car-price-prediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"import_data\">Import Data</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Setup</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " load data and store in dataframe df:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>aspiration</th>\n",
       "      <th>num-of-doors</th>\n",
       "      <th>body-style</th>\n",
       "      <th>drive-wheels</th>\n",
       "      <th>engine-location</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>...</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>horsepower-binned</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>88.6</td>\n",
       "      <td>0.811148</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>11.190476</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>122</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>94.5</td>\n",
       "      <td>0.822681</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950.0</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>...</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450.0</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>Medium</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   symboling  normalized-losses         make aspiration num-of-doors  \\\n",
       "0          3                122  alfa-romero        std          two   \n",
       "1          3                122  alfa-romero        std          two   \n",
       "2          1                122  alfa-romero        std          two   \n",
       "3          2                164         audi        std         four   \n",
       "4          2                164         audi        std         four   \n",
       "\n",
       "    body-style drive-wheels engine-location  wheel-base    length  ...  \\\n",
       "0  convertible          rwd           front        88.6  0.811148  ...   \n",
       "1  convertible          rwd           front        88.6  0.811148  ...   \n",
       "2    hatchback          rwd           front        94.5  0.822681  ...   \n",
       "3        sedan          fwd           front        99.8  0.848630  ...   \n",
       "4        sedan          4wd           front        99.4  0.848630  ...   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm city-mpg highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0       21          27  13495.0   \n",
       "1                9.0       111.0    5000.0       21          27  16500.0   \n",
       "2                9.0       154.0    5000.0       19          26  16500.0   \n",
       "3               10.0       102.0    5500.0       24          30  13950.0   \n",
       "4                8.0       115.0    5500.0       18          22  17450.0   \n",
       "\n",
       "  city-L/100km  horsepower-binned  diesel  gas  \n",
       "0    11.190476             Medium       0    1  \n",
       "1    11.190476             Medium       0    1  \n",
       "2    12.368421             Medium       0    1  \n",
       "3     9.791667             Medium       0    1  \n",
       "4    13.055556             Medium       0    1  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='dataset/automobileEDA.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"pattern_visualization\">Analyzing Individual Feature Patterns using Visualization</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import visualization packages \"Matplotlib\" and \"Seaborn\", don't forget about \"%matplotlib inline\" to plot in a Jupyter notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>How to choose the right visualization method?</h4>\n",
    "<p>When visualizing individual variables, it is important to first understand what type of variable you are dealing with. This will help us find the right visualization method for that variable.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "symboling              int64\n",
      "normalized-losses      int64\n",
      "make                  object\n",
      "aspiration            object\n",
      "num-of-doors          object\n",
      "body-style            object\n",
      "drive-wheels          object\n",
      "engine-location       object\n",
      "wheel-base           float64\n",
      "length               float64\n",
      "width                float64\n",
      "height               float64\n",
      "curb-weight            int64\n",
      "engine-type           object\n",
      "num-of-cylinders      object\n",
      "engine-size            int64\n",
      "fuel-system           object\n",
      "bore                 float64\n",
      "stroke               float64\n",
      "compression-ratio    float64\n",
      "horsepower           float64\n",
      "peak-rpm             float64\n",
      "city-mpg               int64\n",
      "highway-mpg            int64\n",
      "price                float64\n",
      "city-L/100km         float64\n",
      "horsepower-binned     object\n",
      "diesel                 int64\n",
      "gas                    int64\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "# list the data types for each column\n",
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for example, we can calculate the correlation between variables  of type \"int64\" or \"float64\" using the method \"corr\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</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>diesel</th>\n",
       "      <th>gas</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Continuous numerical variables:</h2> \n",
    "\n",
    "<p>Continuous numerical variables are variables that may contain any value within some range. Continuous numerical variables can have the type \"int64\" or \"float64\". A great way to visualize these variables is by using scatterplots with fitted lines.</p>\n",
    "\n",
