSWSseJuS00/E+8nH1F49mZp7HgCfL9GxpJfStI9IEshcMJ/Ciy+AhgZqbr+bhvMn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\nSMVfRCQNqfiLiKSh/wfOtFi4ctYpUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1334d3750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the predicted probabilities again\n",
    "plt.scatter(glass.al, glass.assorted)\n",
    "plt.plot(glass.al, assorted_pred_prob, color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.10592543]])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute predicted log-odds for al=2 using the equation\n",
    "logodds = logreg.intercept_ + logreg.coef_ * 2\n",
    "logodds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.89949172]])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert log-odds to odds\n",
    "odds = np.exp(logodds)\n",
    "odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.47354338]])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert odds to probability\n",
    "prob = odds/(1 + odds)\n",
    "prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.47354338])"
      ]
     },
     "execution_count": 104,
     "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": 105,
   "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>feature</th>\n",
       "      <th>coef</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>al</td>\n",
       "      <td>[2.01099096417]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  feature             coef\n",
       "0      al  [2.01099096417]"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine the coefficient for al\n",
    "pd.DataFrame(zip(feature_cols, logreg.coef_), columns=['feature', 'coef'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation:** A 1 unit increase in 'al' is associated with a 2.0109 unit increase in the log-odds of 'assorted'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.87045351351387434"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# increasing al by 1 (so that al=3) increases the log-odds by 2.0109\n",
    "\n",
    "# the -0.10592543 is the logodds we calculated a few cells ago for al=2\n",
    "# I am stepping through the equation by one \"unit\" of al\n",
    "\n",
    "logodds = -0.10592543 + 2.0109\n",
    "odds = np.exp(logodds)\n",
    "prob = odds/(1 + odds)\n",
    "prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.87046377])"
      ]
     },
     "execution_count": 114,
     "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": 115,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.12790736])"
      ]
     },
     "execution_count": 115,
     "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 'assorted' is -4.127"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01586095])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert log-odds to probability\n",
    "# Probability of assorted is low if al = 0\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 assorted=1 should be very low for such a low 'al' value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](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: 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",
    "- Sensitive to irrelevant features\n",
    "- Can't automatically learn feature interactions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bonus: Confusion Matrix\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[160   3]\n",
      " [ 31  20]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "preds = logreg.predict(X)\n",
    "print metrics.confusion_matrix(y, preds)\n",
    "# Note that we can't make this martix using cross_val_score so a train_test_split has to do!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Top Left: True Negatives <Br>\n",
    "##Top Right False Negatives <Br>\n",
    "##Bottom Left: False Negatives <br>\n",
    "##Bottom Right: True Positives <br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise** Calculate:\n",
    "Accuracy\n",
    "Sensitivity\n",
    "Specificity\n",
    "Precision by hand\n",
    "\n",
    "\n",
    "\n",
    "<br><br><br><br><br><br><br><br><br><br><br><br><br>\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#### Accuracy    = (157 + 28) / 214       == .8644\n",
    "#### Sensitivity (Recall) =  28        / (23 + 28) == .5490\n",
    "#### Specificity =  157       / (157 + 6) == .9631\n",
    "#### Precision =  28       / (28 + 6) == .823"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             precision    recall  f1-score   support\n",
      "\n",
      "          0       0.84      0.98      0.90       163\n",
      "          1       0.87      0.39      0.54        51\n",
      "\n",
      "avg / total       0.85      0.84      0.82       214\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print metrics.classification_report(y, preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x133a5fd50>"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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E28AqrEjFKt2GcfenJg2Lz723vl7aeMzvw+ebSGPjbTQ2/gJRs1rbVZWUBELn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\neTRMAf4DUYw0C6hzOp1HXC5X00h0+lJjuNKftnO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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12f6ce690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# MORE DATA\n",
