Supervised Learning -  Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supervised Learning: Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we will be going over linear regression. We'll be going over how to use the scikit-learn regression model, as well as how to train the regressor using the fit() method, and how to predict new labels using the predict() method. We'll be analyzing a data set consisting of house prices in Boston. We'll start off with a single variable linear regression using numpy and then move on to using scikit learn. We'll do an overview of the mathematics behind the method we're using, but mostly we'll dive deeper into pratical \"hands-on\" coding lessons.\n",
    "\n",
    "If you're interested in the deeper mathematics of linear regession methods, check out the [wikipedia page](http://en.wikipedia.org/wiki/Linear_regression) and also check out Andrew Ng's wonderful lectures for free on [youtube](https://www.youtube.com/watch?v=5u4G23_OohI).\n",
    "\n",
    "In this section we will be working through linear regression with the following steps:\n",
    "\n",
    "    Step 1: Getting and setting up the data.\n",
    "    Step 2: Visualizing current data.\n",
    "    Step 3: The mathematics behind the Least Squares Method.\n",
    "    Step 4: Using Numpy for a Univariate Linear Regression.\n",
    "    Step 5: Getting the error.\n",
    "    Step 6: Using scikit learn to implement a multivariate regression.\n",
    "    Step 7: Using Training and Validation.  \n",
    "    Step 8: Predicting Prices\n",
    "    Step 9 : Residual Plots\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1: Getting and setting up the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start by looking a an example of a dataset from scikit-learn. First we'll import our usual data analysis imports, then sklearn's built-in boston dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/bp/opt/miniconda3/envs/udemy/lib/python3.9/site-packages/pandas/core/arrays/masked.py:60: UserWarning: Pandas requires version '1.3.6' or newer of 'bottleneck' (version '1.3.5' currently installed).\n",
      "  from pandas.core import (\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas import Series,DataFrame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imports for plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now import dataset from scikit learn as well as the linear_model module. Note: You may have to run a download, scikit learn will read an error and prompt you to if you don't have the datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# from sklearn.datasets import load_boston # deprecated from v 1.0.0:\n",
    "# https://scikit-learn.org/1.0/modules/generated/sklearn.datasets.load_boston.html?highlight=boston#sklearn.datasets.load_boston\n",
    "data_url = \"http://lib.stat.cmu.edu/datasets/boston\"\n",
    "raw_df = pd.read_csv(data_url, sep=\"\\s+\", skiprows=22, header=None)\n",
    "cols = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV']\n",
    "data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])\n",
    "target = raw_df.values[1::2, 2]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we'll download the data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/q6/kztts0vn7610dqsjfrs11s900000gn/T/ipykernel_15984/2093635263.py:5: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  boston.target = target\n",
      "/var/folders/q6/kztts0vn7610dqsjfrs11s900000gn/T/ipykernel_15984/2093635263.py:6: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  boston.data = data\n"
     ]
    }
   ],
   "source": [
    "# Load the housing dataset\n",
    "# boston = load_boston()\n",
    "# this is ugly but won't work otherwise because the original method returns a custon dataset type\n",
    "boston = DataFrame()\n",
    "boston.target = target\n",
    "boston.data = data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what the data set contains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# print(boston.DESCR)  # deprecated, see in the url the description"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2: Visualizing current data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should always try to do a quick visualization fo the data you have. Let's go ahead an make a histogram of the prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of houses')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram of prices (this is the target of our dataset)\n",
    "plt.hist(boston.target,bins=50)\n",
    "\n",
    "#label\n",
    "plt.xlabel('Price in $1000s')\n",
    "plt.ylabel('Number of houses')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interesting, now let's see a scatter plot of one feature, versus the target. In this case we'll use the housing price versus the number of rooms in the dwelling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Number of rooms')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the column at the 5 index (Labeled RM)\n",
    "plt.scatter(boston.data[:,5],boston.target)\n",
    "\n",
    "#label\n",
    "plt.ylabel('Price in $1000s')\n",
    "plt.xlabel('Number of rooms')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Now we can make out a slight trend that price increases along with the number of rooms in that house, which intuitively makes sense! Now let's use scikit learn to see if we can fit the data linearly.\n",
    "\n",
    "Let's try to do the following:\n",
    "\n",