    "<p>In order to start understanding the (linear) relationship between an individual variable and the price. We can do this by using \"regplot\", which plots the scatterplot plus the fitted regression line for the data.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's see several examples of different linear relationships:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Positive linear relationship</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's find the scatterplot of \"engine-size\" and \"price\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 56381.05843688959)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YwL4TPQAUeVzcsHQeN1w4j4AvN5l5J0sASZCp9gF+6dKlZvv27YU+DaXUKBlj7IWFOaoVsu9ED2s37mXr/jbAHoD98Bkz+dJldUwvKxr18eFkACnze3Dl6K5mrIjIa8aYpal+pyvblVITTjhqZ+nNRa2Q1p4ID7+yn/966wiJXrFz51Vw54pFnDqzbOidM+R2CRUBL+V+74QLIJnQQKKUmjByWSukNxrn168f4rGtBwk63WJzqwLcsbyeSxfV5KTLabIHkAQNJEqpCSFXtUIsY3hhVzP3v7iP5q5eAMr9Hm66ZAEfP2c2XvfoM0dNlQCSoIFEqXFAi1Kll8taITsPdfDTDXvZdbQLAI9L+OR5c/j8xfMp849+QeFUCyAJGkiUKrBcFaWajMEoV7VCDrWHuP/FBja9fzLpxfLF0/jy8nrmVAZGe5pTNoAkaCBRqsByUZRqslVIjMYtWnJQK6QrHOXftxzkt38+RMwJRqfNLGP1ynrOnls56vN0u4Ryv5eKwNQMIAkaSJQqsFwUpZpMFRI7glHagqOrFRKLWzz9xhEe2byfTqdLbEZZEbddUceHlszANcqBdJfYdyBTPYAkaCBRqsByUZRqMlRI7I3FOdEdoTc68oWFxhhe2dvipNO3a3gEvG4+e9E8rj9/LkXe0S0onKgBJN/dnhpIlCqwO5bX83dPv00wEktWxMu2KNVErpBoWYa24Oin9O4+1sWajQ3saGwH7My8HzurlpsvXUh1iW9Ux56oAQTGpttTA4lSBZaLolS5CEaFEIzYWXozmdK7taGVx7c1cqQzRG15gFUXzmNZfTXHu3p58OV9/OntY8nU3xcurOLOFYuom1YyqvObyAEkYSy6PTWQKDUOjLYo1USrkJhtlt6tDa3cs343HpdQ7vfQ0tPLPz//Pme+W8HLe04Qdla4L6wpZvXKRVy4sHqYIw5tMgSQhLHo9tRAotQkUYgKiSPpe+8KR2nNMkvv49sa8biEgNeNMYZIzE7U+PwuuwpFVbGXWy5dyEfPqh1VZt5EACkPeHOW4bfQxqLbUwOJUmpEsu17H02W3iOdIcr9dpfM8e4IvX1ybH3uovmsunAeJUUjfztziVDu3IFMlgCSMBbdnhpIlFIjkk3fe0cwSmswMuIsvVUBH/tbewhHTwaQYp+bhdUl3Hp53YivYTIHkISx6PbUQKKUGpHGtiBugYbj3UTiFj63i2mlvn5976Od0tsRjPLIlgO839yVzMzr97oo99tv/DddsmBEx50KAaSvfHd7aiBRahyYiOlNyoo87G7uxu0S3C4hZhkOtYdZPKMUYwxtwSgdoZHVConELH634xCPbjlAT68dhKpLfJQXeQhFY9RWnJy1lY2pFkDGigYSpQpsoqY3SQaIRJxwvscti6a20Iiy9Bpj2LT7BOs2NXCkIwxASZGbmy5ewLXnzsHnGVlmXg0g+aWBRKkCm6jpTbojceZU+jnRHSESt/C6hGklRXSGYyMKIu8e6WTNhr3sPNwJ2HmsPnHObG66eAEVxSPLzKsBZGxoIFGqwCZqepPEtNL66aXELUPMsghF4kwv92d1nKOdYX724j7WO1N5AS5dVMPty+uZXz2yKaoi9nqTymKfBpAxoIFEqQKbqOlN7lhez/ee2kksHsHncRGOWsQsw6oL52W0f09vjMe2HuTJ15qIxu1+sVOml7J6ZT3nza8a0TlpACkMDSRKFdgdy+v51pNvcKgtRMyy8LhclPk9fO9jpxf61NIyxnD2vEq+8sFTeHxrI0c7Q8wqz2wAPG4Z/uutIzz08n7anfxaNSU+br28jr84feaIAoAGkMLSQKLUOGAAxH5DRE6OX49HfUveLqurZlld5jOntu5rZc3GvRxosbvt/B4XN1w4j89cOI/AMJl5U+XaumhRDWV+D5UBL54clMhVI6OBRKkCW7upgYqAl9qKk5X6xuNge7b5sfpqON7NfRsb2H6gDQABPnLGLL50+UKmlRYNu3+qXFs/eWEP08uKuPL0mVmfj8otDSRKFdhEGGzvDEdpyzI/FkBrT4Sfv7yfZ3YeSS4oPG9+JatXLOKUGaUZHyeZa8vndvJh2ak+fvbSPg0k44AGEqVyLNvFheN5sD2RHDGc5cr03micJ19v4rFXGwk5+86rCnDHinouqa+xu/CycKQzRJXTfZXYd7wF26lMA4lSOTSSxYXjsZaIMYb2YJT2LFemW8bw/LvNPPDSPpq7egEo93u4+dKFfPzs2qzHMUSEkiI3C2tKONHdi9dzMgCNl2CrNJAolVMjWVw43mqJhKNxjnf1Zr2o8M2mdtZsaOC9Y10AeN3CJ8+bw+cvWkCpP7u3GhGhtMhDZbEXr9vF6hWLxl2wVSdpIFEqh0Y63pGLpHqjzddlWYbWYITOLEveHmoPcf+mBjbtPpFsW3HqdL58RR2zKwND7DnYwACSMN6CrepPA4lSOVSo8Y7R5usKRmKc6IoQszK/C+kKR/n3LQf57Z8PEXNG0j9QW8bqFYs4c05FVuefLoD0VYjCXSozGkiUyqFCjXeMNF/XSKb0xuIWT79xmEc2H6AzbO83s7yIL19RzwdPm57VQHomAUSNfxkHEhFZACw2xjwnIgHAY4zpGmJ7P7AJKHKe50ljzP8SkWrgl8BCYD/wGWNMm7PPd4BbgTjwNWPMfzvtFwAPAQHgD8DXjTFGRIqAR4ALgBbgBmPM/oyvXqkcK1QXzEi61LKd0muM4ZW9Lc61hQC7uNRnl83n+gvmZpWZVwPI5JJRIBGRLwO3A9XAImAucB9w5RC79QIfMsZ0i4gXeElEngE+BTxvjLlbRO4C7gK+LSKnA6uAM4DZwHMicqoxJg6scZ5/C3YguRp4BjvotBljThGRVcAPgRuy+gsolWOF6ILJpkttJCVv3z/WxX0b97KjsQMAl8DHzq7llksXUlXsy+pcS/0eqop9GkAmkUzvSL4CLANeBTDG7BaRIf+nGHvOYLfzo9f5MsC1wEqn/WFgA/Btp/1xY0wvsE9E9gDLRGQ/UG6M2QwgIo8A12EHkmuBv3eO9STwryIiZqT1PJWaoDLpUjPG0BmKZVXy9nhXLw++vI8/vX0smbZlWV01dyyvp25aSVbnaN+B+EZcU0SNX5kGkl5jTCTR9ykiHjJIByQibuA14BTg34wxr4rITGPMEQBjzJE+AWkO9h1HQpPTFnUeD2xP7NPoHCsmIh1ADXCiz/aIyO3YdzTMnz8/w0tWauIYrkstHLXzY0VimQ2mhyJxfrmtkV9ub6TX2aduWgl3rqjnwoXZVSUscbqwijxD59JSE1emgWSjiPwtEBCRvwD+GvjP4XZyuqXOFZFK4LcicuYQm6caoTNDtA+1z8DzWAesA1i6dKnerahJKVWXmmUZ2oIROjKc0hu3DH96+ygPvryflp4IAFXFXr54WR3XnDkrq8y6xT47gPiHScaoJr5MA8ld2OMRbwF3YI9T/CzTJzHGtIvIBuyxjWMiUuvcjdQCiWo2TUDfQgZzgcNO+9wU7X33aXLukiqA1kzPS6nJLBiJ0dIdyXhh4esH2vjpxr00HO8BwOdx8ekL5nLjsnn9xl6GowFk6sn0X0cAeNAYcz8ku6wCQNopISIyHYg6QSQAXIU9GP40cDNwt/P9KWeXp4HHROTH2IPti4Gtxpi4iHSJyMXYYzQ3AT/ps8/NwGbgemC9jo+oqS5uGVp6eukOZzal92BLkPs27WVLw8nPYFd9YAa3XV7HjCyqHWoAmboyDSTPYweCxOB5APgTcOkQ+9QCDztBxwU8YYz5vYhsBp4QkVuBg8CnAYwxb4vIE8A7QAz4itM1BrCak9N/n3G+AB4AHnUG5luxZ30pVVD3Pvc+P3tpHz2ROCU+N7ddXsfXrjp1TJ67KxylNcMpvR3BKA9t3s9/vnE4mZn3rDkVrF5Zz5JZ5Rk/Z0mRh4qABpCpTDL5AC8iO4wx5w7XNhEsXbrUbN++vdCnoSape597n3vW78El9hRZy9hfX//QKXkNJtlk6Y3ELH7z50P8x6sH6Om1t59d6ef25fVcccq0jBcU6iD61CIirxljlqb6XaZ3JD0icr4x5nXngBcAoVydoFKTxc9e2odLwOOyp7i6BGKWxc9e2peXQJJNll5jDBvfP866Tfs42hkG7Cm5X7hkAdedOzvjdR06jVcNlGkg+QbwKxFJDHLXogv/lBqkJxJn4PurS+z2XMsmS+87hzv56Ya9vHOkEwC3S7j23Nl84eIFVAxYEZ+O3oGodDIKJMaYbSKyBDgNe8rtLmNMdilClZoCSnz2YsC+s2QtY7fnSjaD6Uc7wtz/YgMvvHc82XbZohpuX17PvOrMEkkW+zxUlWgAUekNGUhE5EPGmPUi8qkBv1osIhhjfpPHc1Nqwrnt8jruWb+HmGX1GyO57fK6nBw/08H07t4Yj716kF+/3kQ0bm+7eEYpq1cu4tx5lRk9V8DnpqrYp4PoaljD3ZGsANYDH0/xOwNoIFGqj8Q4SK5nbWWaHytuGX7/5mEeeuVAchHitFIft15ex1+cPhNXBgPpRV431cU+Ajm8i1KT27CztkTEBVxvjHlibE4pv3TWlppIjDF0hKK0BYceTDfG8Oq+VtZubOBAq728y+91ceOF8/n00rkZ3VX4PC6qS3xZLT5UU8eoZm0ZYywR+SowKQKJUhNFpvmx9h7v5r6NDbx2oA2wBzGvPnMWX7psITWlRcM+j8/joqrYR0mRBhA1Mpn+y3lWRL6JXUekJ9FojNF0JErlmDGG1p7h82O19kR48OV9/HHn0eSCwgvmV3LnikUsmlE67PN43S6qSnyUagBRo5Tpv6AvYY+J/PWA9vyWfVNqAhpN7fRQxL4LGWpKbzga51evNfGLrQcJR+3t5lcXc+eKei6qqx52QaEGEJVrmf5LOh07iFyOHVBexC5spZTqY6S10zOZ0msZw3PvNvPAi/s43t0LQEXAyy2XLuBjZ9XiGWZBoQYQlS+Z/ot6GOgE7nV+vtFp+0w+TkqpiWoktdMzmdL7RlM7azbs5f1jdro7r1v41Hlz+NxFCyj1D/3fWAOIyrdM/2WdZow5p8/PL4jIG/k4IaUmsmxqp0diFi09Q0/pbWoLsnZTAy/vaUm2ffC06dx2RR21FYEhz0UDiBormf4L+7OIXGyM2QIgIhcBL+fvtJQaG6MZz0glk9rpmeTH6gxFeXTLAX6343DyTuX02jJWr1zEGbMrhjwHr9tFZbGXMn9mqU+UGq1MA8lFwE0ictD5eT7wroi8hV2e/ey8nJ1SeTTS8YyhDFc7fbjB9Gjc4qkdh3l0ywG6nPGSWeV+vnxFHStPmz7kQLoGEFUomQaSq/N6FkoVwEjGM4aTrnb6FadOp7krnHYw3RjDS3taWLepgUPtdmLtEp+bz100n0+dP3fITLsaQFShZZq08UC+T0RNbrnuQsqFbMYzsjGwdnpnOEpTWzDtYPr7x7r46Ya9vNnUAdjZgj9+9mxuvnQBlcW+tM+jAUSNFzoKp/IuH11IuZDJeMZoDFdsqrkzzAMv7+fZd44l2y6ur+aO5fUsqClJe1wNIGq80UCi8i4fXUi5MNx4xkgNN5geisT5xbaDPLG9KZn+pH5aCXeuqGfpwuq0x9UAosYrDSQq7/LVhTRa6cYzRhPchio2FbcMz+w8ys9f3kdb0E5/Ul3i44uXLuTqM2fhdqUeSNcAosY7DSQq7/LdhTQaA8czRsqyDC09EbrCqfNjbd/fyn0bG2g4YaeqK/K4+MzSuay6cH7adO0aQNREoYFE5V22XUipBuaBcTdYn9DdG6OluzflYPr+lh7Wbmzg1X0n85t++PSZ3Hp5HdPLUmfm1QCiJpph65FMNlqPpDASwWG4LqS+A/OJoNMZimKw80r1DUTf/8QZBQ0m0bhFS3eEYGTwlN62YISHXznA7988nMzMe/bcClavWMRps8pSHk8DiBrPRlWPRKlcyLQLKdXA/KG2EAjJlCADB+vHemrxUMWmIjGLX7/exGOvHqTHSX0ytyrA7VfUc9kpNSkXFGoAUROdBhI1rqQamI9Z1qA34MRg/VhPLU5XbMoYwwvvHef+Fxs41mln5i3ze7jpkgV84pzZeFNk5tUAoiYLDSRqXEk1MO9xuaw04OIAACAASURBVOyyf30kBuvHamrx+neP8W8v7KWpPUhteYBVF85jWb09Vfftwx2s2bCXd450OecrXHfebD5/0QLKA4ODhAYQNdloIFHjSqqB+TK/BwMpB+u/+9TOUU0tzqRb7Jm3jvAPv38Ht0so93to6enlnvW7+ULPArbub2XD+8eT215+yjRuX16XckaaBhA1WWkgUeNKqrUd3/vY6UDq9R7zNo18avGGXc1868k36ArHiFkWJ7p6+daTb/Cj689h5ZIZycH0tRsbcLvswX8An9tFe7CXH/3pPRIjJKfOLGX1ykWcM7dy0PNoAFGTnQYSNe6kG5hP1Taa1ek//OMu2oJR3C7B43ZhDLQFo9z9zLucO78yOZh+pDNEud+THGRv6YkQdyLI9NIibr2ijqs+MAPXgHGcRAApLfIMW/5WqYlMA4ma0EazOr3hRA8uIRkARMDCouFED609keR2s8r8HOoI0RmKEnEiiAAzy/08eMtS/N7+Cwq9bhcVxV7KNICoKUIDiZrwcrE6ve803r4Tevc2d9MTiXGi+2RgKfG5KSny8I0rF/cLInoHoqaq9EUORklE5onICyLyroi8LSJfd9qrReRZEdntfK/qs893RGSPiLwnIh/p036BiLzl/O5ecf6XikiRiPzSaX9VRBbm63rU5FNXU4xlIB63sIwhbhksA/MqA7R09/Kj/36P2x99jT3H7bQmZUUeakq8LJ5Rxt9cdWpy1pbX7WJaWRFzqwKU+b0aRNSUk887khjwfxljXheRMuA1EXkWuAV43hhzt4jcBdwFfFtETgdWAWcAs4HnRORUY0wcWAPcDmwB/oBdaOsZ4FagzRhzioisAn4I3JDHa1KTyLc+soRvPvkGPZEYlmVwuYQyr4f6GaV84cGthKP2WpEFNcXcuaKeZQur+wWJgV1Y47HmilJjIW93JMaYI8aY153HXcC7wBzgWuBhZ7OHgeucx9cCjxtjeo0x+4A9wDIRqQXKjTGbjd3/8MiAfRLHehK4UvTjoMpARzDKohmlfPsjSzh9VgU1JT5mlQWwDDz3bjPhqEVlwMs3rlrMz25aykV1J1ele1wn70DKnTuQxMLI5q5wv4WRG3Y1F/hKlcq/MRkjcbqczgNeBWYaY46AHWxEJPGRbQ72HUdCk9MWdR4PbE/s0+gcKyYiHUANcGLA89+OfUfD/Pnzc3VZKk/y+cl+4Mr0ZfXV+Lwu1mzYy+7mbgC8buGvzp/LZy+aT2lR/4WRFcVeyv2Dx0DGa80VpcZC3gOJiJQCvwa+YYzpHOKGIdUvzBDtQ+3Tv8GYdcA6sJM2DnfOKrfSBYZ0WX7zkfIkbhlaB6R5b2wNsm5TAy/vbUm2fWjJDG67vI5ZFf5km9slVAZ8lAfSD6KP15orSo2FvAYSEfFiB5H/MMb8xmk+JiK1zt1ILZC4928C5vXZfS5w2Gmfm6K97z5NIuIBKoBWVN5leteQLhfW9U3tPPn6oUHtJT53zj/Zd4WjtPZEkmneO0JRHt18gKfeOJxsO2N2OX+9chEfqC1P7ucSoSLgpSLgxZWm6FTCeK65olS+5S2QOGMVDwDvGmN+3OdXTwM3A3c735/q0/6YiPwYe7B9MbDVGBMXkS4RuRi7a+wm4CcDjrUZuB5Yb6ZaXvwCyCZR4tpNDUTjcVq6Y0TiFj63iyKPi3vW70GwCzxNKy2iPOAlGImxp7kbr1uIWgaf28X0siJKizwj+mQ/sGZ6NG7xux2HeXTzAbp77dTvs8r93L68nhWnTkvebbhEKHcCSLqqhQPdsbyebz75BofaQ8Qtg9sllBZ5kqvylZrM8nlHchnwBeAtEdnhtP0tdgB5QkRuBQ4CnwYwxrwtIk8A72DP+PqKM2MLYDXwEBDAnq31jNP+APCoiOzBvhNZlcfrUY5UwaE84El517C7uYuOYBSXS3C7hEjcSqZXB4hH4vZdDcWAIWoZELs7KWYZDreHqSn1srCmNOPzG1gz3RjDi7tPsO7FBg63hwF7LcjnL17AJ8+bg89jzzkZSQDpSwCMsybFSMp+V6Umo7wFEmPMS6QewwC4Ms0+PwB+kKJ9O3BmivYwTiBSY2dgcIhZhhNdEaLxrkHbRmIW9Fk9HhtQy9wAxsCB1iA+t+B15hEaK7HS3NDaE+X/++TQKU8SXW0HWnuYWebnhqV2dt5dRztZs2Evbx3qBMAl8PFzZnPzJQuoLPYBIGInY6ws9o0ogIAdXMsDXmY5NVMAHWxXU4aubFdZGxgcRMASM6hGB9gzoEJRu6a5SIqZEH2PGzfMKPUR8HnsmVXO3U7A6xqygNWGXc1876mduFz2ncaJ7l5+/Nz7zK4MsKOxPXn8i+uruXP5IubXFDvnPfoAkqCD7Woq00CisjYoODjRwece/GZ86sxy9p3opitsd4MNxeMSOsMxZlYEknU8gpEYM8r8Q47L/NuGPYhAkduNZRl6emO0BaM0d9kFphZNL2H1ikWcv8BOojDaLqxU5lUVs7+lm85Q/+6+bLrklJqo8rYgUU1ep84sp6bEh8ctxI3B4xZqSnwsnlk+aNs7ltfj87iZVeHntJllKYMN2H2glmWIxC2CkRjGGIKRWDKTb991GiL2d48L7l2/m4OtQaKxOPtaethzoofWoF3j3SXwrY+cxn2fv4DzF1QhIlQW+5hXXUx1yejvQvq6pL6a5q4IkbiFSyASt2juinCJk0ZFqclM70imsJEu/LukvprXD7YRsyyKnE/eXrc7Zer2gdl5F00v5VBbkM7eeL/tPC4Bsb97XZJcHFg/rQQY3HVkz4xycbg9hABHOiMMNL+6mGvOnIWIUOb3UBnw4klR8jYXNje0Mr3Ul7zz8rldlPk9bG5o5Wt5eUalxg8NJFPUcEWdhtrvkS0HsCwLy4KgZRHtjvA/PnjKsEHIAJXFPq45cxb3rt9DzDII4HHZ3U0WBmMs9p7oIeqka997vJtvPfkGNSU+QtE4fq+bWNyeidUVjtLTG6fLmco7UCgSo9TvoarYl7JmeqZ/p0yCbWNbkGmlRUwvO7mQ0RijYyRqStCurSkqUdTJgF3UCbuo0w//uGvI/e5+5l3ag1FcYq8HKXIKQv3hrSMpt0+Vg+rJ1w+xeEYps8qLKPa5QQSPWyjxuemNQTRuBxjBHoBv7YnQ3RsjHLWcmiBxDrWHONrZmzaIALR0R5hR5h9VEMk0f9a8qmJC0f53WbogUU0VGkimqL5FnQTBJYJL7Pah7GsJ2vu5BBHB5bL329eS+pN3qrENr1swxvQbO5lV4ScUtZKzugwnZ3jFDTR39XLn8npiccP+E8HkWpS5VYFUT2vvl+XfJNW5R2JxjnaEee9YF0c7wkRicdZuahi07R3L64nGTcrxHaUmO+3aKqCpkHY83bTYjlCUf7j2zH6VDTtCUXq7B491AMQsw09e2JOciVXu93DTJQv4+Dmz+eg9LyZL3/aValw/m7/5+8c6nXK7dlCLxeOEovFBa2FgdJUalZroNJAUSDZpRvKhrqaYPcd7kD5TeC0Dp0wbuiumfloJ7x/rIhLv/3l/bmVRyu2HykE1sLLhjeu2cKK7JdVhsJy7Eo9L+OR5c/j8xfMp83sp9nlYNL2EPc09ybuYRLfYKdP7T73N9m8ejMSx+gSoxOLJvivz+8pFpUalJiLt2iqQdF0+qbpN8uGuaz5AZbEXcUHcGMQFlcVe7rrmA0Pud82Zs1J++u/qjaUcOxiqy2fDrmZuXLeFy3+4nhvXbRl2quzyxdP4+S0XsnrlImaU+5ldGWBWhZ+//ejpVJf6KPK68LqFIq+L6lLfoGvJ9m8es07WZxc5maYhZmk6N6X60juSAin0SuiVS2bwT9efk3VXzOaGVnxuIdInmggQisRTpgNJ1+UD/dPFH+sM8fj2RmaU+TjeFem3At7jEhbWlPD3nziDIq+b6mIfAZ+733MMvJZL6qtZu6mB7z61M9mFle3f3CWCx2WX3zXGDibuPiv6lVI2DSQFMh7Sjo+kK6axLZi8I+n7dhqJG3Y3D861le55bly3Ba9bCHjdyWy5wd44neFoMoh4XHYKE5/HxZ0r6plV4e/390r3HOm6sMqKPISi8Yz/5vXTStjtZCNOdP/FLZNc26KUsmnXVoFM1Fk+86qKSWbqTwxGOFLl2kqnsS2Iz+0iErPoCEXZ3xKkPRTFMuDzuKgt91NT4rXvRD5+BtcvnZc2iAyUbraVMSarv/m3r15CVbEXwU42KUBVsZdvX70k5fYDu+q0zK6aKvSOpEAm6iyfO5bXs6XBHhDvW/nF7UqdayuVaNxiRlkRh9pCdIZj/dZf1JT4WPuFC5hV4aey2Nev1G2m3j/WSWc4hgvBLUIsbmjpiRCLW/zTp8/N+G++cskMfpRh91+hJ08oVUgaSAoo17N8RjqdOJv9Vi6ZwZJZZexp7iJxA1LkcVFZ7KVu2tAJChN1QvYc70YQjjlTeQH8Hhelfg/f/sgSltSWZx1A+l5De8i+4/A4dUZEEnm8TNZ/80y315rtairTQJJjhVobMtJPxCPZ79tXL0nuE/C6CUXjw3bLBSMxmlpD/PurB3hiWyNhJwr5PS4CPjcLa0q4/Yp6rjm7dtTXfqQ9hGUgGo/bq/adecGJAlb5UOjJE0oVkgaSHCpk98ZIPxGPZL9suuUiMYv/3HGIf3l+N4ecN3iwxxq+eNlC/vLs2dSUFlHu9yRL3WYbjAdeg9/rJhyz14DEnZK95SXZVVnM1ryqYnYd7aAjFMMydubhioCHJbMq8vacSo0XGkhyqJDdGyP9RDzS/Ybr8rEsQ1swwpoNe3nolf391l6UFLn5xpWLqSkt4m9/8xZN7aFkwACyDsaNbUHcAg3Hu4nELdxOBS2XCKfNLMvojmm0ZpX72NxwMu+XZaAtGGNWuS9vz6nUeKGBJIcK2b0x0unEif1icZOsSuh2CQurRz4NuSscZUdjOz99YS+bG06uVC8r8jCtzIcx8NirBwjFzKCAUeJzZ1wPvu9xdzd343ZK/xpn3YfB8O7RLkp8bm67vC6vwfz5Xcdxy8nV74kFjM/vOp6351RqvNDpvzlUyAywI51OfMfyejpCUQ61h4g6U1wTs5yynb7aG4vz9uEOvve7ndzy823JIOL3uphXHWBOVYASn4fSIg/7W0MpV5nvae7mRFeEmLO2JFEPPt0aFeDkdGRnLCRuGSxIdm1198a4/8WGvE7H7YnE8biFIo8bv9dNkceNxy1p06koNZloIMmhQq4NWblkBt//xBnMKPPTEYoyo8zP9z9xxrCfwlcumYHf48Iy9qymmGWoLvZSHvCmTR0ycL3E+nePcaQ9xI//9D6fWbuZ3+04TNwy1Fb4WVhdzIxSH+V+L163CxFJBtuA193vuAGvm5gxyXrwiazEyNBrVLojceZU+pMVGwemMLEMdPXG+e5v38zkTzkiJT43AzOnWMZuV2qy066tHCr02pCRTCfesKuZI51hPC77TdsYaAtFCfhSd8klJhREYnG6wjEOt4XYtr8Fv9dDt1MbpKTIzU0XL+CGC+fz/tEu/vEP7xKOxvvN8KqfVpJylXliKUom9eATEt1z9U6SxrcOdSR/l8hmYgwc6uxNtXtO3HZ5Hfes30PMskvtWk4SzNsur8vbcyo1XmggyZOJktZv7aYGvC67sJWInQoEC4519XLevKqU23eFI7QF+wwsW9DdG8MlcO25c7j18oXUTy+l2Odh4bQSfB5X2lxbwUisX4BZPKOMtmBkQMnaodeo3LG8vt+xEgaGHpPHF+VrV50KwM9e2kdPJJ4cl0m0KzWZaSDJoYm2unnDrmZeP9hGJHayoJQrkeXWSMouObtGR+qqhHMqAnz/2jMo8/efcJDuTmmoZI6zKjyD1qikmxY88E4wcUeQ5DwuznM309euOlUDh5qSNJDk0ERa3Zyo2d43iMDJN+B5lf5+52yM4XBHmM5Q+tK2Te2hQUFkKCMJMOmCdN9j3fvc+/zL87vta3GuxyVw5zjPY6bURKWBJIcm0urmvjXbB/K4pN8gcWcowsOvHOCBl/YRHaIWh8F+Ex/tp/J02YIznRas3UxKjS0NJDk0r6qY/S3ddIb6v9nlc0X1SCVqtguDx3PmVPrpicQJR+P84a0j3Pv8bvanqck+0M9e2peXN+zdzV10BKO4nLUiiWnB0XjqacHazaTU2NFAkkOX1FezdX8rLrG7UiJxi+auCDdeOHTlv0JKzIzqG1COdoSZUe7nCw+8yrb9bfZ2QFWJD4xJeycD0BVO3/U1GpGYlZwWnDhvS0xWqeuVUvmh60hyaHNDK9NLffjcLruuhtvF9FIfmxtaC31qg9TVFNsL9/qs5UvojRsa20LJIHLe/EoeuXUZAa+L2ZUB5g+x6j1fE6O8zvRfyzIYY7CcE880db1SKn/yFkhE5EERaRaRnX3aqkXkWRHZ7Xyv6vO774jIHhF5T0Q+0qf9AhF5y/ndveJk9hORIhH5pdP+qogszNe1ZKqxLci00iLqp5eyZFY59dNLmVZaNC7HSD56Vm3K2ut9uV3C/77+bB677SKuWDyd+dX22o/yQOYD6rly6sxySovcRC2LcMwialmUFrlZPLN8zM9FKdVfPu9IHgKuHtB2F/C8MWYx8LzzMyJyOrAKOMPZ56cikhjtXQPcDix2vhLHvBVoM8acAvwz8MO8XUmGCpkiJVvP7DzKcB/m45bhM0vnEXBmofVduT8So6kgeEl9NZ3hOG6XUOSxx0k6w3EuqR+/3YZKTRV5CyTGmE3AwD6da4GHnccPA9f1aX/cGNNrjNkH7AGWiUgtUG6M2WzshEqPDNgncawngSsTdyuFUujyuRt2NXPNv2zitO8+w2nffYar/3lj2jfrvce7sz5+Ig2L15X9nzmxxqa5K9xv+m6mwWRzQyvlfru+e2/MELcM5X73uOw2VGqqGesxkpnGmCMAzvfEvM05QGOf7ZqctjnO44Ht/fYxxsSADqAm1ZOKyO0isl1Eth8/nr9srCPNd5ULiXUh7x3tojdm0Ruz2HWsm7/+j9f6vVmHo3G27W8hGjfDdm2lE4ymH+BOF2TWbmogGu9fRz0aj6fN5zXQ7uYuusNxvG4Xfq8Lr9tFdzg+ZDJHpdTYGC+ztlK9+5