notebooks/05_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression\n",
    "\n",
    "*Adapted from Chapter 3 of [An Introduction to Statistical Learning](http://www-bcf.usc.edu/~gareth/ISL/)*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 1: Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **Classification problem:** supervised learning problem with a categorical response\n",
    "- **Regression problem**: supervised learning problem with a continuous response\n",
    "- **Linear regression:** machine learning model that can be used for regression problems\n",
    "\n",
    "Why are we learning linear regression?\n",
    "\n",
    "- widely used\n",
    "- runs fast\n",
    "- easy to use (no tuning is required)\n",
    "- highly interpretable\n",
    "- basis for many other methods\n",
    "\n",
    "Lesson goals:\n",
    "\n",
    "- Conceptual understanding of linear regression and how it \"works\"\n",
    "- Familiarity with key terminology\n",
    "- Ability to apply linear regression to a machine learning problem using scikit-learn\n",
    "- Ability to interpret model coefficients\n",
    "- Familiarity with different approaches for feature selection\n",
    "- Understanding of three different evaluation metrics for regression\n",
    "- Understanding of linear regression's strengths and weaknesses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Libraries\n",
    "\n",
    "- [Statsmodels](http://statsmodels.sourceforge.net/): \"statistics in Python\"\n",
    "    - robust functionality for linear modeling\n",
    "    - useful for teaching purposes\n",
    "    - will not be used in the course outside of this lesson\n",
    "- [scikit-learn](http://scikit-learn.org/stable/): \"machine learning in Python\"\n",
    "    - significantly more functionality for general purpose machine learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.cross_validation import cross_val_score\n",
    "from sklearn import metrics\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# visualization\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reading the advertising data"
   ]
  },
  {
   "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>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": 4,
     "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 observations?\n",
    "\n",
    "- Each observation represents **one market** (200 markets in the dataset)\n",
    "\n",
    "What are the features?\n",
    "\n",
    "- **TV:** advertising dollars spent on TV for a single product (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",
    "\n",
    "- **Sales:** sales of a single product in a given market (in thousands of widgets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questions about the data\n",
    "\n",
    "You are asked by the company: On the basis of this data, how should we spend our advertising money in the future?\n",
    "\n",
    "You come up with more specific questions:\n",
    "\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?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use a **scatter plot** to visualize the relationship between the features and the response."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x117dbcbd0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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QZFkc8ZNGfvCKw93922N/XZiLYhCFZtKsvanSPpsAZBnx8y7yLVAtjfzALsBwoxhEoZk0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\nIiKmof8Hij1m1uhKSFMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117dbcc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scatter plot in Seaborn\n",
    "sns.pairplot(data, x_vars=['TV','Radio','Newspaper'], y_vars='Sales', size=6, aspect=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x103ee8650>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AjwJgMkhtTcs6S5WO6c6NrKurI7gUSOC7L15GYrOw8uF9vfjWl7xwOWoPB5Io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\nixm/+jSXCCbSubXyXS4bxga7IIkibGYRY6PaFl3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7T353TNHMGheRN5setMuNtXCdspTB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\nUSlSq/LlF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LsuOplgMP9JNtNCEJwTcU/3EJFQHfHkOM0N4UnFZrW1homIeK2Seh2yexBG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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103ee8690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# include a \"regression line\"\n",
    "sns.pairplot(data, x_vars=['TV','Radio','Newspaper'], y_vars='Sales', size=6, aspect=0.7, kind='reg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11c41a150>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BKaKo8rp+wHJGccAeWiKPWF0MxcrTUC5CQERRo+a206cG0H6b5Dp/+bnAFFFUua0f6Osg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\npFb6f36x8vzBJhabAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c2cf690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scatter plot in Pandas\n",
    "fig, axs = plt.subplots(1, 3, sharey=True)\n",
    "data.plot(kind='scatter', x='TV', y='Sales', ax=axs[0], figsize=(16, 6))\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": [
    "Use a **scatter matrix** to visualize the relationship between all numerical variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x11c270450>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VPDds3+DHGIsA+B6Av+Ccf5sxFuSci4bxDwB8DcBrAOSluQIAZvO13doasKyfVrVF7ZSm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Ti0rz2Pp9LXZ8SQEdB4v88c34fD+ztNn8+pd52pHKWOZ/qTy02+Wg/2i5Dpe3fy9y80pairp8rc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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11be42590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scatter matrix in Seaborn\n",
    "sns.pairplot(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use a **correlation matrix** to visualize the correlation between all numerical variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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>TV</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.054809</td>\n",