    "    1.) Use pandas to transform the boston dataset into a DataFrame: \n",
    "    \n",
    "    2.) Then use seaborn to perform an lmplot on that DataFrame to reproduce the scatter plot with a linear fit line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reset data as pandas DataFrame\n",
    "boston_df = DataFrame(data, columns=cols[0:-1])\n",
    "\n",
    "# label columns\n",
    "# boston_df = DataFrame(boston)\n",
    "# boston_df.columns = boston.feature_names\n",
    "\n",
    "#show\n",
    "boston_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's add the target of the boston data set, the price. We'll create a new column in our DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Set price column for target\n",
    "boston_df['Price'] = boston.target"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's see the resultign DataFrame!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>Price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  Price  \n",
       "0     15.3  396.90   4.98   24.0  \n",
       "1     17.8  396.90   9.14   21.6  \n",
       "2     17.8  392.83   4.03   34.7  \n",
       "3     18.7  394.63   2.94   33.4  \n",
       "4     18.7  396.90   5.33   36.2  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Show result\n",
    "boston_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, you might be reminded of the seaborn lmplot function we used during the visualization lectures. You could use it here to do a linear fit automatically!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x2a01bf5b0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Using seabron to create a linear fit\n",
    "sns.lmplot(data=boston_df, x='RM', y='Price',)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, we won't be able to do this when we move to more complicated regression models, so we'll stay focused on using the scikit learn library!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3: The mathematics behind the Least Squares Method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this particular lecture we'll use the least squares method as the way to estimate the coefficients. Here's a quick breakdown of how this method works mathematically:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take a quick look at the plot we created above using seaborn. Now consider each point, and know that they each have a coordinate in the form (X,Y). Now draw an imaginary line between each point and our current \"best-fit\" line. We'll call the distanace between each point and our current best-fit line, D. To get a quick image of what we're currently trying to visualize, take a look at the picture below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Quick display of image form wikipedia\n",
    "from IPython.display import Image\n",
    "url = 'http://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Linear_least_squares_example2.svg/220px-Linear_least_squares_example2.svg.png'\n",
    "Image(url)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now as before, we're labeling each green line as having a distance D, and each red point as having a coordinate of (X,Y). Then we can define our best fit line as the line having the property were:\n",
    "$$ D_{1}^2 + D_{2}^2 + D_{3}^2 + D_{4}^2 + ....+ D_{N}^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So how do we find this line? The least-square line approximating the set of points:\n",
    "\n",
    "$$ (X,Y)_{1},(X,Y)_{2},(X,Y)_{3},(X,Y)_{4},(X,Y)_{5}, $$\n",
    "\n",
    "has the equation:\n",
    "$$ Y = a_{0} +a_{1}X $$\n",
    "this is basically just a rewritten form of the standard equation for a line:\n",
    "$$Y=mx+b$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can solve for these constants a0 and a1 by simultaneously solving these equations:\n",
    "$$ \\Sigma Y = a_{0}N + a_{1}\\Sigma X $$\n",
    "$$ \\Sigma XY = a_{0}\\Sigma X + a_{1}\\Sigma X^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are called the normal equations for the least squares line. There are further steps that can be taken in rearranging these equations  to solve for y, but we'll let scikit-learn do the rest of the heavy lifting here. If you want further informatino on the mathematics of the above formulas, check out this great [video](https://www.youtube.com/watch?v=Qa2APhWjQPc).\n",
    "\n",
    "For now, we'll use numpy to do a simple single variable linear regression. Afterwards we'll unleash the power of scikit learn to do a full multivariate linear regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4: Using Numpy for a Univariate Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numpy has a built in Least Square Method in its linear algebra library. We'll use this first for our Univariate regression and then move on to scikit learn for out Multi variate regression.\n",
    "\n",
    "We will start by setting up the X and Y arrays for numpy to take in. An important note for the X array: Numpy expects a two-dimensional array, the first dimension is the different example values, and the second dimension is the attribute number. In this case we have our value as the mean number of rooms per house, and this is a single attribute, but we need to consider the bias term (`b`). So we need to append an array of `\"1\"` to the feature array. We'll do this by creating a matrix in the form [X 1]\n",
    "\n",