    "\n",
    "# Logistic Regression is a high bias low variance model that is also non-parametric\n",
    "\n",
    "from sklearn.datasets import make_circles\n",
    "from sklearn.cross_validation import cross_val_score\n",
    "circles_X, circles_y = make_circles(n_samples=1000, random_state=123, noise=0.1, factor=0.2)\n",
    "plt.scatter(circles_X[:,0], circles_X[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qAUGRBLu4n5cmb8BUDv34Kp2MZezx9iZw+HA+TE7G19eXCePG4e/tfd41tbQK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1326fc050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# It has a linear decision boundary, IE the shape is draws between classes are lines!\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "import numpy as np\n",
    "\n",
    "h = .02  # step size in the mesh\n",
    "\n",
    "# Create color maps\n",
    "cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])\n",
    "cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])\n",
    "\n",
    "# we create an instance of Neighbours Classifier and fit the data.\n",
    "logreg = LogisticRegression()\n",
    "logreg.fit(circles_X, circles_y)\n",
    "\n",
    "# Plot the decision boundary. For that, we will assign a color to each\n",
    "# point in the mesh [x_min, m_max]x[y_min, y_max].\n",
    "x_min, x_max = circles_X[:, 0].min() - 1, circles_X[:, 0].max() + 1\n",
    "y_min, y_max = circles_X[:, 1].min() - 1, circles_X[:, 1].max() + 1\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                     np.arange(y_min, y_max, h))\n",
    "Z = logreg.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "# Put the result into a color plot\n",
    "Z = Z.reshape(xx.shape)\n",
    "plt.figure()\n",
    "plt.pcolormesh(xx, yy, Z, cmap=cmap_light)\n",
    "\n",
    "# Plot also the training points\n",
    "plt.scatter(circles_X[:, 0], circles_X[:, 1], c=circles_y, cmap=cmap_bold)\n",
    "plt.xlim(xx.min(), xx.max())\n",
    "plt.ylim(yy.min(), yy.max())\n",
    "plt.title(\"Circle classification Logistic Regression\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48899999999999999"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg = LogisticRegression()\n",
    "cross_val_score(logreg, circles_X, circles_y, cv=5, scoring='accuracy').mean()\n",
    "# lame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier  # compare to knn\n",
    "knn = KNeighborsClassifier(n_neighbors=7)\n",
    "cross_val_score(knn, circles_X, circles_y, cv=5, scoring='accuracy').mean()\n",
    "# not as lame, remember?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0.,   0.,   5., ...,   0.,   0.,   0.],\n",
       "       [  0.,   0.,   0., ...,  10.,   0.,   0.],\n",
       "       [  0.,   0.,   0., ...,  16.,   9.,   0.],\n",
       "       ..., \n",
       "       [  0.,   0.,   1., ...,   6.,   0.,   0.],\n",
       "       [  0.,   0.,   2., ...,  12.,   0.,   0.],\n",
       "       [  0.,   0.,  10., ...,  12.,   1.,   0.]])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "# new dataset, handwritten digits!\n",
    "digits = datasets.load_digits()\n",
    "digits.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPoAAAD9CAYAAACV6WqFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkRtyXKgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1339809d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(digits.images[-5], cmap=plt.cm.gray_r, interpolation='nearest')\n",
    "# the number 9\n",
    "\n",
    "\n",
    "digits.target[-5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data.shape\n",
    "# 1,797 observations, 64 features (8 x 8 image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "digits_X, digits_y = digits.data, digits.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.92101881133607011"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg = LogisticRegression()\n",
    "cross_val_score(logreg, digits_X, digits_y, cv=5, scoring='accuracy').mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9627899114966898"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare to KNN\n",
    "knn = KNeighborsClassifier(n_neighbors=5)\n",
    "cross_val_score(knn, digits_X, digits_y, cv=5, scoring='accuracy').mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Thought Exercise, why would KNN potentially be a better model than logsitci regression\n",
    "# for handwriting?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# OK so wait, when should we use Logistic Regression?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Using dataset of a 1978 survey conducted to measure likliehood of women to perform extramarital affairs\n",
    "# http://statsmodels.sourceforge.net/stable/datasets/generated/fair.html\n",
    "\n",
    "import statsmodels.api as sm\n",
    "affairs_df = sm.datasets.fair.load_pandas().data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "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>rate_marriage</th>\n",
       "      <th>age</th>\n",
       "      <th>yrs_married</th>\n",
       "      <th>children</th>\n",
       "      <th>religious</th>\n",
       "      <th>educ</th>\n",