       "      <td>0.056648</td>\n",
       "      <td>0.782224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Radio</th>\n",
       "      <td>0.054809</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.354104</td>\n",
       "      <td>0.576223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Newspaper</th>\n",
       "      <td>0.056648</td>\n",
       "      <td>0.354104</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.228299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sales</th>\n",
       "      <td>0.782224</td>\n",
       "      <td>0.576223</td>\n",
       "      <td>0.228299</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 TV     Radio  Newspaper     Sales\n",
       "TV         1.000000  0.054809   0.056648  0.782224\n",
       "Radio      0.054809  1.000000   0.354104  0.576223\n",
       "Newspaper  0.056648  0.354104   1.000000  0.228299\n",
       "Sales      0.782224  0.576223   0.228299  1.000000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute correlation matrix\n",
    "data.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11f575cd0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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m1IqI2Bw4FXhlZu4LPCciXtc3tIqHcCmwHXAacB3wqYrvk6TG9Hq9yksf+wDXAmTmzcDi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\nhxaSCQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f53ead0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# display correlation matrix in Seaborn using a heatmap\n",
    "sns.heatmap(data.corr())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correlation is a quantification of how two variables are related in a *linear* fashion\n",
    "\n",
    "But does NOT reveal if there is any causation between variables\n",
    "\n",
    "In general, machine learning is great at revealing when variables are correlated, but not if there is any causation between them"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 2: Simple linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple linear regression is an approach for predicting a **continuous response** using a **single feature**. It takes the following form:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1x$\n",
    "\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",
    "$\\beta_0$ and $\\beta_1$ are called the **model coefficients**:\n",
    "\n",
    "- We must \"learn\" the values of these coefficients to create our model.\n",
    "- 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",
    "- Coefficients are estimated during the model fitting process using the **least squares criterion**.\n",
    "- We are find the line (mathematically) which minimizes the **sum of squared residuals** (or \"sum of squared errors\")."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Estimating coefficients](images/estimating_coefficients.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this diagram:\n",
    "\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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Slope-intercept](images/slope_intercept.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do the model coefficients relate to the least squares line?\n",
    "\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",
    "\n",
    "Linear Regression is highly **parametric**, meaning that is relies heavily ont he underlying shape of the data. If the data fall into a line, then lienar regression will do well. If the data does not fall in line (get it?) linear regression is likely to fail.\n",
    "\n",
    "\n",
    "Let's estimate the model coefficients for the advertising data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    7.032594\n",
       "TV           0.047537\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### STATSMODELS ###\n",
    "\n",
    "# create a fitted model\n",
    "lm = smf.ols(formula='Sales ~ TV', data=data).fit()\n",
    "\n",
    "# print the coefficients\n",
    "lm.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.03259354913\n",
      "[ 0.04753664]\n"
     ]
    }
   ],
   "source": [
    "### SCIKIT-LEARN ###\n",
    "\n",
    "# create X and y\n",
    "feature_cols = ['TV']\n",
    "X = data[feature_cols]\n",
    "y = data.Sales\n",
    "\n",
    "# instantiate and fit\n",
    "linreg = LinearRegression()\n",
    "linreg.fit(X, y)\n",
    "\n",
    "# print the coefficients\n",
    "print linreg.intercept_\n",
    "print linreg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpreting model coefficients\n",
    "\n",
    "How do we interpret the TV coefficient ($\\beta_1$)?\n",
    "\n",
    "- A \"unit\" increase in TV ad spending is **associated with** a 0.0475 \"unit\" increase in Sales.\n",
    "- Meaning: An additional $1,000 spent on TV ads is **associated with** an increase in sales of 47.5 widgets.\n",
    "- This is not a statement of **causation**.\n",
    "\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": [
    "## 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",
    "$$y = 7.0326 + 0.0475 \\times 50$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.4076"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# manually calculate the prediction\n",
    "7.0326 + 0.0475*50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9.40942557])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### STATSMODELS ###\n",
    "\n",
    "# you have to create a DataFrame since the Statsmodels formula interface expects it\n",
    "X_new = pd.DataFrame({'TV': [50]})\n",
    "\n",
    "# predict for a new observation\n",
    "lm.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9.40942557])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### SCIKIT-LEARN ###\n",
    "\n",
    "# predict for a new observation\n",