    "See also [here](https://numpy.org/doc/stable/reference/generated/numpy.linalg.lstsq.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Set up X as median room values, but it needs to have the \"1\" array appended\n",
    "X = np.vstack([boston_df.RM, np.ones(len(boston_df.RM))]).T\n",
    "\n",
    "# Set up Y as the target price of the houses.\n",
    "Y = boston_df.Price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have our X and Y, let's go ahead and use numpy to create the single variable linear regression.\n",
    "\n",
    "We know that a line has the equation:\n",
    "$$y=mx+b$$\n",
    "which we can rewrite using matrices:\n",
    "$$y=Ap$$\n",
    "where:\n",
    "$$A = \\begin{bmatrix}x & 1\\end{bmatrix}$$\n",
    "and\n",
    "$$p= \\begin{bmatrix}m \\\\b\\end{bmatrix}$$\n",
    "\n",
    "This is the same as the first equation if you carry out the linear algebra. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Now we can get the best fit values!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Now get out m and b values for our best fit line\n",
    "m, b = np.linalg.lstsq(X, Y, rcond=None)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally let's plot it all together! Note that we use the original format of the boston information. We only did our matrix transformations to utilize the numpy least square method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2a00894c0>]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# First the original points, Price vs Avg Number of Rooms\n",
    "plt.plot(boston_df.RM,boston_df.Price,'o')\n",
    "\n",
    "# Next the best fit line\n",
    "x = boston_df.RM\n",
    "plt.plot(x, m*x + b, 'r', label='Best Fit Line')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 5: Getting the error "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Great! We've just completed a single variable regression using the least squares method with Python! Let's see if we can find the error in our fitted line. Checking out the documentation [here](http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html), we see that the resulting array has the total squared error. For each element, it checks the the difference between the line and the true value (our original D value), squares it, and returns the sum of all these. This was the summed D^2 value we discussed earlier. \n",
    "\n",
    "It's probably easier to understand the root mean squared error, which is similar to the standard deviation. In this case, to find the root mean square error we divide by the number of elements and then take the square root. There is also an issue of bias and an unbiased regression, but we'll delve into those topics later.\n",
    "\n",
    "For now let's see how we can get the root mean squared error of the line we just fitted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The root mean squared error was 6.60 k$\n"
     ]
    }
   ],
   "source": [
    "# Get the resulting array\n",
    "result = np.linalg.lstsq(X,Y, rcond=None)\n",
    "\n",
    "# Get the total error\n",
    "error_total = result[1]\n",
    "result\n",
    "\n",
    "# Get the root mean square error\n",
    "rmse = np.sqrt(error_total[0]/len(X)) # note this is\n",
    "\n",
    "# Print\n",
    "print(\"The root mean squared error was %.2f k$\" %rmse)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the root mean square error (RMSE) corresponds approximately to the standard deviation we can now say that the price of a house won't vary more than 2 times the RMSE 95% of the time. Note: Review the Normal Distribution Appendix lecture if this doesn't make sense to you or check out this [link](http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule).\n",
    "\n",
    "Thus we can reasonably expect a house price to be within $13,200 of our line fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 6: Using scikit learn to implement a multivariate regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we'll keep moving along with using scikit learn to do a multi variable regression. This will be a similar apporach to the above example, but sci kit learn will be able to take into account more than just a single data variable effecting the target!\n",
    "\n",
    "We'll start by importing the [linear regression library](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html) from the sklearn module.\n",
    "\n",
    "The sklearn.linear_model.LinearRegression class is an estimator. Estimators predict a value based on the observed data. In scikit-learn, all estimators implement the fit() and predict() methods. The former method is used to learn the parameters of a model, and the latter method is used to predict the value of a response variable for an explanatory variable using the learned parameters. It is easy to experiment with different models using scikit-learn because all estimators implement the fit and predict methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Import for Linear Regression\n",
    "import sklearn\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we create a LinearRegression object, afterwards, type lm. then press tab to see the list of methods availble on this object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create a LinearRegression Object\n",
    "lreg = LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The functions we will be using are:\n",
    "\n",
    "lreg.fit() which fits a linear model\n",
    "\n",
    "lreg.predict() which is used to predict Y using the linear model with estimated coefficients\n",