       "      <th>occupation</th>\n",
       "      <th>occupation_husb</th>\n",
       "      <th>affairs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.111111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.230769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>2.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>16.5</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.727273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.666666</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   rate_marriage   age  yrs_married  children  religious  educ  occupation  \\\n",
       "0            3.0  32.0          9.0       3.0        3.0  17.0         2.0   \n",
       "1            3.0  27.0         13.0       3.0        1.0  14.0         3.0   \n",
       "2            4.0  22.0          2.5       0.0        1.0  16.0         3.0   \n",
       "3            4.0  37.0         16.5       4.0        3.0  16.0         5.0   \n",
       "4            5.0  27.0          9.0       1.0        1.0  14.0         3.0   \n",
       "\n",
       "   occupation_husb   affairs  \n",
       "0              5.0  0.111111  \n",
       "1              4.0  3.230769  \n",
       "2              5.0  1.400000  \n",
       "3              5.0  0.727273  \n",
       "4              4.0  4.666666  "
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affairs_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "affairs_df['affair_binary'] = (affairs_df['affairs'] > 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x134050a90>"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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rdh3q38CdObTdzGyxeNh3CUm6Cdion8cn1fy6zQCHe6sXJOls4OxBNc7MLCee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\nSHXzqob1vfug9D7tXjuIp9V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      "text/plain": [
       "<matplotlib.figure.Figure at 0x133fa0ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(affairs_df.corr())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "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>rate_marriage</th>\n",
       "      <th>age</th>\n",
       "      <th>yrs_married</th>\n",
       "      <th>children</th>\n",
       "      <th>religious</th>\n",
       "      <th>educ</th>\n",
       "      <th>occupation</th>\n",
       "      <th>occupation_husb</th>\n",
       "      <th>affairs</th>\n",
       "      <th>affair_binary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>rate_marriage</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.111127</td>\n",
       "      <td>-0.128978</td>\n",
       "      <td>-0.129161</td>\n",
       "      <td>0.078794</td>\n",
       "      <td>0.079869</td>\n",
       "      <td>0.039528</td>\n",
       "      <td>0.027745</td>\n",
       "      <td>-0.178068</td>\n",
       "      <td>-0.331776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>-0.111127</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.894082</td>\n",
       "      <td>0.673902</td>\n",
       "      <td>0.136598</td>\n",
       "      <td>0.027960</td>\n",
       "      <td>0.106127</td>\n",
       "      <td>0.162567</td>\n",
       "      <td>-0.089964</td>\n",
       "      <td>0.146519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yrs_married</th>\n",
       "      <td>-0.128978</td>\n",
       "      <td>0.894082</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.772806</td>\n",
       "      <td>0.132683</td>\n",
       "      <td>-0.109058</td>\n",
       "      <td>0.041782</td>\n",
       "      <td>0.128135</td>\n",
       "      <td>-0.087737</td>\n",
       "      <td>0.203109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>children</th>\n",
       "      <td>-0.129161</td>\n",
       "      <td>0.673902</td>\n",
       "      <td>0.772806</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.141845</td>\n",
       "      <td>-0.141918</td>\n",
       "      <td>-0.015068</td>\n",
       "      <td>0.086660</td>\n",
       "      <td>-0.070278</td>\n",
       "      <td>0.159833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>religious</th>\n",
       "      <td>0.078794</td>\n",
       "      <td>0.136598</td>\n",
       "      <td>0.132683</td>\n",
       "      <td>0.141845</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.032245</td>\n",
       "      <td>0.035746</td>\n",
       "      <td>0.004061</td>\n",
       "      <td>-0.125933</td>\n",
       "      <td>-0.129299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>educ</th>\n",
       "      <td>0.079869</td>\n",
       "      <td>0.027960</td>\n",
       "      <td>-0.109058</td>\n",
       "      <td>-0.141918</td>\n",
       "      <td>0.032245</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.382286</td>\n",
       "      <td>0.183932</td>\n",
       "      <td>-0.017740</td>\n",
       "      <td>-0.075280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>occupation</th>\n",
       "      <td>0.039528</td>\n",
       "      <td>0.106127</td>\n",
       "      <td>0.041782</td>\n",
       "      <td>-0.015068</td>\n",
       "      <td>0.035746</td>\n",
       "      <td>0.382286</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.201156</td>\n",
