model-development.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "# Model Development\n",
    "\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "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:\n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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",
       "      <td>0</td>\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",
       "      <td>1</td>\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",
       "      <td>2</td>\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",
       "      <td>3</td>\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",
       "      <td>4</td>\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": 3,
     "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Linear Regression</h4>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Lets load the modules for linear regression</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Create the linear regression object</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 5,
     "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>\n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[['highway-mpg']]\n",
    "Y = df['price']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the linear model using highway-mpg.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can output a prediction \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
       "       20345.17153508])"
      ]
     },
     "execution_count": 8,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.305858157415"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>What is the value of the Slope (b)?</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is the final estimated linear model we get?</h3>\n"
   ]
  },
  {
   "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",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm = LinearRegression()\n",
    "lm"
   ]
  },
  {
   "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",
    "-->\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",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 12,
     "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",
    "lm.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[['engine-size']], 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",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Slope</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7963.338906281042"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Intercept</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([166.86001569])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm.coef_"
   ]
  },
  {
   "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",
    "-->\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",
    "\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code below and press Shift+Enter to execute \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",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Multiple Linear Regression</h4>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(Z, df['price'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.624626329234"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "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": [
    "<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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "lm2 = LinearRegression()\n",
    "lm2.fit(df[['normalized-losses','highway-mpg']],df['price'])"
   ]
  },
  {
   "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",
    "-->\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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   1.49789586, -820.45434016])"
      ]
     },
     "execution_count": 21,
     "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",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>2)  Model Evaluation using Visualization</h3>\n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "import the visualization package: seaborn\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's visualize **highway-mpg** as potential predictor variable of price:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 48265.361769907184)"
      ]
     },
     "execution_count": 23,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 47422.919330307624)"
      ]
     },
     "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": [
    "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>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>peak-rpm</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>highway-mpg</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>price</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             peak-rpm  highway-mpg     price\n",
       "peak-rpm     1.000000    -0.058598 -0.101616\n",
       "highway-mpg -0.058598     1.000000 -0.704692\n",
       "price       -0.101616    -0.704692  1.000000"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "df[['peak-rpm','highway-mpg','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",
    "-->\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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression</h3>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First lets make a prediction \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": 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(Y_hat, 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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 3: Polynomial Regression and Pipelines</h2>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><b>Quadratic - 2nd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X +b_2 X^2 \n",
    "$$\n",
    "\n",
    "<center><b>Cubic - 3rd order</b></center>\n",
    "$$\n",
    "Yhat = a + b_1 X +b_2 X^2 +b_3 X^3\\\\\n",
    "$$\n",
    "\n",
    "<center><b>Higher order</b>:</center>\n",
    "$$\n",
    "Y = a + b_1 X +b_2 X^2 +b_3 X^3 ....\\\\\n",
    "$$\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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We will use the following function to plot the data:</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "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\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "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 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": true
   },
   "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": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 33,
     "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>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            11             10             9           8         7\n",
      "-1.243e-08 x  + 4.722e-06 x  - 0.0008028 x + 0.08056 x - 5.297 x\n",
      "          6        5             4             3             2\n",
      " + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
     ]
    }
   ],
   "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(p1)"
   ]
  },
  {
   "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(p1)\n",
    "PlotPolly(p1,x,y, 'Highway MPG')\n",
    "\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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "Yhat = a + b_1 X_1 +b_2 X_2 +b_3 X_1 X_2+b_4 X_1^2+b_5 X_2^2\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can perform a polynomial transform on multiple features. First, we import the module:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a <b>PolynomialFeatures</b> object of degree 2: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False,\n",
       "                   order='C')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_pr=pr.fit_transform(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The original data is of 201 samples and 4 features \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "after the transformation, there 201 samples and 15 features\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z_pr.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Pipeline</h2>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "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 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('polynomial',\n",
       "                 PolynomialFeatures(degree=2, include_bias=False,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "                                  normalize=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 42,
     "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. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('polynomial',\n",
       "                 PolynomialFeatures(degree=2, include_bias=False,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "                                  normalize=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 43,
     "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\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
      ]
     },
     "execution_count": 44,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('scale',\n",
       "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
       "                ('polynomial',\n",
       "                 PolynomialFeatures(degree=2, include_bias=False,\n",
       "                                    interaction_only=False, order='C')),\n",
       "                ('model',\n",
       "                 LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "                                  normalize=False))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write your code below and press Shift+Enter to execute \n",
    "Input = [('scale',StandardScaler()),('polynomial', PolynomialFeatures(include_bias=False)),('model',LinearRegression())]\n",
    "pipe = Pipeline(Input)\n",
    "pipe.fit(Z,y)"
   ]
  },
  {
   "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",
    "-->\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 4: Measures for In-Sample Evaluation</h2>\n"
   ]
  },
  {
   "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",
    "<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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Model 1: Simple Linear Regression</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "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\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [13728.4631336  13728.4631336  17399.38347881 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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we compare the predicted results with the actual results \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "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\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we produce a prediction \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_predict_multifit = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we compare the predicted results with the actual results \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the R^2\n"
   ]
  },
  {
   "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\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "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\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "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\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>MSE</h3>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the MSE:  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361218"
      ]
     },
     "execution_count": 55,
     "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>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "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 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_input=np.arange(1, 100, 1).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Fit the model \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.fit(X, Y)\n",
    "lm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce a prediction\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-7796.47889059, -7629.6188749 , -7462.75885921, -7295.89884352,\n",
       "       -7129.03882782])"
      ]
     },
     "execution_count": 59,
     "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 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "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>\n"
   ]
  },
  {
   "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",
    "<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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Regression model (SLR) vs Multiple Linear Regression model (MLR)</h3>\n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Linear Model (SLR) vs Polynomial Fit</h3>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Multiple Linear Regression (MLR) vs Polynomial Fit</h3>\n"
   ]
  },
  {
   "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>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Conclusion:</h2>\n"
   ]
  },
  {
   "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>\n"
   ]
  }
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