Model-Development.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Model Development</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Lets develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>We often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n",
    "\n",
    "<p>A Model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "path = 'https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "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>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# path of data \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Linear Regression and Multiple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Linear Regression</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>One example of a Data  Model that we will be using is</p>\n",
    "<b>Simple Linear Regression</b>.\n",
    "\n",
    "<br>\n",
    "<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
    "<ul>\n",
    "    <li>The predictor/independent variable (X)</li>\n",
    "    <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
    "</ul>\n",
    "\n",
    "<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    " Y: Response \\ Variable\\\\\n",
    " X: Predictor \\ Variables\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <b>Linear function:</b>\n",
    "$$\n",
    "Yhat = a + b  X\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li>a refers to the <b>intercept</b> of the regression line, in other words: the value of Y when X is 0</li>\n",
    "    <li>b refers to the <b>slope</b> of the regression line, in other words: the value with which Y changes when X increases by 1 unit</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Lets load the modules for linear regression\n",
    "from sklearn.linear_model import LinearRegression\n",
    "#Create the linear regression object\n",
    "lm = LinearRegression()\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets create a linear function with \"highway-mpg\" as the predictor variable and the \"price\" as the response variable to see whether highway-mpg would help us to predict the car price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df[['highway-mpg']]\n",
    "Y = df['price']\n",
    "#Fit the linear model using highway-mpg\n",
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can output a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
       "       20345.17153508])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "Yhat[0:5]   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Lets get the value of intercept (a) and Slope (b)</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "38423.305858157386\n",
      "[-821.73337832]\n"
     ]
    }
   ],
   "source": [
    "print(lm.intercept_)\n",
    "print(lm.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plugging in the actual values we get:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>price</b> = 38423.31 - 821.73 x  <b>highway-mpg</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets create a linear function with \"engine-size\" as the predictor variable and the \"price\" as the response variable to see whether engine-size would help us to predict the car price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm1 = LinearRegression()\n",
    "X = df[['engine-size']]\n",
    "Y = df['price']\n",
    "lm1.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Yhat=lm1.predict(X)\n",
    "Yhat[0:5]   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-7963.338906281049\n",
      "[166.86001569]\n"
     ]
    }
   ],
   "source": [
    "print(lm1.intercept_)\n",
    "print(lm1.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plugging in the values ,we get\n",
    "\n",
    "<b>price</b> = -7963.338906281049 + 166.86001569 x <b>engine-size</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Multiple Linear Regression</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>This method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\n",
    "Most of the real-world regression models involve multiple predictors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Y: Response \\ Variable\\\\\n",
    "X_1 :Predictor\\ Variable \\ 1\\\\\n",
    "X_2: Predictor\\ Variable \\ 2\\\\\n",
    "X_3: Predictor\\ Variable \\ 3\\\\\n",
    "X_4: Predictor\\ Variable \\ 4\\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "a: intercept\\\\\n",
    "b_1 :coefficients \\ of\\ Variable \\ 1\\\\\n",
    "b_2: coefficients \\ of\\ Variable \\ 2\\\\\n",
    "b_3: coefficients \\ of\\ Variable \\ 3\\\\\n",
    "b_4: coefficients \\ of\\ Variable \\ 4\\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equation is given by"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>From the previous section  we know that other good predictors of price could be:</p>\n",
    "<ul>\n",
    "    <li>Horsepower</li>\n",
    "    <li>Curb-weight</li>\n",
    "    <li>Engine-size</li>\n",
    "    <li>Highway-mpg</li>\n",
    "</ul>\n",
    "Let's develop a model using these variables as the predictor variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\n",
    "#Fit the linear model\n",
    "lm.fit(Z, df['price'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-15806.624626329198\n",
      "[53.49574423  4.70770099 81.53026382 36.05748882]\n"
     ]
    }
   ],
   "source": [
    "print(lm.intercept_)\n",
    "print(lm.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Price</b> = -15678.742628061467 + 52.65851272 x <b>horsepower</b> + 4.69878948 x <b>curb-weight</b> + 81.95906216 x <b>engine-size</b> + 33.58258185 x <b>highway-mpg</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>  Model Evaluation using Visualization</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To evaluate our models and to choose the best one? One way to do this is by using visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import the visualization package: seaborn\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Regression Plot</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n",
    "\n",
    "<p>This plot will show a combination of a scattered data points (a <b>scatter plot</b>), as well as the fitted <b>linear regression</b> line going through the data. This will give us a reasonable estimate of the relationship between the two variables, the strength of the correlation, as well as the direction (positive or negative correlation).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's visualize Horsepower as potential predictor variable of price:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 49561.33945258835)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width=12\n",
    "height=10\n",
    "plt.figure(figsize = (width,height))\n",
    "sns.regplot(x='horsepower',y='price',data=df)\n",
    "plt.ylim(0,)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see from this plot that <b>price is negatively correlated to highway-mpg, since the regression slope is negative</b>\n",
    "One thing to keep in mind when looking at a regression plot is to pay attention to how scattered the data points are around the regression line. This will give you a good indication of the variance of the data, and whether a linear model would be the best fit or not. If the data is too far off from the line, this linear model might not be the best model for this data. \n",
    "    \n",