    "linreg.predict(50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, we would predict Sales of **9,409 widgets** in that market."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Does the scale of the features matter?\n",
    "\n",
    "Let's say that TV was measured in dollars, rather than thousands of dollars. How would that affect the model?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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",
       "      <th>TV_dollars</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",
       "      <td>230100.0</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",
       "      <td>44500.0</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",
       "      <td>17200.0</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",
       "      <td>151500.0</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",
       "      <td>180800.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  Radio  Newspaper  Sales  TV_dollars\n",
       "1  230.1   37.8       69.2   22.1    230100.0\n",
       "2   44.5   39.3       45.1   10.4     44500.0\n",
       "3   17.2   45.9       69.3    9.3     17200.0\n",
       "4  151.5   41.3       58.5   18.5    151500.0\n",
       "5  180.8   10.8       58.4   12.9    180800.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['TV_dollars'] = data.TV * 1000\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.03259354913\n",
      "[  4.75366404e-05]\n"
     ]
    }
   ],
   "source": [
    "### SCIKIT-LEARN ###\n",
    "\n",
    "# create X and y\n",
    "feature_cols = ['TV_dollars']\n",
    "X = data[feature_cols]\n",
    "y = data.Sales\n",
    "\n",
    "# instantiate and fit\n",
    "linreg = LinearRegression()\n",
    "linreg.fit(X, y)\n",
    "\n",
    "# print the coefficients\n",
    "print linreg.intercept_\n",
    "print linreg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How do we interpret the TV_dollars coefficient ($\\beta_1$)?\n",
    "\n",
    "- A \"unit\" increase in TV ad spending is **associated with** a 0.0000475 \"unit\" increase in Sales.\n",
    "- Meaning: An additional dollar spent on TV ads is **associated with** an increase in sales of 0.0475 widgets.\n",
    "- Meaning: An additional $1,000 spent on TV ads is **associated with** an increase in sales of 47.5 widgets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 9.40942557])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# predict for a new observation\n",
    "linreg.predict(50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scale of the features is **irrelevant** for linear regression models, since it will only affect the scale of the coefficients, and we simply change our interpretation of the coefficients."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 3: A deeper understanding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bias and variance\n",
    "\n",
    "Linear regression is a low variance/high bias model:\n",
    "\n",
    "- **Low variance:** Under repeated sampling from the underlying population, the line will stay roughly in the same place\n",
    "- **High bias:** The line will rarely fit the data well\n",
    "\n",
    "A closely related concept is **confidence intervals**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Confidence intervals\n",
    "\n",
    "Statsmodels calculates 95% confidence intervals for our model coefficients, which are interpreted as follows: If the population from which this sample was drawn was **sampled 100 times**, approximately **95 of those confidence intervals** would contain the \"true\" coefficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>6.129719</td>\n",
       "      <td>7.935468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TV</th>\n",
       "      <td>0.042231</td>\n",
       "      <td>0.052843</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  0         1\n",
       "Intercept  6.129719  7.935468\n",
       "TV         0.042231  0.052843"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### STATSMODELS ###\n",
    "\n",
    "# print the confidence intervals for the model coefficients\n",
    "lm.conf_int()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- We only have a **single sample of data**, and not the **entire population of data**.\n",
    "- The \"true\" coefficient is either within this interval or it isn't, but there's no way to actually know.\n",
    "- We estimate the coefficient with the data we do have, and we show uncertainty about that estimate by giving a range that the coefficient is **probably** within.\n",
    "- From Quora: [What is a confidence interval in layman's terms?](http://www.quora.com/What-is-a-confidence-interval-in-laymans-terms/answer/Michael-Hochster)\n",
    "\n",
    "Note: 95% confidence intervals are just a convention. You can create 90% confidence intervals (which will be more narrow), 99% confidence intervals (which will be wider), or whatever intervals you like.\n",
    "\n",
    "A closely related concept is **hypothesis testing**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis testing and p-values\n",
    "\n",
    "General process for hypothesis testing:\n",
    "\n",
    "- You start with a **null hypothesis** and an **alternative hypothesis** (that is opposite the null).\n",
    "- You check whether the data supports **rejecting the null hypothesis** or **failing to reject the null hypothesis**.\n",
    "\n",
    "For model coefficients, here is the conventional hypothesis test:\n",
    "\n",
    "- **null hypothesis:** There is no relationship between TV ads and Sales (and thus $\\beta_1$ equals zero)\n",
    "- **alternative hypothesis:** There is a relationship between TV ads and Sales (and thus $\\beta_1$ is not equal to zero)\n",
    "\n",
    "How do we test this hypothesis?\n",
    "\n",
    "- The **p-value** is the probability that the relationship we are observing is occurring purely by chance.\n",
