06_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data science pipeline: pandas, seaborn, scikit-learn\n",
    "*From the video series: [Introduction to machine learning with scikit-learn](https://github.com/justmarkham/scikit-learn-videos)*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Agenda\n",
    "\n",
    "- How do I use the **pandas library** to read data into Python?\n",
    "- How do I use the **seaborn library** to visualize data?\n",
    "- What is **linear regression**, and how does it work?\n",
    "- How do I **train and interpret** a linear regression model in scikit-learn?\n",
    "- What are some **evaluation metrics** for regression problems?\n",
    "- How do I choose **which features to include** in my model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Types of supervised learning\n",
    "\n",
    "- **Classification:** Predict a categorical response\n",
    "- **Regression:** Predict a continuous response"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reading data using pandas\n",
    "\n",
    "**Pandas:** popular Python library for data exploration, manipulation, and analysis\n",
    "\n",
    "- Anaconda users: pandas is already installed\n",
    "- Other users: [installation instructions](http://pandas.pydata.org/pandas-docs/stable/install.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# conventional way to import pandas\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  Radio  Newspaper  Sales\n",
       "1  230.1   37.8       69.2   22.1\n",
       "2   44.5   39.3       45.1   10.4\n",
       "3   17.2   45.9       69.3    9.3\n",
       "4  151.5   41.3       58.5   18.5\n",
       "5  180.8   10.8       58.4   12.9"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read CSV file directly from a URL and save the results\n",
    "data = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)\n",
    "\n",
    "# display the first 5 rows\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primary object types:\n",
    "\n",
    "- **DataFrame:** rows and columns (like a spreadsheet)\n",
    "- **Series:** a single column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>38.2</td>\n",
       "      <td>3.7</td>\n",
       "      <td>13.8</td>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>94.2</td>\n",
       "      <td>4.9</td>\n",
       "      <td>8.1</td>\n",
       "      <td>9.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>177.0</td>\n",
       "      <td>9.3</td>\n",
       "      <td>6.4</td>\n",
       "      <td>12.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>283.6</td>\n",
       "      <td>42.0</td>\n",
       "      <td>66.2</td>\n",
       "      <td>25.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>200</th>\n",
       "      <td>232.1</td>\n",
       "      <td>8.6</td>\n",
       "      <td>8.7</td>\n",
       "      <td>13.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        TV  Radio  Newspaper  Sales\n",
       "196   38.2    3.7       13.8    7.6\n",
       "197   94.2    4.9        8.1    9.7\n",
       "198  177.0    9.3        6.4   12.8\n",
       "199  283.6   42.0       66.2   25.5\n",
       "200  232.1    8.6        8.7   13.4"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display the last 5 rows\n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 4)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check the shape of the DataFrame (rows, columns)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the features?\n",
    "- **TV:** advertising dollars spent on TV for a single product in a given market (in thousands of dollars)\n",
    "- **Radio:** advertising dollars spent on Radio\n",
    "- **Newspaper:** advertising dollars spent on Newspaper\n",
    "\n",
    "What is the response?\n",
    "- **Sales:** sales of a single product in a given market (in thousands of items)\n",
    "\n",
    "What else do we know?\n",
    "- Because the response variable is continuous, this is a **regression** problem.\n",
    "- There are 200 **observations** (represented by the rows), and each observation is a single market."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing data using seaborn\n",
    "\n",
    "**Seaborn:** Python library for statistical data visualization built on top of Matplotlib\n",
    "\n",
    "- Anaconda users: run **`conda install seaborn`** from the command line\n",
    "- Other users: [installation instructions](http://stanford.edu/~mwaskom/software/seaborn/installing.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# conventional way to import seaborn\n",
    "import seaborn as sns\n",
    "\n",
    "# allow plots to appear within the notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0xaaf8fd0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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jq3hpMclgA/CNr+7AE3dvY5KBiCq6KbbqrVAs4vp8DDbBAzsrxCyPxwJRZ2FFAxHVZOWW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CAAAg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\nEBEREREREREt8wfBxGXLfvrNrgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x83f3e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize the relationship between the features and the response using scatterplots\n",
    "sns.pairplot(data, x_vars=['TV','Radio','Newspaper'], y_vars='Sales', size=7, aspect=0.7, kind='reg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear regression\n",
    "\n",
    "**Pros:** fast, no tuning required, highly interpretable, well-understood\n",