gh2ofaZ3CjMeuAdQBLly7Na/aSXJfPzdTaTQ20BiMMfIsPRi2+99ROnj9lJQdbeli7qYHf/vlQRoPiZUWDP2ckAsKg1eOOU2aknuqc7fTdgXTWllLj11gHkmMiUmuMOeJ0WyU+KjcB8/psNxc47LTPTdHed58mEfEAFQzuSpuUUqUKaWwLEk/zntrYFuLe9bt55JX9dDrTcz3Om/lQUmVATwSEdLtWBlL/kxptIPC6hVA0u2SOSqmxMdZdW08DNzuPbwae6tO+ypmJVYc9qL7V6f7qEpGLnfGPmwbskzjW9cB6Y/KZlm98SDfWUFY09GeCf12/h85wjGKfmy9fUce0Uh/zq/xDpjnvTfEmnwgI6bzqTBkeaLTTd3XWllLjV97uSETkF8BKYJqINAH/C7gbeEJEbgUOAp8GMMa8LSJPAO8AMeArxpjE5+HV2DPAAsAzzhfAA8CjIrIH+05kVb6uZTxJl89ruBjqEvjY2bXcuWIRi2eUsfNQJ81dYaaVuuhpzXx6cuLOIJ10dyqnzixn34nurLL69pVY7Ol2CV6nW01nbSk1PuQtkBhjbkzzqyvTbP8D4Acp2rcDZ6ZoD+MEoqlkYH1yn9vFtFIf7Wky8oIdRH5+yzIuWFhFadHJqbzffPINWroj6fdL0ZYICEezrO2RSPWeKqtvJhKLPfsHIg+bG1r5WlZnopTKtfEy2K4ysGFXM63dEYLROIJ9dxCNWzS1hYastWEZuGLxNFwDZlQFI/EhB92rSwYvPEwEhGyNtuhXYrHn9DJ/ss0YMy4Xeyo11WggmSASYyO9MbvHzwCRuEkOVww3ODQwiHzvqZ0Eh6knniplfCIg3PLQtpT7DDXiMZoZbYkqiAMrKo7HxZ5KTTUaSCaItZsaiMTig9Z+ZDq7YOBMr8a20LD7RNIMeKxcMoN5VYGUx5hbFcjwjLIzsApitl1jSqn80aSNE0RjW5DOoUa5hzFwplcmhrq7+IdrzxxUcbDY5+Yfrh00nJUThVzsqZQamt6RTADhaJwZZUU0ZXAXkc7AmV6ZqCn1Dfn7Yp8by9jpStwuyXsp20It9lRKDU3vSMaxcNROKbL/RA9HO0YeRMCu1JiNxJBKulxYazc1UBHwsnhGGUtmlbN4RhkVAW/GKU+UUpOHBpJxqDcW51hnmENtQf7w1mG++NA2DndkN922LxEGZSUeSonPzbyq4iEDQ2NbcFBwGq9lhZVS+aVdW+NIJGbRHozQ3RvjncOd/HTDXt450jnq486p8CezEicGqj0ukilV+g6pF7mF+un2IsGhptfqLCqlVILekYwDkZhFc2eYprYge5q7+Yffv8NXf/HnZBC5bFHKpMYZcQn843VnDRqo/tqHFlNT6qPI68LrFrs8MDCr4uSsq6ECQ6FT5iulxg+9IymQDbuaWbNxLwdbg8ws83PdubPZdayLX7/eRNSZ47t4RimrVy7i3HmVfOj/bBz2mOVFbjp7T3ZhuQW+fuXi5AD1wIHqs+dWJhcIlhZ5ON7di8ctGGOGnV472gWGSqnJQwNJBlJl2x3NG+bz7xzj755+G5dAic/FgdYevv9f7yTzVE0r9XHb5XVcdfpMfG431cPMngL7bsJAMr27S+xZVWfPrUy7z8BZUInrzDQw6CwqpRRoIBlWYkW51y39su1+n8Gf8IcTtwztwQg/eWEPgiFuwcHWXiLOYIVL4OZLFvLppXPxe92U+b3UlPgGrUpPxQChqIXX5UqmWQ9FLe5+5t2Mz1MDg1JqJDSQDCNdtt21mxoyftONW4aOUJTOUBTLGA629hCOxPtVGiz3eyjyuPjCJQvwul1MLyvC32dWVLnfk6wlkkribiQRdETAWIZ9LTqLSimVXzrYPozRTHONW4bWngiNrUHagxFOdPfyT396j9aeaDKIFHvdLKgKUBHwMqeqmOoSH3OrAv2CCMBtl9fl7qKUUiqH9I5kGCOZ5mo5dyAdzh1IOBrnV6818YutBwk7AcTtEqqKvVQGPPTGDHFj+OoHF1FZnHo85GtXncoT2xtpak+d3mRaiZf2UAwxJysIWgYWTy8ZxdUrpdTw9I5kGNlMc7UsQ1tPhIOtQdqCEWKWxZ/eOcbND27j5y/vJxy1qAh4+fqVp/D9j5/B3MpienrjzKrw8/9edxZXnT5ryHP5x+vOYn51MZUBT3LluQh88txa/unT51JV7EWAWNxCgKpiL9++eknu/yhKKdWHTIHqtP0sXbrUbN++Pat9hpvNZFmGzrB9BxJ3pl690dTOmg17ef9YN2DnuvrUeXP43EULKPXbdzdlfi/VJT7cGQymZ3Iu2c66UkqpTInIa8aYpSl/p4Fk5FIFkKa2IOs27eOlPSeS233wtOncdkUdtc5iv1SD6UopNZ4NFUh0jGQEEmMgneGTAaQzFOXRLQd4asdhYk7b6bVlrF65iDNmVwAgYk8hriz2IpL5XYhSSo1nGkiyMHAaL0A0bvHUjsM8uuUAXc703Fnlfr58RR0rT5ueDBgBn5uakiJ8Hh2WUkpNLhpIMpAqgBhjeGlPC+s2NXCo3U7xXuJz89mL5vNX589NBgy3S6gu8VHmH1z/XCmlJgMNJENIFUAA3jvaxZqNe3mzqQOwFwJ+/OzZ3Hzpgn7Td0cymK6UUhONBpIU0gWQ5s4wD7y8n2ffOZZsu6iumjtW1LOw5uR6DZ/HxbRSHUxXSk0NGkj6SBdAgpEYj29r5IntTURi9oLC+mkl3LminqULq5PbuUSoKvZRHvDoYLpSasrQQMLglegJccvw328f5cGX99PaEwGgusTHFy9dyNVnzurXZVXs8zCt1IfHrYPpSqmpZUoHklTrQBJeO9DGmo17aTjeA0CRx8Vnls5l1YXzCfhOdll5XC6qS32UFk3pP6VSagqbku9+QwWQAy09rN3UwJaG1mTbh0+fyZcuW8iMcn+/bcsDXqqLM0vzrpRSk9WUCyRxy9DYFhwUQNqCER5+5QC/f/NwssDUOXMrWL1yEafOLOu3rQ6mK6XUSVMykPQNIpGYxa9fb+KxVw/SE7HL1M6pDHD78nouP6Wm36C5DqYrpdRgUy6QJBhjeOG949z/YgPHOnsBKPN7uOmSBXzinNl4BwyalxR5qCnRwXSllBpowgcSEbkauAdwAz8zxtw93D5vH+5gzYa9vHOkCwCPS7j23Nl84eIFlAf6r0D3uFzUlPoo0cF0pZRKaUK/O4qIG/g34C+AJmCbiDxtjHkn3T6HO0L8j1/sSP58+SnTuH15XcpCVRUBL1U6mK6UUkOa0IEEWAbsMcY0AIjI48C1QNpA0hWOUQqcOrOU1SsXcc7cykHb6GC6UkplbqIHkjlAY5+fm4CLBm4kIrcDtzs/dh/44V++dwB4FqYBJwZuP8lMhWuEqXGdeo2Tx0S8zgXpfjHRA0mqPqdBlbqMMeuAdYN2FtmerlDLZDEVrhGmxnXqNU4ek+06J/oUpCZgXp+f5wKHC3QuSik1JU30QLINWCwidSLiA1YBTxf4nJRSakqZ0F1bxpiYiHwV+G/s6b8PGmPezuIQg7q7JqGpcI0wNa5Tr3HymFTXKcYMGlJQSimlMjbRu7aUUkoVmAYSpZRSozJlAomI7BeRt0Rkh4hsd9qqReRZEdntfK8q9HlmS0QeFJFmEdnZpy3tdYnId0Rkj4i8JyIfKcxZZyfNNf69iBxyXs8dIvLRPr+biNc4T0ReEJF3ReRtEfm60z5pXsshrnGyvZZ+EdkqIm841/n/OO2T5rUcxBgzJb6A/cC0AW3/G7jLeXwX8MNCn+cIrms5cD6wc7jrAk4H3gCKgDpgL+Au9DWM8Br/Hvhmim0nZBQnRQAABO9JREFU6jXWAuc7j8uA951rmTSv5RDXONleSwFKncde4FXg4sn0Wg78mjJ3JGlcCzzsPH4YuK6A5zIixphNQOuA5nTXdS3wuDGm1xizD9iDnWZmXEtzjelM1Gs8Yox53XncBbyLnblh0ryWQ1xjOhPuGgGMrdv50et8GSbRaznQVAokBviTiLzmpEwBmGmMOQL2P3JgRsHOLrfSXVeqlDJD/Uce774qIm86XV+JboIJf40ishA4D/uT7KR8LQdcI0yy11JE3CKyA2gGnjXGTNrXEqZWILnMGHM+cA3wFRFZXugTKoCMUspMEGuARcC5wBHg/zjtE/oaRaQU+DXwDWNM51CbpmibENeZ4hon3WtpjIkbY87FzraxTETOHGLzCXudCVMmkBhjDjvfm4HfYt86HhORWgDne3PhzjCn0l3XpEkpY4w55vxntYD7OdkVMGGvUUS82G+w/2GM+Y3TPKley1TXOBlfywRjTDuwAbiaSfZa9jUlAomIlIhIWeIx8GFgJ3Y6lZudzW4GnirMGeZcuut6GlglIkUiUgcsBrYW4PxGLfEf0vFJ7NcTJug1il27+QHgXWPMj/v8atK8lumucRK+ltNFpNJ5HACuAnYxiV7LQQo92j8WX0A99qyIN4C3gf/ptNcAzwO7ne/VhT7XEVzbL7C7A6LYn2xuHeq6gP+JPSvkPeCaQp//KK7xUeAt4E3s/4i1E/waL8fuzngT2OF8fXQyvZZDXONkey3PBv7sXM9O4O+c9knzWg780hQpSimlRmVKdG0ppZTKHw0kSimlRkUDiVJKqVHRQKKUUmpUNJAopZQaFQ0kSuWZiMwWkSfz/Bx/SKxdUGqs6fRfpZRSo6J3JEoNQUQ+79SW2CEia51kfN0i8gOn3sQWEZnpbLvI+XmbiHxfRLqd9oWJWioicouI/EZE/ujUpfjffZ7rwyKyWUReF5FfOTmpBp5PrYhscs5np4hc4bTvF5FpInJnn7oe+0TkhUyPrdRIaSBRKg0R+QBwA3bCz3OBOPA5oATYYow5B9gEfNnZ5R7gHmPMhQydK+lc57hnATc4BZ+mAd8FrjJ2ctHtwN+k2PezwH8753MO9urwJGPMfc7vLsTOAvDjLI6t1Ih4Cn0CSo1jVwIXANvsNFEEsBPtRYDfO9u8BvyF8/gSTtaYeAz4pzTHfd4Y0wEgIu8AC4BK7AJHLzvP5QM2p9h3G/Cgk/zwd8aYHSm2ATuorTfG/KeI/GWGx1ZqRDSQKJWeAA8bY77Tr1Hkm+bk4GKc7P8f9fZ5nNhfsOtW3DjguS4C1jo//p0x5mmnBMLHgEdF5EfGmEcG7HMLdnD6ap/rGHRspXJFu7aUSu954HoRmQHJmtsLhth+C/BXzuNVWT7XFuAyETnFea5iETnVGPOqMeZc5+tp5/mbjTH3Y2fSPb/vQUTkAuCbwOeNnZY97bGzPD+l0tJAolQaxph3sMcW/iQibwLPYtcdT+cbwN+IyFZnu44snus4cAvwC+e5tgBLUmy6EtghIn/GDlr3DPj9V4Hq/7+9O7ZBGIqBAHpuWYdBaKFlppTswkp0lKbJAsSBNO8NYLk7fZ2ln+S5Fu6PL2bDJs5/YSdVdUry7u6uqmuSW3dfjt4Lfk1HAvs5J1nWD5xeSe4H7wN/4UUCwIiOBIARQQLAiCABYESQADAiSAAY+QD9lcfaG3wonwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Engine size as potential predictor variable of price\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n",
    "plt.ylim(0,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the engine-size goes up, the price goes up: this indicates a positive direct correlation between these two variables. Engine size seems like a pretty good predictor of price since the regression line is almost a perfect diagonal line.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can examine the correlation between 'engine-size' and 'price' and see it's approximately  0.87"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>engine-size</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.872335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.872335</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             engine-size     price\n",
       "engine-size     1.000000  0.872335\n",
