LinearRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Linear Regression\n",
    "\n",
    "*Adapted from a tutorial by Kevin Markham (http://www.dataschool.io/linear-regression-in-python/)*, who \n",
    "*Adapted from Chapter 3 of [An Introduction to Statistical Learning](http://www-bcf.usc.edu/~gareth/ISL/)*\n",
    "\n",
    "||continuous|categorical|\n",
    "|---|---|---|\n",
    "|**supervised**|**regression**|classification|\n",
    "|**unsupervised**|dimension reduction|clustering|\n",
    "\n",
    "## Motivation\n",
    "\n",
    "Why are we learning linear regression?\n",
    "- widely used\n",
    "- runs fast\n",
    "- easy to use (not a lot of tuning required)\n",
    "- highly interpretable\n",
    "- basis for many other methods\n",
    "\n",
    "## Libraries\n",
    "\n",
    "Will be using [Statsmodels](http://statsmodels.sourceforge.net/) for **teaching purposes** since it has some nice characteristics for linear modeling. However, we recommend that you spend most of your energy on [scikit-learn](http://scikit-learn.org/stable/) since it provides significantly more useful functionality for machine learning in general."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# imports\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# this allows plots to appear directly in the notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Advertising Data\n",
    "\n",
    "Let's take a look at some data, ask some questions about that data, and then use linear regression to answer those questions!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>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": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read data into a DataFrame\n",
    "data = pd.read_csv('http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv', index_col=0)\n",
    "data.head()"
   ]
  },
  {
   "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 widgets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 4)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# print the shape of the DataFrame\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 200 **observations**, and thus 200 markets in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x113767810>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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hhBCSPkHHyDalC+MoCMljGJp0dhCa9Bqwx9AkT6ToDSmmiRBtdM2bU/QF7WnqWh0hJAVc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\nioiIiIiISKdoQ1ZEREREREQ65f8D5YYB7rrX9EYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fb3b250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize the relationship between the features and the response using scatterplots\n",
    "fig, axs = plt.subplots(1, 3, sharey=True)\n",
    "data.plot(kind='scatter', x='TV', y='Sales', ax=axs[0], figsize=(16, 8))\n",
    "data.plot(kind='scatter', x='Radio', y='Sales', ax=axs[1])\n",
    "data.plot(kind='scatter', x='Newspaper', y='Sales', ax=axs[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions About the Advertising Data\n",
    "\n",
    "Let's pretend you work for the company that manufactures and markets this widget. The company might ask you the following: On the basis of this data, how should we spend our advertising money in the future?\n",
    "\n",
    "This general question might lead you to more specific questions:\n",
    "1. Is there a relationship between ads and sales?\n",
    "2. How strong is that relationship?\n",
    "3. Which ad types contribute to sales?\n",
    "4. What is the effect of each ad type of sales?\n",
    "5. Given ad spending in a particular market, can sales be predicted?\n",
    "\n",
    "We will explore these questions below!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple Linear Regression\n",
    "\n",
    "Simple linear regression is an approach for predicting a **quantitative response** using a **single feature** (or \"predictor\" or \"input variable\"). It takes the following form:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1x$\n",
    "\n",
    "What does each term represent?\n",
    "- $y$ is the response\n",
    "- $x$ is the feature\n",
    "- $\\beta_0$ is the intercept\n",
    "- $\\beta_1$ is the coefficient for x\n",
    "\n",
    "Together, $\\beta_0$ and $\\beta_1$ are called the **model coefficients**. To create your model, you must \"learn\" the values of these coefficients. And once we've learned these coefficients, we can use the model to predict Sales!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating (\"Learning\") Model Coefficients\n",
    "\n",
    "Generally speaking, coefficients are estimated using the **least squares criterion**, which means we are find the line (mathematically) which minimizes the **sum of squared residuals** (or \"sum of squared errors\"):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"08_estimating_coefficients.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What elements are present in the diagram?\n",
    "- The black dots are the **observed values** of x and y.\n",
    "- The blue line is our **least squares line**.\n",
    "- The red lines are the **residuals**, which are the distances between the observed values and the least squares line.\n",
    "\n",
    "How do the model coefficients relate to the least squares line?\n",
    "- $\\beta_0$ is the **intercept** (the value of $y$ when $x$=0)\n",
    "- $\\beta_1$ is the **slope** (the change in $y$ divided by change in $x$)\n",
    "\n",
    "Here is a graphical depiction of those calculations:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"08_slope_intercept.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use **Statsmodels** to estimate the model coefficients for the advertising data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    7.032594\n",
       "TV           0.047537\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this is the standard import if you're using \"formula notation\" (similar to R)\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# create a fitted model in one line\n",
    "lm = smf.ols(formula='Sales ~ TV', data=data).fit()\n",
    "\n",
    "# print the coefficients\n",
    "lm.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting Model Coefficients\n",
    "\n",
    "How do we interpret the TV coefficient ($\\beta_1$)?\n",
    "- A \"unit\" increase in TV ad spending is **associated with** a 0.047537 \"unit\" increase in Sales.\n",
    "- Or more clearly: An additional $1,000 spent on TV ads is **associated with** an increase in sales of 47.537 widgets.\n",
    "\n",
    "Note that if an increase in TV ad spending was associated with a **decrease** in sales, $\\beta_1$ would be **negative**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the Model for Prediction\n",
    "\n",
    "Let's say that there was a new market where the TV advertising spend was **$50,000**. What would we predict for the Sales in that market?\n",
    "\n",
    "$$y = \\beta_0 + \\beta_1x$$\n",
    "$$y = 7.032594 + 0.047537 \\times 50$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.409444"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# manually calculate the prediction\n",
    "7.032594 + 0.047537*50"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, we would predict Sales of **9,409 widgets** in that market.\n",
    "\n",
    "Of course, we can also use Statsmodels to make the prediction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>TV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td> 50</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   TV\n",
       "0  50"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# you have to create a DataFrame since the Statsmodels formula interface expects it\n",
    "X_new = pd.DataFrame({'TV': [50]})\n",
    "X_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9.40942557])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use the model to make predictions on a new value\n",
    "lm.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the Least Squares Line\n",
    "\n",
    "Let's make predictions for the **smallest and largest observed values of x**, and then use the predicted values to plot the least squares line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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>TV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>   0.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td> 296.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV\n",
       "0    0.7\n",
       "1  296.4"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a DataFrame with the minimum and maximum values of TV\n",
    "X_new = pd.DataFrame({'TV': [data.TV.min(), data.TV.max()]})\n",
    "X_new.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  7.0658692 ,  21.12245377])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# make predictions for those x values and store them\n",
    "preds = lm.predict(X_new)\n",
    "preds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x14625128>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bbz+5erd+0o/7k7TFUz6rpbz84IIER5M769raWut+eRu+/myCykEZhKBiTD0p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\ntmnTZsaPn8yxx1YyYcL33fk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      "text/plain": [
       "<matplotlib.figure.Figure at 0xbf92b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# first, plot the observed data\n",
    "data.plot(kind='scatter', x='TV', y='Sales')\n",
    "\n",
    "# then, plot the least squares line\n",
    "plt.plot(X_new, preds, c='red', linewidth=2)"
   ]
  }
 ],
 "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
}