    "<p>Let's compare this plot to the regression plot of \"peak-rpm\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 47422.919330307624)"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(width, height))\n",
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\" we see that the points for \"highway-mpg\" are much closer to the generated line and on the average decrease. The points for \"peak-rpm\" have more spread around the predicted line, and it is much harder to determine if the points are decreasing or increasing as the \"highway-mpg\" increases.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "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>peak-rpm</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>-0.058598</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             peak-rpm  highway-mpg     price\n",
       "peak-rpm     1.000000    -0.058598 -0.101616\n",
       "highway-mpg -0.058598     1.000000 -0.704692\n",
       "price       -0.101616    -0.704692  1.000000"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " df[['peak-rpm','highway-mpg','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable \"peak-rpm\" has a stronger correlation with \"price\", it is approximate -0.704692  compared to   \"highway-mpg\" which is approximate -0.101616."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Residual Plot</h3>\n",
    "\n",
    "<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n",
    "\n",
    "<p><b>Residual</b> : The difference between the observed value (y) and the predicted value. It is the distance from the data point to the fitted regression line. (Yhat) is called the residual</p>\n",
    "\n",
    "<p><b>Residual plot</b> : It is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
    "<p>We should always look at the spread of the residuals:</p>\n",
    "\n",
    "<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data ( Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 33129.935334087364)"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width,height))\n",
    "sns.residplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see from this residual plot - residuals are not randomly spread around the x-axis,thus a non-linear model is more appropriate for this data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Visualizing a model for Multiple Linear Regression<p>\n",
    "<p><b> Distribution plot</b> : Compare the distribution of the fitted values that result from the model and distribution of the actual values.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Yhat = lm.predict(Z)\n",
    "plt.figure(figsize=(width,height))\n",
    "ax1=sns.distplot(df['price'],hist=False,color=\"r\",label=\"Actual Values\")\n",
    "sns.distplot(Yhat,hist=False,color=\"b\",label=\"Fitted Values\",ax=ax1)\n",
    "\n",
    "plt.title(\"Actual vs Fitted Values for Price\")\n",
    "plt.xlabel(\"Price (in dollars)\")\n",
    "plt.ylabel(\"Proportion of Cars\")\n",
    "\n",
    "plt.show()\n",
    "plt.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see that the fitted values are reasonably close to the actual values, since the two distributions overlap a bit. However, there is definitely some room for improvement.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Polynomial Regression and Pipelines</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Polynomial regression</b> is a particular case of the general linear regression model or multiple linear regression models.\n",
    "<p>We get non-linear relationships by squaring or setting higher-order terms of the predictor variables.\n",
    "<p>There are different orders of polynomial regression:</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><b>Quadratic - 2nd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X^2 +b_2 X^2 \n",
    "$$\n",
    "\n",
    "\n",
    "<center><b>Cubic - 3rd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X^2 +b_2 X^2 +b_3 X^3\\\\\n",
    "$$\n",
    "\n",
    "\n",
    "<center><b>Higher order</b>:</center>\n",
    "$$\n",
    "Y = a + b_1 X^2 +b_2 X^2 +b_3 X^3 ....\\\\\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>A linear model did not provide the best fit while using highway-mpg as the predictor variable. Let's see if we can try fitting a polynomial model to the data instead.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#We will use the following function to plot the data:\n",
    "def PlotPolly(model, independent_variable, dependent_variabble, Name):\n",
    "    x_new = np.linspace(15, 55, 100)\n",
    "    y_new = model(x_new)\n",
    "\n",
    "    plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n",
    "    plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n",
    "    ax = plt.gca()\n",
    "    ax.set_facecolor((0.898, 0.898, 0.898))\n",
    "    fig = plt.gcf()\n",
    "    plt.xlabel(Name)\n",
    "    plt.ylabel('Price of Cars')\n",
    "\n",
    "    plt.show()\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        3         2\n",
      "-1.557 x + 204.8 x - 8965 x + 1.379e+05\n"
     ]
    }
   ],
   "source": [
    "x = df['highway-mpg']\n",
    "y = df['price']\n",
    "#Let's fit the polynomial using the function polyfit,then use the function to display the polynomial function.\n",
    "f = np.polyfit(x, y, 3)\n",
    "p = np.poly1d(f)\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's plot the function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "PlotPolly(p, x, y, 'highway-mpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyfit(x, y, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function  \"hits\" more of the data points.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        3         2\n",
      "-1.557 x + 204.8 x - 8965 x + 1.379e+05\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Create 11 order polynomial model with the variables x and y from above\n",
    "f1 = np.polyfit(x, y, 11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p)\n",
    "PlotPolly(p1,x,y, 'Length')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2)polynomial with two variables is given by:</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b_1 X_1 +b_2 X_2 +b_3 X_1 X_2+b_4 X_1^2+b_5 X_2^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perform a polynomial transform on multiple features. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#import the module\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "#create a PolynomialFeatures object of degree 2 \n",
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Z_pr=pr.fit_transform(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The original data is of 201 samples and 4 features "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the transformation, there are 201 samples and 15 features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z_pr.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Pipeline</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Data Pipelines simplify the steps of processing the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Use the module Pipeline to create a pipeline and also use StandardScaler as a step in our pipeline\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#create the pipeline by creating a list of tuples including the name of the model/estimator & its corresponding constructor.\n",
    "Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False))])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Input the list as an argument to the pipeline constructor \n",