    "- If the 95% confidence interval for a coefficient **does not include zero**, the p-value will be **less than 0.05**, and we will reject the null (and thus believe the alternative).\n",
    "- If the 95% confidence interval **includes zero**, the p-value will be **greater than 0.05**, and we will fail to reject the null."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    1.406300e-35\n",
       "TV           1.467390e-42\n",
       "dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### STATSMODELS ###\n",
    "\n",
    "# print the p-values for the model coefficients\n",
    "lm.pvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, a p-value less than 0.05 is one way to decide whether there is **likely** a relationship between the feature and the response. In this case, the p-value for TV is far less than 0.05, and so we **believe** that there is a relationship between TV ads and Sales.\n",
    "\n",
    "Note that we generally ignore the p-value for the intercept."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How well does the model fit the data?\n",
    "\n",
    "R-squared:\n",
    "\n",
    "- A common way to evaluate the overall fit of a linear model\n",
    "- Defined as the **proportion of variance explained**, meaning the proportion of variance in the observed data that is explained by the model\n",
    "- Also defined as the reduction in error over the **null model**, which is the model that simply predicts the mean of the observed response\n",
    "- Between 0 and 1, and higher is better\n",
    "\n",
    "Here's an example of what R-squared \"looks like\":"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![R-squared](images/r_squared.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R-squared value for our simple linear model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61187505085007099"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### STATSMODELS ###\n",
    "\n",
    "# print the R-squared value for the model\n",
    "lm.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61187505085007099"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### SCIKIT-LEARN ###\n",
    "\n",
    "# calculate the R-squared value for the model\n",
    "y_pred = linreg.predict(X)\n",
    "metrics.r2_score(y, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The threshold for a **\"good\" R-squared value** is highly dependent on the particular domain.\n",
    "- R-squared is more useful as a tool for **comparing models**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 4: Multiple Linear Regression\n",
    "\n",
    "Simple linear regression can easily be extended to include multiple features, which is called **multiple linear regression**:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1x_1 + ... + \\beta_nx_n$\n",
    "\n",
    "Each $x$ represents a different feature, and each feature has its own coefficient:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1 \\times TV + \\beta_2 \\times Radio + \\beta_3 \\times Newspaper$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.93888936946\n",
      "[ 0.04576465  0.18853002 -0.00103749]\n"
     ]
    }
   ],
   "source": [
    "### SCIKIT-LEARN ###\n",
    "\n",
    "# create X and y\n",
    "feature_cols = ['TV', 'Radio', 'Newspaper']\n",
    "X = data[feature_cols]\n",
    "y = data.Sales\n",
    "\n",
    "# instantiate and fit\n",
    "linreg = LinearRegression()\n",
    "linreg.fit(X, y)\n",
    "\n",
    "# print the coefficients\n",
    "print linreg.intercept_\n",
    "print linreg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('TV', 0.045764645455397608),\n",
       " ('Radio', 0.18853001691820462),\n",
       " ('Newspaper', -0.0010374930424762972)]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pair the feature names with the coefficients\n",
    "zip(feature_cols, linreg.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a given amount of Radio and Newspaper spending, an increase of $1000 in **TV** spending is associated with an **increase in Sales of 45.8 widgets**.\n",
    "\n",
    "For a given amount of TV and Newspaper spending, an increase of $1000 in **Radio** spending is associated with an **increase in Sales of 188.5 widgets**.\n",
    "\n",
    "For a given amount of TV and Radio spending, an increase of $1000 in **Newspaper** spending is associated with an **decrease in Sales of 1.0 widgets**. How could that be?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature selection\n",
    "\n",
    "How do I decide **which features to include** in a linear model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using p-values\n",
    "\n",
    "We could try a model with all features, and only keep features in the model if they have **small p-values**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept    1.267295e-17\n",
      "TV           1.509960e-81\n",
      "Radio        1.505339e-54\n",
      "Newspaper    8.599151e-01\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "### STATSMODELS ###\n",
    "\n",
    "# create a fitted model with all three features\n",
    "lm = smf.ols(formula='Sales ~ TV + Radio + Newspaper', data=data).fit()\n",
    "\n",
    "# print the p-values for the model coefficients\n",
    "print lm.pvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This indicates we would reject the null hypothesis for **TV and Radio** (that there is no association between those features and Sales), and fail to reject the null hypothesis for **Newspaper**. Thus, we would keep TV and Radio in the model.\n",
    "\n",
    "However, this approach has **drawbacks**:\n",
    "\n",
    "- Linear models rely upon a lot of **assumptions** (such as the features being independent), and if those assumptions are violated (which they usually are), p-values are less reliable.\n",
