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": 4,
   "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": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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": 5,
     "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": 6,
   "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": 7,
   "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": 7,
     "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": 8,
   "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": 9,
   "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": 9,
     "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": 10,
   "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": 10,
     "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": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.3058581574"
      ]
     },
     "execution_count": 11,
     "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": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 12,
     "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": 13,
   "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": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1 = LinearRegression()\n",
    "lm1"
   ]
  },
  {
   "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": 14,
   "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": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "X = df[['engine-size']]\n",
    "Y = df[['price']]\n",
    "lm1.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": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[166.86001569]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.coef_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Intercept</h4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7963.33890628])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm1.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": [
    "# You can type you answer here\n",
    "yhat = -7963.3389+166.86*x"
   ]
  },
  {
   "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": 17,
   "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": 18,
   "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": 18,
     "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": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.62462632922"
      ]
     },
     "execution_count": 19,
     "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": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
      ]
     },
     "execution_count": 20,
     "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": 21,
   "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": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm2 = LinearRegression()\n",
    "X = df[['normalized-losses','highway-mpg']]\n",
    "Y = df[['price']]\n",
    "lm2.fit(X,Y)"
   ]
  },
  {
   "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": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm2.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, 48285.93382198697)"
      ]
     },
     "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": 26,
   "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": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[['highway-mpg','peak-rpm','price']].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": 27,
   "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": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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": 31,
   "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": 32,
   "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": 33,
   "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": 34,
   "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": 35,
   "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": 35,
     "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": 36,
   "metadata": {},
   "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": [
    "# Write your code below and press Shift+Enter to execute \n",
    "f1 = np.polyfit(x,y,11)\n",
    "p1 = np.poly1d(f1)\n",
    "print(p)\n",
    "PlotPolly(p1,x,y,'Highway-mpg')"
   ]
  },
  {
   "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": 37,
   "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": 38,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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": 40,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 40,
     "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": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 41,
     "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": 42,
   "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": 43,
   "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": 44,
   "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": 44,
     "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": 46,
   "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": 46,
     "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": 47,
   "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": 47,
     "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": 48,
   "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": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "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": [
    "</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": 49,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.4966263556974878\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": 50,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [[16231.78938339]\n",
      " [16231.78938339]\n",
      " [17052.24372355]\n",
      " [13833.33798916]]\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": 51,
   "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": 52,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value is:  31632832.975589428\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": 53,
   "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": 54,
   "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": 55,
   "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": 56,
   "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": 57,
   "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": 58,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361218"
      ]
     },
     "execution_count": 58,
     "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": 59,
   "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": 60,
   "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": 61,
   "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": 61,
     "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": 68,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (99,1) and (2,1) not aligned: 1 (dim 1) != 2 (dim 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-68-5e2f8b2d15e7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0myhat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/conda/envs/python/lib/python3.6/site-packages/sklearn/linear_model/base.py\u001b[0m in \u001b[0;36mpredict\u001b[0;34m(self, X)\u001b[0m\n\u001b[1;32m    211\u001b[0m             \u001b[0mReturns\u001b[0m \u001b[0mpredicted\u001b[0m \u001b[0mvalues\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    212\u001b[0m         \"\"\"\n\u001b[0;32m--> 213\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_decision_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    214\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    215\u001b[0m     \u001b[0m_preprocess_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstaticmethod\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_preprocess_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/conda/envs/python/lib/python3.6/site-packages/sklearn/linear_model/base.py\u001b[0m in \u001b[0;36m_decision_function\u001b[0;34m(self, X)\u001b[0m\n\u001b[1;32m    196\u001b[0m         \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccept_sparse\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'csr'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'csc'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'coo'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    197\u001b[0m         return safe_sparse_dot(X, self.coef_.T,\n\u001b[0;32m--> 198\u001b[0;31m                                dense_output=True) + self.intercept_\n\u001b[0m\u001b[1;32m    199\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    200\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/conda/envs/python/lib/python3.6/site-packages/sklearn/utils/extmath.py\u001b[0m in \u001b[0;36msafe_sparse_dot\u001b[0;34m(a, b, dense_output)\u001b[0m\n\u001b[1;32m    171\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mret\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    172\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 173\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    174\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    175\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: shapes (99,1) and (2,1) not aligned: 1 (dim 1) != 2 (dim 0)"
     ]
    }
   ],
   "source": [
    "yhat=lm.predict(np.arange(1,100,1).reshape(-1,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'yhat' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-64-0552aadd56e6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnew_input\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0myhat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'yhat' is not defined"
     ]
    }
   ],
   "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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