Chapter 3 - Modeling and prediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 3 - Modeling and prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Titanic dataset\n",
    "\n",
    "We use the Pandas library to import the Titanic survival dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PassengerId</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Name</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Ticket</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Embarked</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Braund, Mr. Owen Harris</td>\n",
       "      <td>male</td>\n",
       "      <td>22</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>A/5 21171</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C85</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>female</td>\n",
       "      <td>35</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>113803</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>C123</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>male</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>373450</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   PassengerId  Survived  Pclass  \\\n",
       "0            1         0       3   \n",
       "1            2         1       1   \n",
       "2            3         1       3   \n",
       "3            4         1       1   \n",
       "4            5         0       3   \n",
       "\n",
       "                                                Name     Sex  Age  SibSp  \\\n",
       "0                            Braund, Mr. Owen Harris    male   22      1   \n",
       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female   38      1   \n",
       "2                             Heikkinen, Miss. Laina  female   26      0   \n",
       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female   35      1   \n",
       "4                           Allen, Mr. William Henry    male   35      0   \n",
       "\n",
       "   Parch            Ticket     Fare Cabin Embarked  \n",
       "0      0         A/5 21171   7.2500   NaN        S  \n",
       "1      0          PC 17599  71.2833   C85        C  \n",
       "2      0  STON/O2. 3101282   7.9250   NaN        S  \n",
       "3      0            113803  53.1000  C123        S  \n",
       "4      0            373450   8.0500   NaN        S  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas\n",
    "data = pandas.read_csv(\"data/titanic.csv\")\n",
    "data[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# We make a 80/20% train/test split of the data\n",
    "data_train = data[:int(0.8*len(data))]\n",
    "data_test = data[int(0.8*len(data)):]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preparing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# The categorical-to-numerical function from chapter 2\n",
    "# Changed to automatically add column names\n",
    "def cat_to_num(data):\n",
    "    categories = unique(data)\n",
    "    features = {}\n",
    "    for cat in categories:\n",
    "        binary = (data == cat)\n",
    "        features[\"%s=%s\" % (data.name, cat)] = binary.astype(\"int\")\n",
    "    return pandas.DataFrame(features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def prepare_data(data):\n",
    "    \"\"\"Takes a dataframe of raw data and returns ML model features\n",
    "    \"\"\"\n",
    "    \n",
    "    # Initially, we build a model only on the available numerical values\n",
    "    features = data.drop([\"PassengerId\", \"Survived\", \"Fare\", \"Name\", \"Sex\", \"Ticket\", \"Cabin\", \"Embarked\"], axis=1)\n",
    "    \n",
    "    # Setting missing age values to -1\n",
    "    features[\"Age\"] = data[\"Age\"].fillna(-1)\n",
    "    \n",
    "    # Adding the sqrt of the fare feature\n",
    "    features[\"sqrt_Fare\"] = sqrt(data[\"Fare\"])\n",
    "    \n",
    "    # Adding gender categorical value\n",
    "    features = features.join( cat_to_num(data['Sex']) )\n",
    "    \n",
    "    # Adding Embarked categorical value\n",
    "    features = features.join( cat_to_num(data['Embarked']) )\n",
    "    \n",
    "    return features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building a logistic regression classifier with Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>sqrt_Fare</th>\n",
       "      <th>Sex=female</th>\n",
       "      <th>Sex=male</th>\n",
       "      <th>Embarked=C</th>\n",
       "      <th>Embarked=Q</th>\n",
       "      <th>Embarked=S</th>\n",
       "      <th>Embarked=nan</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>22</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2.692582</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>38</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>8.442944</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>26</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2.815138</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>35</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7.286975</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2.837252</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Pclass  Age  SibSp  Parch  sqrt_Fare  Sex=female  Sex=male  Embarked=C  \\\n",
       "0       3   22      1      0   2.692582           0         1           0   \n",
       "1       1   38      1      0   8.442944           1         0           1   \n",
       "2       3   26      0      0   2.815138           1         0           0   \n",
       "3       1   35      1      0   7.286975           1         0           0   \n",
       "4       3   35      0      0   2.837252           0         1           0   \n",
       "\n",
       "   Embarked=Q  Embarked=S  Embarked=nan  \n",
       "0           0           1             0  \n",
       "1           0           0             0  \n",
       "2           0           1             0  \n",
       "3           0           1             0  \n",
       "4           0           1             0  "
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#cat_to_num(data['Sex'])\n",
    "features = prepare_data(data_train)\n",
    "features[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr',\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "model = LogisticRegression()\n",
    "model.fit(features, data_train[\"Survived\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0,\n",