    "- Using a p-value cutoff of 0.05 means that if you add 100 features to a model that are **pure noise**, 5 of them (on average) will still be counted as significant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using R-squared\n",
    "\n",
    "We could try models with different sets of features, and **compare their R-squared values**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.89719426108289568"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# R-squared value for the model with two features\n",
    "lm = smf.ols(formula='Sales ~ TV + Radio', data=data).fit()\n",
    "lm.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.89721063817895219"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# R-squared value for the model with three features\n",
    "lm = smf.ols(formula='Sales ~ TV + Radio + Newspaper', data=data).fit()\n",
    "lm.rsquared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This would seem to indicate that the best model includes **all three features**. Is that right?\n",
    "\n",
    "- R-squared will always increase as you add more features to the model, even if they are **unrelated** to the response.\n",
    "- As such, using R-squared as a model evaluation metric can lead to **overfitting**.\n",
    "- **Adjusted R-squared** is an alternative that penalizes model complexity (to control for overfitting), but it generally [under-penalizes complexity](http://scott.fortmann-roe.com/docs/MeasuringError.html).\n",
    "\n",
    "As well, R-squared depends on the same assumptions as p-values, and it's less reliable if those assumptions are violated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using train/test split (or cross-validation)\n",
    "\n",
    "A better approach to feature selection!\n",
    "\n",
    "- They attempt to directly estimate how well your model will **generalize** to out-of-sample data.\n",
    "- They rely on **fewer assumptions** that linear regression.\n",
    "- They can easily be applied to **any model**, not just linear models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation metrics for regression problems\n",
    "\n",
    "Evaluation metrics for classification problems, such as **accuracy**, are not useful for regression problems. 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": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# define true and predicted response values\n",
    "y_true = [100, 50, 30, 20]\n",
    "y_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": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n"
     ]
    }
   ],
   "source": [
    "print metrics.mean_absolute_error(y_true, y_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": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "150.0\n"
     ]
    }
   ],
   "source": [
    "print metrics.mean_squared_error(y_true, y_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": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.2474487139\n"
     ]
    }
   ],
   "source": [
    "print np.sqrt(metrics.mean_squared_error(y_true, y_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, which tends to be useful in the real world.\n",
    "- **RMSE** is even more popular than MSE, because RMSE is interpretable in the \"y\" units.\n",
    "\n",
    "All of these are **loss functions**, because we want to minimize them.\n",
    "\n",
    "Here's an additional example, to demonstrate how MSE/RMSE punish larger errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n",
      "20.0\n"
     ]
    }
   ],
   "source": [
    "# same true values as above\n",
    "y_true = [100, 50, 30, 20]\n",
    "\n",
    "# new set of predicted values\n",
    "y_pred = [60, 50, 30, 20]\n",
    "\n",
    "# MAE is the same as before\n",
    "print metrics.mean_absolute_error(y_true, y_pred)\n",
    "\n",
    "# RMSE is larger than before\n",
    "print np.sqrt(metrics.mean_squared_error(y_true, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using train/test split for feature selection\n",
    "\n",
    "Let's use train/test split with RMSE to decide whether Newspaper should be kept in the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# define a function that accepts X and y and computes testing RMSE\n",
    "def cross_val_rmse(X, y):\n",
    "    linreg = LinearRegression()\n",
    "    scores = cross_val_score(linreg, X, y, cv=5, scoring='mean_squared_error')\n",
    "    return np.sqrt(abs(scores)).mean() # return average RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7175247278732086"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# include Newspaper\n",
    "feature_cols = ['TV', 'Radio', 'Newspaper']\n",
    "X = data[feature_cols]\n",
    "cross_val_rmse(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7026625340333177"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# exclude Newspaper BETTER\n",
    "feature_cols = ['TV', 'Radio']\n",
    "X = data[feature_cols]\n",
    "cross_val_rmse(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.2756686834314559"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# only TV, not good enough\n",
    "feature_cols = ['TV']\n",
    "X = data[feature_cols]\n",
    "cross_val_rmse(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing linear regression with other models\n",
    "\n",
    "Advantages of linear regression:\n",
    "\n",
    "- Simple to explain\n",
    "- Highly interpretable\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",
    "\n",
    "Disadvantages of linear regression:\n",
    "\n",
    "- Presumes a linear relationship between the features and the response\n",
    "- Performance is (generally) not competitive with the best supervised learning methods due to high bias\n",
    "- Sensitive to irrelevant features (scaling won't help but feature selection will)\n",
    "- Makes improper predictions (lines are not bound on any side)\n",
    "- Can't automatically learn feature interactions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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