       "price           0.872335  1.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Highway mpg is a potential predictor variable of price "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f34891e5860>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>As the highway-mpg goes up, the price goes down: this indicates an inverse/negative relationship between these two variables. Highway mpg could potentially be a predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'highway-mpg' and 'price' and see it's approximately  -0.704"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>highway-mpg</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>-0.704692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             highway-mpg     price\n",
       "highway-mpg     1.000000 -0.704692\n",
       "price          -0.704692  1.000000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Weak Linear Relationship</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if \"Peak-rpm\" as a predictor variable of \"price\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f348915e9e8>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Peak rpm does not seem like a good predictor of the price at all since the regression line is close to horizontal. Also, the data points are very scattered and far from the fitted line, showing lots of variability. Therefore it's it is not a reliable variable.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can examine the correlation between 'peak-rpm' and 'price' and see it's approximately -0.101616 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.101616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.101616</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          peak-rpm     price\n",
       "peak-rpm  1.000000 -0.101616\n",
       "price    -0.101616  1.000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 id=\"correlation_causation\">Correlation and Causation</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><b>Correlation</b>: a measure of the extent of interdependence between variables.</p>\n",
    "\n",
    "<p><b>Causation</b>: the relationship between cause and effect between two variables.</p>\n",
    "\n",
    "<p>It is important to know the difference between these two and that correlation does not imply causation. Determining correlation is much simpler  the determining causation as causation may require independent experimentation.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p3>Pearson Correlation</p>\n",
    "<p>The Pearson Correlation measures the linear dependence between two variables X and Y.</p>\n",
    "<p>The resulting coefficient is a value between -1 and 1 inclusive, where:</p>\n",
    "<ul>\n",
    "    <li><b>1</b>: Total positive linear correlation.</li>\n",
    "    <li><b>0</b>: No linear correlation, the two variables most likely do not affect each other.</li>\n",
    "    <li><b>-1</b>: Total negative linear correlation.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Pearson Correlation is the default method of the function \"corr\".  Like before we can calculate the Pearson Correlation of the of the 'int64' or 'float64'  variables.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
       "      <th>width</th>\n",
       "      <th>height</th>\n",
       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</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>diesel</th>\n",
       "      <th>gas</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.466264</td>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.365404</td>\n",
       "      <td>-0.242423</td>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.233118</td>\n",
       "      <td>-0.110581</td>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.008245</td>\n",
       "      <td>-0.182196</td>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.279740</td>\n",
       "      <td>-0.035527</td>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.066171</td>\n",
       "      <td>-0.196735</td>\n",
       "      <td>0.196735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>normalized-losses</th>\n",
       "      <td>0.466264</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.101546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>-0.535987</td>\n",
       "      <td>-0.056661</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>-0.307237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>-0.365404</td>\n",
       "      <td>0.019424</td>\n",
       "      <td>0.876024</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>-0.211187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>-0.242423</td>\n",
       "      <td>0.086802</td>\n",
       "      <td>0.814507</td>\n",
       "      <td>0.857170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>-0.244356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>-0.550160</td>\n",
       "      <td>-0.373737</td>\n",
       "      <td>0.590742</td>\n",
       "      <td>0.492063</td>\n",
       "      <td>0.306002</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>-0.281578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>-0.233118</td>\n",
       "      <td>0.099404</td>\n",
       "      <td>0.782097</td>\n",
       "      <td>0.880665</td>\n",
       "      <td>0.866201</td>\n",
       "      <td>0.307581</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>-0.221046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.110581</td>\n",
       "      <td>0.112360</td>\n",
       "      <td>0.572027</td>\n",
       "      <td>0.685025</td>\n",
       "      <td>0.729436</td>\n",
       "      <td>0.074694</td>\n",
       "      <td>0.849072</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>-0.070779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>-0.140019</td>\n",
       "      <td>-0.029862</td>\n",
       "      <td>0.493244</td>\n",
       "      <td>0.608971</td>\n",
       "      <td>0.544885</td>\n",
       "      <td>0.180449</td>\n",
       "      <td>0.644060</td>\n",
       "      <td>0.572609</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>-0.054458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.008245</td>\n",
       "      <td>0.055563</td>\n",
       "      <td>0.158502</td>\n",
       "      <td>0.124139</td>\n",
       "      <td>0.188829</td>\n",
       "      <td>-0.062704</td>\n",
       "      <td>0.167562</td>\n",
       "      <td>0.209523</td>\n",
       "      <td>-0.055390</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>-0.241303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>-0.182196</td>\n",
       "      <td>-0.114713</td>\n",