       "      <td>0.004469</td>\n",
       "      <td>0.028981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>occupation_husb</th>\n",
       "      <td>0.027745</td>\n",
       "      <td>0.162567</td>\n",
       "      <td>0.128135</td>\n",
       "      <td>0.086660</td>\n",
       "      <td>0.004061</td>\n",
       "      <td>0.183932</td>\n",
       "      <td>0.201156</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.015614</td>\n",
       "      <td>0.017637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>affairs</th>\n",
       "      <td>-0.178068</td>\n",
       "      <td>-0.089964</td>\n",
       "      <td>-0.087737</td>\n",
       "      <td>-0.070278</td>\n",
       "      <td>-0.125933</td>\n",
       "      <td>-0.017740</td>\n",
       "      <td>0.004469</td>\n",
       "      <td>-0.015614</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.464046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>affair_binary</th>\n",
       "      <td>-0.331776</td>\n",
       "      <td>0.146519</td>\n",
       "      <td>0.203109</td>\n",
       "      <td>0.159833</td>\n",
       "      <td>-0.129299</td>\n",
       "      <td>-0.075280</td>\n",
       "      <td>0.028981</td>\n",
       "      <td>0.017637</td>\n",
       "      <td>0.464046</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 rate_marriage       age  yrs_married  children  religious  \\\n",
       "rate_marriage         1.000000 -0.111127    -0.128978 -0.129161   0.078794   \n",
       "age                  -0.111127  1.000000     0.894082  0.673902   0.136598   \n",
       "yrs_married          -0.128978  0.894082     1.000000  0.772806   0.132683   \n",
       "children             -0.129161  0.673902     0.772806  1.000000   0.141845   \n",
       "religious             0.078794  0.136598     0.132683  0.141845   1.000000   \n",
       "educ                  0.079869  0.027960    -0.109058 -0.141918   0.032245   \n",
       "occupation            0.039528  0.106127     0.041782 -0.015068   0.035746   \n",
       "occupation_husb       0.027745  0.162567     0.128135  0.086660   0.004061   \n",
       "affairs              -0.178068 -0.089964    -0.087737 -0.070278  -0.125933   \n",
       "affair_binary        -0.331776  0.146519     0.203109  0.159833  -0.129299   \n",
       "\n",
       "                     educ  occupation  occupation_husb   affairs  \\\n",
       "rate_marriage    0.079869    0.039528         0.027745 -0.178068   \n",
       "age              0.027960    0.106127         0.162567 -0.089964   \n",
       "yrs_married     -0.109058    0.041782         0.128135 -0.087737   \n",
       "children        -0.141918   -0.015068         0.086660 -0.070278   \n",
       "religious        0.032245    0.035746         0.004061 -0.125933   \n",
       "educ             1.000000    0.382286         0.183932 -0.017740   \n",
       "occupation       0.382286    1.000000         0.201156  0.004469   \n",
       "occupation_husb  0.183932    0.201156         1.000000 -0.015614   \n",
       "affairs         -0.017740    0.004469        -0.015614  1.000000   \n",
       "affair_binary   -0.075280    0.028981         0.017637  0.464046   \n",
       "\n",
       "                 affair_binary  \n",
       "rate_marriage        -0.331776  \n",
       "age                   0.146519  \n",
       "yrs_married           0.203109  \n",
       "children              0.159833  \n",
       "religious            -0.129299  \n",
       "educ                 -0.075280  \n",
       "occupation            0.028981  \n",
       "occupation_husb       0.017637  \n",
       "affairs               0.464046  \n",
       "affair_binary         1.000000  "
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "affairs_df.corr()\n",
    "# Obviously affairs will correlate to affair_binary but what else?\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# It seems children, yrs_married, rate_married, and age all correlate to affair_binary\n",
    "# Remember correlations are NOT the single way to identify which features to use\n",
    "# Correlations only give us a number determining how linearlly correlated the variables are\n",
    "# We may find another variable that affects affairs by evaluating the coefficients of our LR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "affairs_X = affairs_df.drop(['affairs', 'affair_binary'], axis=1)\n",
    "affairs_y = affairs_df['affair_binary']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.71630094  0.69749216  0.74137931  0.71226415  0.70125786  0.73113208\n",
      "  0.71855346  0.70125786  0.74685535  0.75314465]\n",
      "0.72196378226\n"
     ]
    }
   ],
   "source": [
    "model = LogisticRegression()\n",
    "from sklearn.cross_validation import cross_val_score\n",
    "# check the accuracy on the training set\n",
    "scores = cross_val_score(model, affairs_X, affairs_y, cv=10)\n",
    "print scores\n",
    "print scores.mean()\n",
    "\n",
    "# Looks pretty good"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "      <th>3</th>\n",
       "      <td>children</td>\n",
       "      <td>[-0.00117231032]</td>\n",