    "\n",
    "lreg.score() which returns the coefficient of determination (R^2). A measure of how well observed outcomes are replicated by the model, learn more about it [here](http://en.wikipedia.org/wiki/Coefficient_of_determination)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We'll start the multi variable regression analysis by seperating our boston dataframe into the data columns and the target columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Data Columns\n",
    "X_multi = boston_df.drop(columns='Price')\n",
    "\n",
    "# Targets\n",
    "Y_target = boston_df.Price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we're ready to pass the X and Y using the linear regression object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Implement Linear Regression\n",
    "lreg.fit(X_multi,Y_target)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Let's go ahead check the intercept and number of coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " The estimated intercept coefficient is 36.46 \n"
     ]
    }
   ],
   "source": [
    "print(' The estimated intercept coefficient is %.2f ' %lreg.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " The number of coefficients used was 13 \n"
     ]
    }
   ],
   "source": [
    "print(' The number of coefficients used was %d ' % len(lreg.coef_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! So we have basically made an equation for a line, but instead of just oneo coefficient m and an intercept b, we now have 13 coefficients. To get an idea of what this looks like check out the [documentation](http://scikit-learn.org/stable/modules/linear_model.html) for this equation:\n",
    "$$ y(w,x) = w_0 + w_1 x_1 + ... + w_p x_p $$\n",
    "\n",
    "Where $$w = (w_1, ...w_p)$$ as the coefficients and $$ w_0 $$ as the intercept "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What we'll do next is set up a DataFrame showing all the Features and their estimated coefficients obtained form the linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "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>Features</th>\n",
       "      <th>Coefficient Estimate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>CRIM</td>\n",
       "      <td>-0.108011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ZN</td>\n",
       "      <td>0.046420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>INDUS</td>\n",
       "      <td>0.020559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>CHAS</td>\n",
       "      <td>2.686734</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NOX</td>\n",
       "      <td>-17.766611</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>RM</td>\n",
       "      <td>3.809865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>AGE</td>\n",
       "      <td>0.000692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>DIS</td>\n",
       "      <td>-1.475567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>RAD</td>\n",
       "      <td>0.306049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>TAX</td>\n",
       "      <td>-0.012335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>PTRATIO</td>\n",
       "      <td>-0.952747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>B</td>\n",
       "      <td>0.009312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>LSTAT</td>\n",
       "      <td>-0.524758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Price</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Features  Coefficient Estimate\n",
       "0      CRIM             -0.108011\n",
       "1        ZN              0.046420\n",
       "2     INDUS              0.020559\n",
       "3      CHAS              2.686734\n",
       "4       NOX            -17.766611\n",
       "5        RM              3.809865\n",
       "6       AGE              0.000692\n",
       "7       DIS             -1.475567\n",
       "8       RAD              0.306049\n",
       "9       TAX             -0.012335\n",
       "10  PTRATIO             -0.952747\n",
       "11        B              0.009312\n",
       "12    LSTAT             -0.524758\n",
       "13    Price                   NaN"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set a DataFrame from the Features\n",
    "coeff_df = DataFrame(boston_df.columns)\n",
    "coeff_df.columns = ['Features']\n",
    "\n",
    "# Set a new column lining up the coefficients from the linear regression\n",
    "coeff_df[\"Coefficient Estimate\"] = pd.Series(lreg.coef_)\n",
    "\n",
    "# Show\n",
    "coeff_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like we initially plotted out, it seems the highest correlation between a feature and a house price was the number of rooms.\n",
    "\n",
    "Now let's move on to Predicting prices!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 7: Using Training and Validation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a dataset a training set is implemented to build up a model, while a validation set is used to validate the model built. Data points in the training set are excluded from the validation set. The correct way to pick out samples from your dataset to be part either the training or validation (also called test) set is *randomly*.\n",
    "\n",
    "Fortunately, scikit learn has a built in function specifically for this called train_test_split.\n",
    "\n",
