model-development.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "    <a href=\"https://cocl.us/corsera_da0101en_notebook_top\">\n",
    "         <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/TopAd.png\" width=\"750\" align=\"center\">\n",
    "    </a>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/CCLog.png\" width = 300, align = \"center\"></a>\n",
    "\n",
    "<h1 align=center><font size=5>Data Analysis with Python</font></h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Module 4: Model Development</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>In this section, we will 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": [
    "Some questions we want to ask in this module\n",
    "<ul>\n",
    "    <li>do I know if the dealer is offering fair value for my trade-in?</li>\n",
    "    <li>do I know if I put a fair value on my car?</li>\n",
    "</ul>\n",
    "<p>Data Analytics, 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": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "load data and store in dataframe df:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": 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": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# path of data \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": "markdown",
   "metadata": {},
   "source": [
    "<h3>1. 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 line0, 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": "markdown",
   "metadata": {},
   "source": [
    "<h4>Lets load the modules for linear regression</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Create the linear regression object</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How could Highway-mpg help us predict car price?</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this example, we want to look at how highway-mpg can help us predict car price.\n",
    "Using simple linear regression, we will create a linear function with \"highway-mpg\" as the predictor variable and the \"price\" as the response variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "X = df[['highway-mpg']]\n",
    "Y = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using highway-mpg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": 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": [
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can output a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": 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>What is the value of the intercept (a)?</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.3058581574"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the Slope (b)?</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is the final estimated linear model we get?</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear model with the structure:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b  X\n",
    "$$"
   ]
  },
  {
   "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": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 a): </h1>\n",
    "\n",
    "<b>Create a linear regression object?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "lin_obj = LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm1 = LinearRegression()\n",
    "lm1 \n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question #1 b): </h1>\n",
    "\n",
    "<b>Train the model using 'engine-size' as the independent variable and 'price' as the dependent variable?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df[['engine-size']]\n",
    "Y = df['price']\n",
    "lin_obj.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm1.fit(df[['highway-mpg']], df[['price']])\n",
    "lm1\n",
    "\n",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 c):</h1>\n",
    "\n",
    "<b>Find the slope and intercept of the model?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Slope</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([166.86001569])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_obj.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Intercept</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7963.338906281042"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "lin_obj.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# Slope \n",
    "lm1.coef_\n",
    "# Intercept\n",
    "lm1.intercept_\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #1 d): </h1>\n",
    "\n",
    "<b>What is the equation of the predicted line. You can use x and yhat or 'engine-size' or 'price'?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yhat=-7963.34 + 166.86*X\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# using X and Y  \n",
    "Yhat=-7963.34 + 166.86*X\n",
    "\n",
    "Price=-7963.34 + 166.86*engine-size\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Multiple Linear Regression</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>What if we want to predict car price using more than one variable?</p>\n",
    "\n",
    "<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\n",
    "Multiple Linear Regression is very similar to Simple Linear Regression, but 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. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>"
   ]
  },
  {
   "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": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using the four above-mentioned variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(Z, df['price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the value of the intercept(a)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.62462632922"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the values of the coefficients (b1, b2, b3, b4)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " What is the final estimated linear model that we get?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw above, we should get a final linear function with the structure:\n",
    "\n",
    "$$\n",
    "Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
    "$$\n",
    "\n",
    "What is the linear function we get in this example?"
   ]
  },
  {
   "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": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1> Question  #2 a): </h1>\n",
    "Create and train a Multiple Linear Regression model \"lm2\" where the response variable is price, and the predictor variable is 'normalized-losses' and  'highway-mpg'.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_obj2 = LinearRegression()\n",
    "Z1 = df[[ 'normalized-losses','highway-mpg']]\n",
    "Y = df[['price']]\n",
    "lin_obj2.fit(Z1,Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm2 = LinearRegression()\n",
    "lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  #2 b): </h1>\n",
    "<b>Find the coefficient of the model?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1.49789586, -820.45434016]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_obj2.intercept_\n",
    "lin_obj2.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "lm2.coef_\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>2)  Model Evaluation using Visualization</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've developed some models, how do we evaluate our models and how do we choose the best one? One way to do this is by using visualization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "import the visualization package: seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "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": 24,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 48286.42555099927)"
      ]
     },
     "execution_count": 24,
     "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=\"highway-mpg\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see from this plot that price is negatively correlated to highway-mpg, since the regression slope is negative.\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. Let's compare this plot to the regression plot of \"peak-rpm\".</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 47422.919330307624)"