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       "      <td>religious</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>educ</td>\n",
       "      <td>[-0.0328106363897]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>occupation</td>\n",
       "      <td>[0.161411859069]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>occupation_husb</td>\n",
       "      <td>[0.0145734984752]</td>\n",
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      ],
      "text/plain": [
       "                 0                   1\n",
       "0    rate_marriage   [-0.702300201706]\n",
       "1              age  [-0.0546769400998]\n",
       "2      yrs_married    [0.105079088955]\n",
       "3         children    [-0.00117231032]\n",
       "4        religious   [-0.367121091053]\n",
       "5             educ  [-0.0328106363897]\n",
       "6       occupation    [0.161411859069]\n",
       "7  occupation_husb   [0.0145734984752]"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Explore individual features that make the biggest impact\n",
    "# religious, yrs_married, and occupation. But one of these variables doesn't quite make sense right?\n",
    "pd.DataFrame(zip(affairs_X.columns, np.transpose(model.coef_)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Dummy Variables:\n",
    "\n",
    "# Encoding qualitiative (nominal) data using separate columns (see slides for linear regression for more)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/dummy.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      "text/plain": [
       "   rate_marriage   age  yrs_married  children  religious  educ  occupation  \\\n",
       "0            3.0  32.0          9.0       3.0        3.0  17.0         2.0   \n",
       "1            3.0  27.0         13.0       3.0        1.0  14.0         3.0   \n",
       "2            4.0  22.0          2.5       0.0        1.0  16.0         3.0   \n",
       "3            4.0  37.0         16.5       4.0        3.0  16.0         5.0   \n",
       "4            5.0  27.0          9.0       1.0        1.0  14.0         3.0   \n",
       "\n",
       "   occupation_husb   affairs affair_binary  occ__2.0  occ__3.0  occ__4.0  \\\n",
       "0              5.0  0.111111          True       1.0       0.0       0.0   \n",
       "1              4.0  3.230769          True       0.0       1.0       0.0   \n",
       "2              5.0  1.400000          True       0.0       1.0       0.0   \n",
       "3              5.0  0.727273          True       0.0       0.0       0.0   \n",
       "4              4.0  4.666666          True       0.0       1.0       0.0   \n",
       "\n",
       "   occ__5.0  occ__6.0  \n",
       "0       0.0       0.0  \n",
       "1       0.0       0.0  \n",
       "2       0.0       0.0  \n",
       "3       1.0       0.0  \n",
       "4       0.0       0.0  "
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "occuptation_dummies = pd.get_dummies(affairs_df['occupation'], prefix='occ_').iloc[:, 1:]\n",
    "\n",
    "# concatenate the dummy variable columns onto the original DataFrame (axis=0 means rows, axis=1 means columns)\n",
    "affairs_df = pd.concat([affairs_df, occuptation_dummies], axis=1)\n",
    "affairs_df.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "      <td>0.727273</td>\n",
       "      <td>True</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.666666</td>\n",
       "      <td>True</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   rate_marriage   age  yrs_married  children  religious  educ  occupation  \\\n",
       "0            3.0  32.0          9.0       3.0        3.0  17.0         2.0   \n",
       "1            3.0  27.0         13.0       3.0        1.0  14.0         3.0   \n",
       "2            4.0  22.0          2.5       0.0        1.0  16.0         3.0   \n",
       "3            4.0  37.0         16.5       4.0        3.0  16.0         5.0   \n",
       "4            5.0  27.0          9.0       1.0        1.0  14.0         3.0   \n",
       "\n",
       "   occupation_husb   affairs affair_binary  occ__2.0  occ__3.0  occ__4.0  \\\n",
       "0              5.0  0.111111          True       1.0       0.0       0.0   \n",
       "1              4.0  3.230769          True       0.0       1.0       0.0   \n",
       "2              5.0  1.400000          True       0.0       1.0       0.0   \n",
       "3              5.0  0.727273          True       0.0       0.0       0.0   \n",
       "4              4.0  4.666666          True       0.0       1.0       0.0   \n",
       "\n",
       "   occ__5.0  occ__6.0  occ_husb__2.0  occ_husb__3.0  occ_husb__4.0  \\\n",
       "0       0.0       0.0            0.0            0.0            0.0   \n",
       "1       0.0       0.0            0.0            0.0            1.0   \n",
       "2       0.0       0.0            0.0            0.0            0.0   \n",
       "3       1.0       0.0            0.0            0.0            0.0   \n",
       "4       0.0       0.0            0.0            0.0            1.0   \n",
       "\n",
       "   occ_husb__5.0  occ_husb__6.0  \n",
       "0            1.0            0.0  \n",
       "1            0.0            0.0  \n",