    "\n",
    "**Cons:** unlikely to produce the best predictive accuracy (presumes a linear relationship between the features and response)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Form of linear regression\n",
    "\n",
    "$y = \\beta_0 + \\beta_1x_1 + \\beta_2x_2 + ... + \\beta_nx_n$\n",
    "\n",
    "- $y$ is the response\n",
    "- $\\beta_0$ is the intercept\n",
    "- $\\beta_1$ is the coefficient for $x_1$ (the first feature)\n",
    "- $\\beta_n$ is the coefficient for $x_n$ (the nth feature)\n",
    "\n",
    "In this case:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1 \\times TV + \\beta_2 \\times Radio + \\beta_3 \\times Newspaper$\n",
    "\n",
    "The $\\beta$ values are called the **model coefficients**. These values are \"learned\" during the model fitting step using the \"least squares\" criterion. Then, the fitted model can be used to make predictions!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparing X and y using pandas\n",
    "\n",
    "- scikit-learn expects X (feature matrix) and y (response vector) to be NumPy arrays.\n",
    "- However, pandas is built on top of NumPy.\n",
    "- Thus, X can be a pandas DataFrame and y can be a pandas Series!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  Radio  Newspaper\n",
       "1  230.1   37.8       69.2\n",
       "2   44.5   39.3       45.1\n",
       "3   17.2   45.9       69.3\n",
       "4  151.5   41.3       58.5\n",
       "5  180.8   10.8       58.4"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a Python list of feature names\n",
    "feature_cols = ['TV', 'Radio', 'Newspaper']\n",
    "\n",
    "# use the list to select a subset of the original DataFrame\n",
    "X = data[feature_cols]\n",
    "\n",
    "# equivalent command to do this in one line\n",
    "X = data[['TV', 'Radio', 'Newspaper']]\n",
    "\n",
    "# print the first 5 rows\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "(200, 3)\n"
     ]
    }
   ],
   "source": [
    "# check the type and shape of X\n",
    "print(type(X))\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    22.1\n",
       "2    10.4\n",
       "3     9.3\n",
       "4    18.5\n",
       "5    12.9\n",
       "Name: Sales, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# select a Series from the DataFrame\n",
    "y = data['Sales']\n",
    "\n",
    "# equivalent command that works if there are no spaces in the column name\n",
    "y = data.Sales\n",
    "\n",
    "# print the first 5 values\n",
    "y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.series.Series'>\n",
      "(200L,)\n"
     ]
    }
   ],
   "source": [
    "# check the type and shape of y\n",
    "print(type(y))\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting X and y into training and testing sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 3)\n",
      "(150L,)\n",
      "(50, 3)\n",
      "(50L,)\n"
     ]
    }
   ],
   "source": [
    "# default split is 75% for training and 25% for testing\n",
    "print(X_train.shape)\n",
    "print(y_train.shape)\n",
    "print(X_test.shape)\n",
    "print(y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear regression in scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# import model\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# instantiate\n",
    "linreg = LinearRegression()\n",
    "\n",
    "# fit the model to the training data (learn the coefficients)\n",
    "linreg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpreting model coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.87696662232\n",
      "[ 0.04656457  0.17915812  0.00345046]\n"
     ]
    }
   ],
   "source": [
    "# print the intercept and coefficients\n",
    "print(linreg.intercept_)\n",
    "print(linreg.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('TV', 0.046564567874150288),\n",
       " ('Radio', 0.17915812245088836),\n",
       " ('Newspaper', 0.0034504647111804065)]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pair the feature names with the coefficients\n",
    "zip(feature_cols, linreg.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$y = 2.88 + 0.0466 \\times TV + 0.179 \\times Radio + 0.00345 \\times Newspaper$$\n",
    "\n",
    "How do we interpret the **TV coefficient** (0.0466)?\n",
    "\n",
    "- For a given amount of Radio and Newspaper ad spending, **a \"unit\" increase in TV ad spending** is associated with a **0.0466 \"unit\" increase in Sales**.\n",
    "- Or more clearly: For a given amount of Radio and Newspaper ad spending, **an additional $1,000 spent on TV ads** is associated with an **increase in sales of 46.6 items**.\n",
    "\n",
    "Important notes:\n",
    "\n",
    "- This is a statement of **association**, not **causation**.\n",
    "- If an increase in TV ad spending was associated with a **decrease** in sales, $\\beta_1$ would be **negative**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# make predictions on the testing set\n",
    "y_pred = linreg.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need an **evaluation metric** in order to compare our predictions with the actual values!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model evaluation metrics for regression\n",
    "\n",
    "Evaluation metrics for classification problems, such as **accuracy**, are not useful for regression problems. Instead, we need evaluation metrics designed for comparing continuous values.\n",
    "\n",