      ]
     },
     "execution_count": 25,
     "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": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #3:</h1>\n",
    "<b>Given the regression plots above is \"peak-rpm\" or \"highway-mpg\" more strongly correlated with \"price\". Use the method  \".corr()\" to verify your answer.</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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>highway-mpg</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>-0.058598</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             highway-mpg  peak-rpm     price\n",
       "highway-mpg     1.000000 -0.058598 -0.704692\n",
       "peak-rpm       -0.058598  1.000000 -0.101616\n",
       "price          -0.704692 -0.101616  1.000000"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = df[[\"highway-mpg\",\"peak-rpm\",\"price\"]]\n",
    "A.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692  compared to   \"peak-rpm\" which is approximate     -0.101616. You can verify it using the following command:\n",
    "df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n",
    "\n",
    "-->"
   ]
  },
  {
   "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>What is a <b>residual</b>?</p>\n",
    "\n",
    "<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n",
    "\n",
    "<p>So what is a <b>residual plot</b>?</p>\n",
    "\n",
    "<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
    "\n",
    "<p>What do we pay attention to when looking at a residual plot?</p>\n",
    "\n",
    "<p>We 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. Why is that? Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "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(df['highway-mpg'], df['price'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>What is this plot telling us?</i>\n",
    "\n",
    "<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, which leads us to believe that maybe 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>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
    "\n",
    "<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>: We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First lets make a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "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",
    "\n",
    "\n",
    "ax1 = sns.distplot(df['price'], hist=False, color=\"r\", label=\"Actual Value\")\n",
    "sns.distplot(Yhat, hist=False, color=\"b\", label=\"Fitted Values\" , ax=ax1)\n",
    "\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()"
   ]
  },
  {
   "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>Part 3: 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.</p> \n",
    "<p>We get non-linear relationships by squaring or setting higher-order terms of the predictor variables.</p>\n",
    "\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>We saw earlier that 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": "markdown",
   "metadata": {},
   "source": [
    "<p>We will use the following function to plot the data:</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "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": "markdown",
   "metadata": {},
   "source": [
    "lets get the variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "x = df['highway-mpg']\n",
    "y = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's fit the polynomial using the function <b>polyfit</b>, then use the function <b>poly1d</b> to display the polynomial function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        3         2\n",
      "-1.557 x + 204.8 x - 8965 x + 1.379e+05\n"
     ]
    }
   ],
   "source": [
    "# Here we use a polynomial of the 3rd order (cubic) \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": 38,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": 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": 39,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 39,
     "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": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question  #4:</h1>\n",
    "<b>Create 11 order polynomial model with the variables x and y from above?</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.24263391e-08,  4.72184893e-06, -8.02843483e-04,  8.05640304e-02,\n",
       "       -5.29740982e+00,  2.39470329e+02, -7.58845740e+03,  1.68447254e+05,\n",
       "       -2.56531153e+06,  2.55140622e+07, -1.49106965e+08,  3.87930088e+08])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyfit(x, y, 11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "# calculate polynomial\n",
    "# Here we use a polynomial of the 11rd order (cubic) \n",
    "f1 = np.polyfit(x, y, 11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p)\n",
    "PlotPolly(p1,x,y, 'Highway MPG')\n",
    "\n",
    "-->"
   ]
  },
  {
   "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. First, we import the module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a <b>PolynomialFeatures</b> object of degree 2: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "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": 44,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "after the transformation, there 201 samples and 15 features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 45,
     "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. We use the module <b>Pipeline</b> to create a pipeline. We also use <b>StandardScaler</b> as a step in our pipeline.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create the pipeline, by creating a list of tuples including the name of the model or estimator and its corresponding constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we input the list as an argument to the pipeline constructor "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": 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": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe=Pipeline(Input)\n",
    "pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can normalize the data,  perform a transform and fit the model simultaneously. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/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/envs/python/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": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe.fit(Z,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Similarly,  we can normalize the data, perform a transform and produce a prediction  simultaneously"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/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": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
    "<h1>Question #5:</h1>\n",
    "<b>Create a pipeline that Standardizes the data, then perform prediction using a linear regression model using the features Z and targets y</b>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/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/envs/python/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/envs/python/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": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
    "\n",
    "pipe=Pipeline(Input)\n",
    "\n",
    "pipe.fit(Z,y)\n",
    "\n",
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "</div>\n",
    "Double-click <b>here</b> for the solution.\n",
    "\n",
    "<!-- The answer is below:\n",
    "\n",
    "Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
    "\n",
    "pipe=Pipeline(Input)\n",
    "\n",
    "pipe.fit(Z,y)\n",
    "\n",
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:10]\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 4: 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>\n",