       "2            1.0            0.0  \n",
       "3            1.0            0.0  \n",
       "4            0.0            0.0  "
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "occuptation_dummies = pd.get_dummies(affairs_df['occupation_husb'], prefix='occ_husb_').iloc[:, 1:]\n",
    "\n",
    "# concatenate the dummy variable columns onto the original DataFrame (axis=0 means rows, axis=1 means columns)\n",
    "affairs_df = pd.concat([affairs_df, occuptation_dummies], axis=1)\n",
    "affairs_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# remove appropiate columns for feature set\n",
    "affairs_X = affairs_df.drop(['affairs', 'affair_binary', 'occupation', 'occupation_husb'], axis=1)\n",
    "affairs_y = affairs_df['affair_binary']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.72588752748978946"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LogisticRegression()\n",
    "model = model.fit(affairs_X, affairs_y)\n",
    "\n",
    "# check the accuracy on the training set\n",
    "model.score(affairs_X, affairs_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "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>features</th>\n",
       "      <th>coef</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>rate_marriage</td>\n",
       "      <td>[-0.697845453825]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>age</td>\n",
       "      <td>[-0.0563368031972]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>yrs_married</td>\n",
       "      <td>[0.103893444136]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>children</td>\n",
       "      <td>[0.0181853982481]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>religious</td>\n",
       "      <td>[-0.368506616998]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>educ</td>\n",
       "      <td>[0.00864804494766]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>occ__2.0</td>\n",
       "      <td>[0.298118794658]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>occ__3.0</td>\n",
       "      <td>[0.608150180777]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>occ__4.0</td>\n",
       "      <td>[0.346511273036]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>occ__5.0</td>\n",
       "      <td>[0.942259498161]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>occ__6.0</td>\n",
       "      <td>[0.918150144304]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>occ_husb__2.0</td>\n",
       "      <td>[0.219957140288]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>occ_husb__3.0</td>\n",
       "      <td>[0.32476602929]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>occ_husb__4.0</td>\n",
       "      <td>[0.189354154353]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>occ_husb__5.0</td>\n",
       "      <td>[0.21309298898]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>occ_husb__6.0</td>\n",
       "      <td>[0.214179979671]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         features                coef\n",
       "0   rate_marriage   [-0.697845453825]\n",
       "1             age  [-0.0563368031972]\n",
       "2     yrs_married    [0.103893444136]\n",
       "3        children   [0.0181853982481]\n",
       "4       religious   [-0.368506616998]\n",
       "5            educ  [0.00864804494766]\n",
       "6        occ__2.0    [0.298118794658]\n",
       "7        occ__3.0    [0.608150180777]\n",
       "8        occ__4.0    [0.346511273036]\n",
       "9        occ__5.0    [0.942259498161]\n",
       "10       occ__6.0    [0.918150144304]\n",
       "11  occ_husb__2.0    [0.219957140288]\n",
       "12  occ_husb__3.0     [0.32476602929]\n",
       "13  occ_husb__4.0    [0.189354154353]\n",
       "14  occ_husb__5.0     [0.21309298898]\n",
       "15  occ_husb__6.0    [0.214179979671]"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(zip(affairs_X.columns, np.transpose(model.coef_)), columns = ['features', 'coef'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# compare KNN to LR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.68630248906529234"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn = KNeighborsClassifier(n_neighbors=7)\n",
    "cross_val_score(knn, affairs_X, affairs_y, cv=5, scoring='accuracy').mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.72558005785768587"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg = LogisticRegression()\n",
    "cross_val_score(logreg, affairs_X, affairs_y, cv=5, scoring='accuracy').mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# When we are investigating individual correlations between features and categorical responses\n",
    "# Logistic regression has a good shot :)\n",
    "\n",
    "# KNN relies on the entire n-space to make predictions while LR uses the model parameters to focus\n",
    "# on one or more particular features\n",
    "\n",
    "# LR has concept of \"importance\" of features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Final Thought Experiment\n",
    "\n",
    "# Why might KNN (a kind of look alike model) not perform well here?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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