    "Let's create some example numeric predictions, and calculate **three common evaluation metrics** for regression problems:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# define true and predicted response values\n",
    "true = [100, 50, 30, 20]\n",
    "pred = [90, 50, 50, 30]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mean Absolute Error** (MAE) is the mean of the absolute value of the errors:\n",
    "\n",
    "$$\\frac 1n\\sum_{i=1}^n|y_i-\\hat{y}_i|$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n",
      "10.0\n"
     ]
    }
   ],
   "source": [
    "# calculate MAE by hand\n",
    "print((10 + 0 + 20 + 10)/4.)\n",
    "\n",
    "# calculate MAE using scikit-learn\n",
    "from sklearn import metrics\n",
    "print(metrics.mean_absolute_error(true, pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mean Squared Error** (MSE) is the mean of the squared errors:\n",
    "\n",
    "$$\\frac 1n\\sum_{i=1}^n(y_i-\\hat{y}_i)^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "150.0\n",
      "150.0\n"
     ]
    }
   ],
   "source": [
    "# calculate MSE by hand\n",
    "print((10**2 + 0**2 + 20**2 + 10**2)/4.)\n",
    "\n",
    "# calculate MSE using scikit-learn\n",
    "print(metrics.mean_squared_error(true, pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Root Mean Squared Error** (RMSE) is the square root of the mean of the squared errors:\n",
    "\n",
    "$$\\sqrt{\\frac 1n\\sum_{i=1}^n(y_i-\\hat{y}_i)^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.2474487139\n",
      "12.2474487139\n"
     ]
    }
   ],
   "source": [
    "# calculate RMSE by hand\n",
    "import numpy as np\n",
    "print(np.sqrt((10**2 + 0**2 + 20**2 + 10**2)/4.))\n",
    "\n",
    "# calculate RMSE using scikit-learn\n",
    "print(np.sqrt(metrics.mean_squared_error(true, pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing these metrics:\n",
    "\n",
    "- **MAE** is the easiest to understand, because it's the average error.\n",
    "- **MSE** is more popular than MAE, because MSE \"punishes\" larger errors.\n",
    "- **RMSE** is even more popular than MSE, because RMSE is interpretable in the \"y\" units."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing the RMSE for our Sales predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.40465142303\n"
     ]
    }
   ],
   "source": [
    "print(np.sqrt(metrics.mean_squared_error(y_test, y_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature selection\n",
    "\n",
    "Does **Newspaper** \"belong\" in our model? In other words, does it improve the quality of our predictions?\n",
    "\n",
    "Let's **remove it** from the model and check the RMSE!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.38790346994\n"
     ]
    }
   ],
   "source": [
    "# create a Python list of feature names\n",
    "feature_cols = ['TV', 'Radio']\n",
    "\n",
    "# use the list to select a subset of the original DataFrame\n",
    "X = data[feature_cols]\n",
    "\n",
    "# select a Series from the DataFrame\n",
    "y = data.Sales\n",
    "\n",
    "# split into training and testing sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
    "\n",
    "# fit the model to the training data (learn the coefficients)\n",
    "linreg.fit(X_train, y_train)\n",
    "\n",
    "# make predictions on the testing set\n",
    "y_pred = linreg.predict(X_test)\n",
    "\n",
    "# compute the RMSE of our predictions\n",
    "print(np.sqrt(metrics.mean_squared_error(y_test, y_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The RMSE **decreased** when we removed Newspaper from the model. (Error is something we want to minimize, so **a lower number for RMSE is better**.) Thus, it is unlikely that this feature is useful for predicting Sales, and should be removed from the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resources\n",
    "\n",
    "Linear regression:\n",
    "\n",
    "- [Longer notebook on linear regression](https://github.com/justmarkham/DAT5/blob/master/notebooks/09_linear_regression.ipynb) by me\n",
    "- Chapter 3 of [An Introduction to Statistical Learning](http://www-bcf.usc.edu/~gareth/ISL/) and [related videos](http://www.dataschool.io/15-hours-of-expert-machine-learning-videos/) by Hastie and Tibshirani (Stanford)\n",
    "- [Quick reference guide to applying and interpreting linear regression](http://www.dataschool.io/applying-and-interpreting-linear-regression/) by me\n",
    "- [Introduction to linear regression](http://people.duke.edu/~rnau/regintro.htm) by Robert Nau (Duke)\n",
    "\n",
    "Pandas:\n",
    "\n",
    "- [Three-part pandas tutorial](http://www.gregreda.com/2013/10/26/intro-to-pandas-data-structures/) by Greg Reda\n",
    "- [read_csv](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.read_csv.html) and [read_table](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.read_table.html) documentation\n",
    "\n",
    "Seaborn:\n",
    "\n",
    "- [Official seaborn tutorial](http://web.stanford.edu/~mwaskom/software/seaborn/tutorial.html)\n",
    "- [Example gallery](http://web.stanford.edu/~mwaskom/software/seaborn/examples/index.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comments or Questions?\n",
    "\n",
    "- Email: <kevin@dataschool.io>\n",
    "- Website: http://dataschool.io\n",
    "- Twitter: [@justmarkham](https://twitter.com/justmarkham)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
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   "outputs": [
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