       "      <td>0.250313</td>\n",
       "      <td>0.159733</td>\n",
       "      <td>0.189867</td>\n",
       "      <td>0.259737</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>0.028889</td>\n",
       "      <td>0.001263</td>\n",
       "      <td>0.187923</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.985231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.075819</td>\n",
       "      <td>0.217299</td>\n",
       "      <td>0.371147</td>\n",
       "      <td>0.579821</td>\n",
       "      <td>0.615077</td>\n",
       "      <td>-0.087027</td>\n",
       "      <td>0.757976</td>\n",
       "      <td>0.822676</td>\n",
       "      <td>0.566936</td>\n",
       "      <td>0.098462</td>\n",
       "      <td>-0.214514</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>0.169053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>0.279740</td>\n",
       "      <td>0.239543</td>\n",
       "      <td>-0.360305</td>\n",
       "      <td>-0.285970</td>\n",
       "      <td>-0.245800</td>\n",
       "      <td>-0.309974</td>\n",
       "      <td>-0.279361</td>\n",
       "      <td>-0.256733</td>\n",
       "      <td>-0.267392</td>\n",
       "      <td>-0.065713</td>\n",
       "      <td>-0.435780</td>\n",
       "      <td>0.107885</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.475812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>-0.035527</td>\n",
       "      <td>-0.225016</td>\n",
       "      <td>-0.470606</td>\n",
       "      <td>-0.665192</td>\n",
       "      <td>-0.633531</td>\n",
       "      <td>-0.049800</td>\n",
       "      <td>-0.749543</td>\n",
       "      <td>-0.650546</td>\n",
       "      <td>-0.582027</td>\n",
       "      <td>-0.034696</td>\n",
       "      <td>0.331425</td>\n",
       "      <td>-0.822214</td>\n",
       "      <td>-0.115413</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>-0.265676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.036233</td>\n",
       "      <td>-0.181877</td>\n",
       "      <td>-0.543304</td>\n",
       "      <td>-0.698142</td>\n",
       "      <td>-0.680635</td>\n",
       "      <td>-0.104812</td>\n",
       "      <td>-0.794889</td>\n",
       "      <td>-0.679571</td>\n",
       "      <td>-0.591309</td>\n",
       "      <td>-0.035201</td>\n",
       "      <td>0.268465</td>\n",
       "      <td>-0.804575</td>\n",
       "      <td>-0.058598</td>\n",
       "      <td>0.972044</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>-0.198690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.082391</td>\n",
       "      <td>0.133999</td>\n",
       "      <td>0.584642</td>\n",
       "      <td>0.690628</td>\n",
       "      <td>0.751265</td>\n",
       "      <td>0.135486</td>\n",
       "      <td>0.834415</td>\n",
       "      <td>0.872335</td>\n",
       "      <td>0.543155</td>\n",
       "      <td>0.082310</td>\n",
       "      <td>0.071107</td>\n",
       "      <td>0.809575</td>\n",
       "      <td>-0.101616</td>\n",
       "      <td>-0.686571</td>\n",
       "      <td>-0.704692</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.110326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-L/100km</th>\n",
       "      <td>0.066171</td>\n",
       "      <td>0.238567</td>\n",
       "      <td>0.476153</td>\n",
       "      <td>0.657373</td>\n",
       "      <td>0.673363</td>\n",
       "      <td>0.003811</td>\n",
       "      <td>0.785353</td>\n",
       "      <td>0.745059</td>\n",
       "      <td>0.554610</td>\n",
       "      <td>0.037300</td>\n",
       "      <td>-0.299372</td>\n",
       "      <td>0.889488</td>\n",
       "      <td>0.115830</td>\n",
       "      <td>-0.949713</td>\n",
       "      <td>-0.930028</td>\n",
       "      <td>0.789898</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>0.241282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diesel</th>\n",
       "      <td>-0.196735</td>\n",
       "      <td>-0.101546</td>\n",
       "      <td>0.307237</td>\n",
       "      <td>0.211187</td>\n",
       "      <td>0.244356</td>\n",
       "      <td>0.281578</td>\n",
       "      <td>0.221046</td>\n",
       "      <td>0.070779</td>\n",
       "      <td>0.054458</td>\n",
       "      <td>0.241303</td>\n",
       "      <td>0.985231</td>\n",
       "      <td>-0.169053</td>\n",
       "      <td>-0.475812</td>\n",
       "      <td>0.265676</td>\n",
       "      <td>0.198690</td>\n",
       "      <td>0.110326</td>\n",
       "      <td>-0.241282</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gas</th>\n",
       "      <td>0.196735</td>\n",
       "      <td>0.101546</td>\n",
       "      <td>-0.307237</td>\n",
       "      <td>-0.211187</td>\n",
       "      <td>-0.244356</td>\n",
       "      <td>-0.281578</td>\n",
       "      <td>-0.221046</td>\n",
       "      <td>-0.070779</td>\n",
       "      <td>-0.054458</td>\n",
       "      <td>-0.241303</td>\n",
       "      <td>-0.985231</td>\n",
       "      <td>0.169053</td>\n",
       "      <td>0.475812</td>\n",
       "      <td>-0.265676</td>\n",
       "      <td>-0.198690</td>\n",
       "      <td>-0.110326</td>\n",
       "      <td>0.241282</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   symboling  normalized-losses  wheel-base    length  \\\n",
       "symboling           1.000000           0.466264   -0.535987 -0.365404   \n",
       "normalized-losses   0.466264           1.000000   -0.056661  0.019424   \n",
       "wheel-base         -0.535987          -0.056661    1.000000  0.876024   \n",
       "length             -0.365404           0.019424    0.876024  1.000000   \n",
       "width              -0.242423           0.086802    0.814507  0.857170   \n",
       "height             -0.550160          -0.373737    0.590742  0.492063   \n",
       "curb-weight        -0.233118           0.099404    0.782097  0.880665   \n",
       "engine-size        -0.110581           0.112360    0.572027  0.685025   \n",
       "bore               -0.140019          -0.029862    0.493244  0.608971   \n",
       "stroke             -0.008245           0.055563    0.158502  0.124139   \n",
       "compression-ratio  -0.182196          -0.114713    0.250313  0.159733   \n",
       "horsepower          0.075819           0.217299    0.371147  0.579821   \n",
       "peak-rpm            0.279740           0.239543   -0.360305 -0.285970   \n",
       "city-mpg           -0.035527          -0.225016   -0.470606 -0.665192   \n",
       "highway-mpg         0.036233          -0.181877   -0.543304 -0.698142   \n",