    "The parameters passed are your X and Y, then optionally test_size parameter, representing the proportion of the dataset to include in the test split. As well a train_size parameter. ou can learn more about these parameters [here](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Grab the output and set as X and Y test and train data sets!\n",
    "X_train, X_test, Y_train, Y_test = sklearn.model_selection.train_test_split(X,boston_df.Price)\n",
    "\n",
    "# About 75% of observations are going into the training dataset, as per documentation default value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's go ahead and see what the output of the train_test_split was:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(379, 2) (127, 2) (379,) (127,)\n"
     ]
    }
   ],
   "source": [
    "# Print shapes of the training and testing data sets\n",
    "print(X_train.shape, X_test.shape, Y_train.shape, Y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Now that we have our training and testing sets we can continue on to predicint gprices based on the multiple variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 8: Predicting Prices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have our training and testing sets, let's go ahead and try to use them to predict house prices. We'll use our training set for the prediction and then use our testing set for validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create our regression object\n",
    "lreg = LinearRegression()\n",
    "\n",
    "# Once again do a linear regression, except only on the training sets this time\n",
    "lreg.fit(X_train,Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now run a prediction on both the X training set and the testing set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Predictions on training and testing sets\n",
    "pred_train = lreg.predict(X_train)\n",
    "pred_test = lreg.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will get the mean square error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit a model X_train, and calculate MSE with Y_train: 44.50\n",
      "Fit a model X_train, and calculate MSE with X_test and Y_test: 41.05\n"
     ]
    }
   ],
   "source": [
    "print(\"Fit a model X_train, and calculate MSE with Y_train: %.2f\"  % np.mean((Y_train - pred_train) ** 2))\n",
    "\n",
    "print(\"Fit a model X_train, and calculate MSE with X_test and Y_test: %.2f\"  %np.mean((Y_test - pred_test) ** 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like our mean square error between our training and testing was pretty close. But how do we actually visualize this?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 9 : Residual Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In regression analysis, the difference between the observed value of the dependent variable (y) and the predicted value (ŷ) is called the residual (e). Each data point has one residual, so that:\n",
    "\n",
    "$$Residual = Observed\\:value - Predicted\\:value $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can think of these residuals in the same way as the D value we discussed earlier, in this case however, there were multiple data points considered."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.\n",
    "\n",
    "Residual plots are a good way to visualize the errors in your data.  If you have done a good job then your data should be randomly scattered around line zero. If there is some strucutre or pattern, that means your model is not capturing some thing. There could be an interaction between 2 variables that you're not considering, or may be you are measuring time dependent data. If this is the case go back to your model and check your data set closely.\n",
    "\n",
    "So now let's go ahead and create the residual plot. For more info on the residual plots check out this great [link](http://blog.minitab.com/blog/adventures-in-statistics/why-you-need-to-check-your-residual-plots-for-regression-analysis)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Residual Plots')"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot the training data\n",
    "train = plt.scatter(pred_train,(Y_train-pred_train),c='b',alpha=0.5)\n",
    "\n",
    "# Scatter plot the testing data\n",
    "test = plt.scatter(pred_test,(Y_test-pred_test),c='r',alpha=0.5)\n",
    "\n",
    "# Plot a horizontal axis line at 0\n",
    "plt.hlines(y=0,xmin=-10,xmax=50)\n",
    "\n",
    "#Labels\n",
    "plt.legend((train,test),('Training','Test'),loc='lower left')\n",
    "plt.title('Residual Plots')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! Looks like there aren't any major patterns to be concerned about, it may be interesting to check out the line occuring towards the bottom right, but overall the majority of the residuals seem to be randomly allocated above and below the horizontal. We could also use seaborn to create these plots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='RM', ylabel='Price'>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Residual plot of all the dataset using seaborn\n",
    "sns.residplot(x='RM', y='Price', data=boston_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's it for this lesson. Linear regression is a very broad topic, theres a ton of great information in the sci kit learn documentation, and I encourage you to check it out here:  http://scikit-learn.org/stable/modules/linear_model.html#linear-model"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}