    "pipe=Pipeline(Input)\n",
    "pipe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "/home/jupyterlab/conda/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, y, **fit_params).transform(X)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False))])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Normalize the data and perform a transform and fit the model simultaneously\n",
    "pipe.fit(Z,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  Xt = transform.transform(Xt)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Normalize the data, perform a transform and produce a prediction  simultaneously\n",
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> Lets create a pipeline that Standardizes the data, then perform prediction using a linear regression model using the features Z and targets y</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "/home/jupyterlab/conda/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, y, **fit_params).transform(X)\n",
      "/home/jupyterlab/conda/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
      "  Xt = transform.transform(Xt)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([13699.11161184, 13699.11161184, 19051.65470233, 10620.36193015,\n",
       "       15521.31420211, 13869.66673213, 15456.16196732, 15974.00907672,\n",
       "       17612.35917161, 10722.32509097])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Input = [('scale',StandardScaler()),('model',LinearRegression())]\n",
    "pipe = Pipeline(Input)\n",
    "pipe.fit(Z,y)\n",
    "ypipe = pipe.predict(Z)\n",
    "ypipe[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Measures for In-Sample Evaluation</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
    "\n",
    "<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
    "<ul>\n",
    "    <li><b>R^2 / R-squared</b></li>\n",
    "    <li><b>Mean Squared Error (MSE)</b></li>\n",
    "</ul>\n",
    "    \n",
    "<b>R-squared</b> : R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n",
    "\n",
    "<b>Mean Squared Error (MSE)</b> : The Mean Squared Error measures the average of the squares of errors, that is, the difference between actual value (y) and the estimated value (ŷ).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 1: Simple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's calculate the R^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7609686443622008"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#highway_mpg_fit\n",
    "lm.fit(X, Y)\n",
    "# Find the R^2\n",
    "lm.score(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's calculate the MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13728.4631336 , 13728.4631336 , 17399.38347881, 10224.40280408])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:\n",
    "Yhat=lm.predict(X)\n",
    "Yhat[0:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15021126.02517414"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#import the function mean_squared_error from the module metrics\n",
    "from sklearn.metrics import mean_squared_error\n",
    "#compare the predicted results with the actual results\n",
    "mse = mean_squared_error(df['price'], Yhat)\n",
    "mse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 2: Multiple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's calculate the R^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8093562806577458"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit the model \n",
    "lm.fit(Z, df['price'])\n",
    "# Find the R^2\n",
    "lm.score(Z, df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 80.896 % of the variation of price is explained by this multiple linear regression \"multi_fit\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's calculate the MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11980366.870726489"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Produce a prediction \n",
    "Y_predict_multifit = lm.predict(Z)\n",
    "# Compare the predicted results with the actual results\n",
    "# The mean square error of price and predicted value using multifit is: \n",
    "mean_squared_error(df['price'], Y_predict_multifit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 3: Polynomial Fit</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's calculate the R^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let’s import the function <b>r2_score</b> from the module <b>metrics</b> as we are using a different function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We apply the function to get the value of r^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6741946663906517"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_squared = r2_score(y, p(x))\n",
    "r_squared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say that ~ 67.419 % of the variation of price is explained by this polynomial fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>MSE</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the MSE:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361226"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(df['price'], p(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Prediction and Decision Making</h2>\n",
    "<h3>Prediction</h3>\n",
    "\n",
    "<p>We trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction.</p>\n",
    "<p>Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a new input "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "new_input=np.arange(1, 100, 1).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Fit the model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X, Y)\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce a prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7796.47889059, -7629.6188749 , -7462.75885921, -7295.89884352,\n",
       "       -7129.03882782])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat=lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(new_input, yhat)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Decision Making: Determining a Good Model Fit</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* <b>Model with the higher R-squared value is a better fit</b> for the data.\n",
    "\n",
    "* <b>Model with the smallest MSE value is a better fit</b> for the data.</p>\n",
    "\n",
    "\n",
    "<h4>Let's take a look at the values for the different models.</h4>\n",
    "\n",
    "<p><b>Simple Linear Regression</b> : Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.49659118843391759</li>\n",
    "    <li>MSE: 3.16 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "    \n",
    "<p><b>Multiple Linear Regression</b> : Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.80896354913783497</li>\n",
    "    <li>MSE: 1.2 x10^7</li>\n",
    "</ul>\n",
    "</p>\n",
    "    \n",
    "<p><b>Polynomial Fit</b> : Using Highway-mpg as a Predictor Variable of Price.\n",
    "<ul>\n",
    "    <li>R-squared: 0.6741946663906514</li>\n",
    "    <li>MSE: 2.05 x 10^7</li>\n",
    "</ul>\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Conclusion:</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense, since we have 27 variables in total, and we know that more than one of those variables are potential predictors of the final car price.</p>"
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}