       "price              -0.082391           0.133999    0.584642  0.690628   \n",
       "city-L/100km        0.066171           0.238567    0.476153  0.657373   \n",
       "diesel             -0.196735          -0.101546    0.307237  0.211187   \n",
       "gas                 0.196735           0.101546   -0.307237 -0.211187   \n",
       "\n",
       "                      width    height  curb-weight  engine-size      bore  \\\n",
       "symboling         -0.242423 -0.550160    -0.233118    -0.110581 -0.140019   \n",
       "normalized-losses  0.086802 -0.373737     0.099404     0.112360 -0.029862   \n",
       "wheel-base         0.814507  0.590742     0.782097     0.572027  0.493244   \n",
       "length             0.857170  0.492063     0.880665     0.685025  0.608971   \n",
       "width              1.000000  0.306002     0.866201     0.729436  0.544885   \n",
       "height             0.306002  1.000000     0.307581     0.074694  0.180449   \n",
       "curb-weight        0.866201  0.307581     1.000000     0.849072  0.644060   \n",
       "engine-size        0.729436  0.074694     0.849072     1.000000  0.572609   \n",
       "bore               0.544885  0.180449     0.644060     0.572609  1.000000   \n",
       "stroke             0.188829 -0.062704     0.167562     0.209523 -0.055390   \n",
       "compression-ratio  0.189867  0.259737     0.156433     0.028889  0.001263   \n",
       "horsepower         0.615077 -0.087027     0.757976     0.822676  0.566936   \n",
       "peak-rpm          -0.245800 -0.309974    -0.279361    -0.256733 -0.267392   \n",
       "city-mpg          -0.633531 -0.049800    -0.749543    -0.650546 -0.582027   \n",
       "highway-mpg       -0.680635 -0.104812    -0.794889    -0.679571 -0.591309   \n",
       "price              0.751265  0.135486     0.834415     0.872335  0.543155   \n",
       "city-L/100km       0.673363  0.003811     0.785353     0.745059  0.554610   \n",
       "diesel             0.244356  0.281578     0.221046     0.070779  0.054458   \n",
       "gas               -0.244356 -0.281578    -0.221046    -0.070779 -0.054458   \n",
       "\n",
       "                     stroke  compression-ratio  horsepower  peak-rpm  \\\n",
       "symboling         -0.008245          -0.182196    0.075819  0.279740   \n",
       "normalized-losses  0.055563          -0.114713    0.217299  0.239543   \n",
       "wheel-base         0.158502           0.250313    0.371147 -0.360305   \n",
       "length             0.124139           0.159733    0.579821 -0.285970   \n",
       "width              0.188829           0.189867    0.615077 -0.245800   \n",
       "height            -0.062704           0.259737   -0.087027 -0.309974   \n",
       "curb-weight        0.167562           0.156433    0.757976 -0.279361   \n",
       "engine-size        0.209523           0.028889    0.822676 -0.256733   \n",
       "bore              -0.055390           0.001263    0.566936 -0.267392   \n",
       "stroke             1.000000           0.187923    0.098462 -0.065713   \n",
       "compression-ratio  0.187923           1.000000   -0.214514 -0.435780   \n",
       "horsepower         0.098462          -0.214514    1.000000  0.107885   \n",
       "peak-rpm          -0.065713          -0.435780    0.107885  1.000000   \n",
       "city-mpg          -0.034696           0.331425   -0.822214 -0.115413   \n",
       "highway-mpg       -0.035201           0.268465   -0.804575 -0.058598   \n",
       "price              0.082310           0.071107    0.809575 -0.101616   \n",
       "city-L/100km       0.037300          -0.299372    0.889488  0.115830   \n",
       "diesel             0.241303           0.985231   -0.169053 -0.475812   \n",
       "gas               -0.241303          -0.985231    0.169053  0.475812   \n",
       "\n",
       "                   city-mpg  highway-mpg     price  city-L/100km    diesel  \\\n",
       "symboling         -0.035527     0.036233 -0.082391      0.066171 -0.196735   \n",
       "normalized-losses -0.225016    -0.181877  0.133999      0.238567 -0.101546   \n",
       "wheel-base        -0.470606    -0.543304  0.584642      0.476153  0.307237   \n",
       "length            -0.665192    -0.698142  0.690628      0.657373  0.211187   \n",
       "width             -0.633531    -0.680635  0.751265      0.673363  0.244356   \n",
       "height            -0.049800    -0.104812  0.135486      0.003811  0.281578   \n",
       "curb-weight       -0.749543    -0.794889  0.834415      0.785353  0.221046   \n",
       "engine-size       -0.650546    -0.679571  0.872335      0.745059  0.070779   \n",
       "bore              -0.582027    -0.591309  0.543155      0.554610  0.054458   \n",
       "stroke            -0.034696    -0.035201  0.082310      0.037300  0.241303   \n",
       "compression-ratio  0.331425     0.268465  0.071107     -0.299372  0.985231   \n",
       "horsepower        -0.822214    -0.804575  0.809575      0.889488 -0.169053   \n",
       "peak-rpm          -0.115413    -0.058598 -0.101616      0.115830 -0.475812   \n",
       "city-mpg           1.000000     0.972044 -0.686571     -0.949713  0.265676   \n",
       "highway-mpg        0.972044     1.000000 -0.704692     -0.930028  0.198690   \n",
       "price             -0.686571    -0.704692  1.000000      0.789898  0.110326   \n",
       "city-L/100km      -0.949713    -0.930028  0.789898      1.000000 -0.241282   \n",
       "diesel             0.265676     0.198690  0.110326     -0.241282  1.000000   \n",
       "gas               -0.265676    -0.198690 -0.110326      0.241282 -1.000000   \n",
       "\n",
       "                        gas  \n",
       "symboling          0.196735  \n",
       "normalized-losses  0.101546  \n",
       "wheel-base        -0.307237  \n",
       "length            -0.211187  \n",
       "width             -0.244356  \n",
       "height            -0.281578  \n",
       "curb-weight       -0.221046  \n",
       "engine-size       -0.070779  \n",
       "bore              -0.054458  \n",
       "stroke            -0.241303  \n",
       "compression-ratio -0.985231  \n",
       "horsepower         0.169053  \n",
       "peak-rpm           0.475812  \n",
       "city-mpg          -0.265676  \n",
       "highway-mpg       -0.198690  \n",
       "price             -0.110326  \n",
       "city-L/100km       0.241282  \n",
       "diesel            -1.000000  \n",
