06_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data science pipeline: pandas, seaborn, scikit-learn ([video #6](https://www.youtube.com/watch?v=3ZWuPVWq7p4&list=PL5-da3qGB5ICeMbQuqbbCOQWcS6OYBr5A&index=6))\n",
    "\n",
    "Created by [Data School](https://www.dataschool.io). Watch all 10 videos on [YouTube](https://www.youtube.com/playlist?list=PL5-da3qGB5ICeMbQuqbbCOQWcS6OYBr5A). Download the notebooks from [GitHub](https://github.com/justmarkham/scikit-learn-videos).\n",
    "\n",
    "**Note:** This notebook uses Python 3.9.1 and scikit-learn 0.23.2. The original notebook (shown in the video) used Python 2.7 and scikit-learn 0.16."
   ]
  },
  {
   "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](https://pandas.pydata.org/pandas-docs/stable/getting_started/install.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# added empty cell so that the cell numbering matches the video"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# conventional way to import pandas\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<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 from the 'data' subdirectory using a relative path\n",
    "data = pd.read_csv('data/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": {},
   "outputs": [],
   "source": [
    "# added empty cell so that the cell numbering matches the video"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# display the last 5 rows\n",
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 4)"
      ]
     },
     "execution_count": 6,
     "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://seaborn.pydata.org/installing.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x7fb0288ec550>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1058.4x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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', height=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": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# added empty cell so that the cell numbering matches the video"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# added empty cell so that the cell numbering matches the video"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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": 11,
     "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": 12,
   "metadata": {},
   "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": 13,
   "metadata": {},
   "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": 13,
     "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": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.series.Series'>\n",
      "(200,)\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": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection 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": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 3)\n",
      "(150,)\n",
      "(50, 3)\n",
      "(50,)\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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 17,
     "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": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.8769666223179318\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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('TV', 0.04656456787415029),\n",
       " ('Radio', 0.17915812245088839),\n",
       " ('Newspaper', 0.003450464711180378)]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pair the feature names with the coefficients\n",
    "list(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": 20,
   "metadata": {},
   "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": 21,
   "metadata": {},
   "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": 22,
   "metadata": {},
   "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": 23,
   "metadata": {},
   "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": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.24744871391589\n",
      "12.24744871391589\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": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.404651423032895\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": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3879034699382886\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/DAT4/blob/master/notebooks/08_linear_regression.ipynb) by me\n",
    "- Chapter 3 of [An Introduction to Statistical Learning](https://www.statlearning.com/) and [related videos](https://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](https://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",
    "- [pandas Q&A video series](https://www.dataschool.io/easier-data-analysis-with-pandas/) by me\n",
    "- [Three-part pandas tutorial](http://www.gregreda.com/2013/10/26/intro-to-pandas-data-structures/) by Greg Reda\n",
    "- [read_csv](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.read_csv.html) and [read_table](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.read_table.html) documentation\n",
    "\n",
    "Seaborn:\n",
    "\n",
    "- [Official seaborn tutorial](http://seaborn.pydata.org/tutorial.html)\n",
    "- [Example gallery](http://seaborn.pydata.org/examples/index.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comments or Questions?\n",
    "\n",
    "- Email: <kevin@dataschool.io>\n",
    "- Website: https://www.dataschool.io\n",
    "- Twitter: [@justmarkham](https://twitter.com/justmarkham)"
   ]
  }
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