    "\n",
    "<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n",
    "    \n",
    "<p>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",
    "\n",
    "\n",
    "<b>Mean Squared Error (MSE)</b>\n",
    "\n",
    "<p>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": 52,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.7609686443622008\n"
     ]
    }
   ],
   "source": [
    "#highway_mpg_fit\n",
    "lm.fit(X, Y)\n",
    "# Find the R^2\n",
    "print('The R-square is: ', 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": "markdown",
   "metadata": {},
   "source": [
    "We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [[13728.4631336 ]\n",
      " [13728.4631336 ]\n",
      " [17399.38347881]\n",
      " [10224.40280408]]\n"
     ]
    }
   ],
   "source": [
    "Yhat=lm.predict(X)\n",
    "print('The output of the first four predicted value is: ', Yhat[0:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "lets import the function <b>mean_squared_error</b> from the module <b>metrics</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we compare the predicted results with the actual results "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value is:  15021126.025174143\n"
     ]
    }
   ],
   "source": [
    "mse = mean_squared_error(df['price'], Yhat)\n",
    "print('The mean square error of price and predicted value is: ', 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": 56,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.8093562806577457\n"
     ]
    }
   ],
   "source": [
    "# fit the model \n",
    "lm.fit(Z, df['price'])\n",
    "# Find the R^2\n",
    "print('The R-square is: ', 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": "markdown",
   "metadata": {},
   "source": [
    " we produce a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Y_predict_multifit = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we compare the predicted results with the actual results "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value using multifit is:  11980366.87072649\n"
     ]
    }
   ],
   "source": [
    "print('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": 59,
   "metadata": {},
   "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": 60,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square value is:  0.674194666390652\n"
     ]
    }
   ],
   "source": [
    "r_squared = r2_score(y, p(x))\n",
    "print('The R-square value is: ', 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": 61,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361218"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(df['price'], p(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 5: Prediction and Decision Making</h2>\n",
    "<h3>Prediction</h3>\n",
    "\n",
    "<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "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": 63,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": 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": 64,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 64,
     "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": 65,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-7796.47889059],\n",
       "       [-7629.6188749 ],\n",
       "       [-7462.75885921],\n",
       "       [-7295.89884352],\n",
       "       [-7129.03882782]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat=lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": 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": [
    "<p>Now that we have visualized the different models, and generated the R-squared and MSE values for the fits, how do we determine a good model fit?\n",
    "<ul>\n",
    "    <li><i>What is a good R-squared value?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the model with the higher R-squared value is a better fit</b> for the data.\n",
    "<ul>\n",
    "    <li><i>What is a good MSE?</i></li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "<p>When comparing models, <b>the 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",
    "<p>Simple Linear Regression: 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>Multiple Linear Regression: 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>Polynomial Fit: 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": [
    "<h3>Simple Linear Regression model (SLR) vs Multiple Linear Regression model (MLR)</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Usually, the more variables you have, the better your model is at predicting, but this is not always true. Sometimes you may not have enough data, you may run into numerical problems, or many of the variables may not be useful and or even act as noise. As a result, you should always check the MSE and R^2.</p>\n",
    "\n",
    "<p>So to be able to compare the results of the MLR vs SLR models, we look at a combination of both the R-squared and MSE to make the best conclusion about the fit of the model.\n",
    "<ul>\n",
    "    <li><b>MSE</b>The MSE of SLR is  3.16x10^7  while MLR has an MSE of 1.2 x10^7.  The MSE of MLR is much smaller.</li>\n",
    "    <li><b>R-squared</b>: In this case, we can also see that there is a big difference between the R-squared of the SLR and the R-squared of the MLR. The R-squared for the SLR (~0.497) is very small compared to the R-squared for the MLR (~0.809).</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "This R-squared in combination with the MSE show that MLR seems like the better model fit in this case, compared to SLR."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Model (SLR) vs Polynomial Fit</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n",
    "    <li><b>R-squared</b>: The R-squared for the Polyfit is larger than the R-squared for the SLR, so the Polynomial Fit also brought up the R-squared quite a bit.</li>\n",
    "</ul>\n",
    "<p>Since the Polynomial Fit resulted in a lower MSE and a higher R-squared, we can conclude that this was a better fit model than the simple linear regression for predicting Price with Highway-mpg as a predictor variable.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression (MLR) vs Polynomial Fit</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li><b>MSE</b>: The MSE for the MLR is smaller than the MSE for the Polynomial Fit.</li>\n",
    "    <li><b>R-squared</b>: The R-squared for the MLR is also much larger than for the Polynomial Fit.</li>\n",
    "</ul>"
   ]
  },
  {
   "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>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Thank you for completing this notebook</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "\n",
    "    <p><a href=\"https://cocl.us/corsera_da0101en_notebook_bottom\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/BottomAd.png\" width=\"750\" align=\"center\"></a></p>\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>About the Authors:</h3>\n",
    "\n",
    "This notebook was written by <a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>, <a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>, Bahare Talayian, Eric Xiao, Steven Dong, Parizad, Hima Vsudevan and <a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a> and <a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
    "\n",
    "<p><a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a> is a Data Scientist at IBM, and holds a PhD in Electrical Engineering. His research focused on using Machine Learning, Signal Processing, and Computer Vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "<p>Copyright &copy; 2018 IBM Developer Skills Network. This notebook and its source code are released under the terms of the <a href=\"https://cognitiveclass.ai/mit-license/\">MIT License</a>.</p>"
   ]
  }
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