       "       0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,\n",
       "       0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1,\n",
       "       1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0,\n",
       "       0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,\n",
       "       0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,\n",
       "       0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0,\n",
       "       0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make predictions\n",
    "model.predict(prepare_data(data_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.86033519553072624"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The accuracy of the model on the test data\n",
    "# (this will be introduced in more details in chapter 4)\n",
    "model.score(prepare_data(data_test), data_test[\"Survived\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Non-linear model with Support Vector Machines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0, degree=3, gamma=0.0,\n",
       "  kernel='rbf', max_iter=-1, probability=False, random_state=None,\n",
       "  shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "model = SVC()\n",
    "model.fit(features, data_train[\"Survived\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.86033519553072624"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(prepare_data(data_test), data_test[\"Survived\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classification with multiple classes: hand-written digits\n",
    "\n",
    "We use the popular non-linear multi-class K-nearest neighbor algorithm to predict hand-written digits from the MNIST dataset.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mnist = pandas.read_csv(\"data/mnist_small.csv\")\n",
    "mnist_train = mnist[:int(0.8*len(mnist))]\n",
    "mnist_test = mnist[int(0.8*len(mnist)):]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
       "           metric_params=None, n_neighbors=10, p=2, weights='uniform')"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "knn = KNeighborsClassifier(n_neighbors=10)\n",
    "knn.fit(mnist_train.drop(\"label\", axis=1), mnist_train['label'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Digit 1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Digit 2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Digit 3</th>\n",
       "      <td>0.3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Digit 4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Digit 5</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           0  1  2    3    4  5    6    7    8    9\n",
       "Digit 1  0.0  0  0  0.0  0.0  1  0.0  0.0  0.0  0.0\n",
       "Digit 2  0.0  0  0  1.0  0.0  0  0.0  0.0  0.0  0.0\n",
       "Digit 3  0.3  0  0  0.0  0.0  0  0.6  0.0  0.1  0.0\n",
       "Digit 4  0.0  0  0  0.1  0.0  0  0.0  0.5  0.0  0.4\n",
       "Digit 5  0.0  0  0  0.0  0.7  0  0.0  0.0  0.0  0.3"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = knn.predict_proba(mnist_test.drop(\"label\", axis=1))\n",
    "pandas.DataFrame(preds[:5], index=[\"Digit %d\"%(i+1) for i in range(5)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.81999999999999995"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn.score(mnist_test.drop(\"label\", axis=1), mnist_test['label'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicting numerical values with a regression model\n",
    "\n",
    "We use the the Linear Regression algorithm to predict miles-per-gallon of various automobiles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>modelyear</th>\n",
       "      <th>origin=1</th>\n",
       "      <th>origin=2</th>\n",
       "      <th>origin=3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18</td>\n",
       "      <td>8</td>\n",
       "      <td>307</td>\n",
       "      <td>130</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15</td>\n",
       "      <td>8</td>\n",
       "      <td>350</td>\n",
       "      <td>165</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18</td>\n",
       "      <td>8</td>\n",
       "      <td>318</td>\n",
       "      <td>150</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16</td>\n",
       "      <td>8</td>\n",
       "      <td>304</td>\n",
       "      <td>150</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17</td>\n",
       "      <td>8</td>\n",
       "      <td>302</td>\n",
       "      <td>140</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   mpg  cylinders  displacement  horsepower  weight  acceleration  modelyear  \\\n",
       "0   18          8           307         130    3504          12.0         70   \n",
       "1   15          8           350         165    3693          11.5         70   \n",
       "2   18          8           318         150    3436          11.0         70   \n",
       "3   16          8           304         150    3433          12.0         70   \n",
       "4   17          8           302         140    3449          10.5         70   \n",
       "\n",
       "   origin=1  origin=2  origin=3  \n",
       "0         1         0         0  \n",
       "1         1         0         0  \n",
       "2         1         0         0  \n",
       "3         1         0         0  \n",
       "4         1         0         0  "
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto = pandas.read_csv(\"data/auto-mpg.csv\")\n",
    "\n",
    "# Convert origin to categorical variable\n",
    "auto = auto.join(cat_to_num(auto['origin']))\n",
    "auto = auto.drop('origin', axis=1)\n",
    "\n",
    "# Split in train/test set\n",
    "auto_train = auto[:int(0.8*len(auto))]\n",
    "auto_test = auto[int(0.8*len(auto)):]\n",
    "\n",
    "auto[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "reg = LinearRegression()\n",
    "reg.fit(auto_train.drop('mpg', axis=1), auto_train[\"mpg\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pred_mpg = reg.predict(auto_test.drop('mpg',axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+8YGlvzQiuyo76v0rG9fmLDg0GzPiALYBrRUrM6QdY6hdZ3YtX5G/Ymf+vPyZ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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10938c610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(auto_test.mpg, pred_mpg, 'o')\n",
    "x = linspace(10,40,5)\n",
    "plot(x, x, '-');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}