       "gas                1.000000  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " sometimes we would like to know the significant of the correlation estimate. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>: \n",
    "<p>What is this P-value? The P-value is the probability value that the correlation between these two variables is statistically significant. Normally, we choose a significance level of 0.05, which means that we are 95% confident that the correlation between the variables is significant.</p>\n",
    "\n",
    "By convention, when the\n",
    "<ul>\n",
    "    <li>p-value is $<$ 0.001: we say there is strong evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.05: there is moderate evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $<$ 0.1: there is weak evidence that the correlation is significant.</li>\n",
    "    <li>the p-value is $>$ 0.1: there is no evidence that the correlation is significant.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can obtain this information using  \"stats\" module in the \"scipy\"  library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Wheel-base vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'wheel-base' and 'price'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5846418222655081  with a P-value of P = 8.076488270732955e-20\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['wheel-base'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between wheel-base and price is statistically significant, although the linear relationship isn't extremely strong (~0.585)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'horsepower' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8095745670036559  with a P-value of P =  6.36905742825998e-48\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['horsepower'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between horsepower and price is statistically significant, and the linear relationship is quite strong (~0.809, close to 1)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Length vs Price</h3>\n",
    "\n",
    "Let's calculate the  Pearson Correlation Coefficient and P-value of 'length' and 'price'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.690628380448364  with a P-value of P =  8.016477466159053e-30\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['length'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between length and price is statistically significant, and the linear relationship is moderately strong (~0.691).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'width' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7512653440522674  with a P-value of P = 9.200335510481426e-38\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['width'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "\n",
    "Since the p-value is < 0.001, the correlation between width and price is statistically significant, and the linear relationship is quite strong (~0.751)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the Pearson Correlation Coefficient and P-value of 'curb-weight' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8344145257702846  with a P-value of P =  2.1895772388936997e-53\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['curb-weight'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between curb-weight and price is statistically significant, and the linear relationship is quite strong (~0.834).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Engine-size vs Price</h3>\n",
    "\n",
    "Let's calculate the Pearson Correlation Coefficient and P-value of 'engine-size' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8723351674455185  with a P-value of P = 9.265491622197996e-64\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['engine-size'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =\", p_value) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between engine-size and price is statistically significant, and the linear relationship is very strong (~0.872).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Bore vs Price</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Let's calculate the  Pearson Correlation Coefficient and P-value of 'bore' and 'price':"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5431553832626602  with a P-value of P =   8.049189483935364e-17\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['bore'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P =  \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between bore and price is statistically significant, but the linear relationship is only moderate (~0.521).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We can relate the process for each 'City-mpg'  and 'Highway-mpg':"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>City-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6865710067844677  with a P-value of P =  2.3211320655676368e-29\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['city-mpg'], df['price'])\n",
    "print(\"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h5>Conclusion:</h5>\n",
    "<p>Since the p-value is $<$ 0.001, the correlation between city-mpg and price is statistically significant, and the coefficient of ~ -0.687 shows that the relationship is negative and moderately strong.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway-mpg vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.7046922650589529  with a P-value of P =  1.7495471144476807e-31\n"
     ]
    }
   ],
   "source": [
    "pearson_coef, p_value = stats.pearsonr(df['highway-mpg'], df['price'])\n",
    "print( \"The Pearson Correlation Coefficient is\", pearson_coef, \" with a P-value of P = \", p_value ) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusion:\n",
    "Since the p-value is < 0.001, the correlation between highway-mpg and price is statistically significant, and the coefficient of ~ -0.705 shows that the relationship is negative and moderately strong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Linear Regression and Multiple Linear Regression</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h4>Linear Regression</h4>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<p>One example of a Data  Model that we will be using is</p>\n",
    "<b>Simple Linear Regression</b>.\n",
    "\n",
    "<br>\n",
    "<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
    "<ul>\n",
    "    <li>The predictor/independent variable (X)</li>\n",
    "    <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
    "</ul>\n",
    "\n",
    "<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    " Y: Response \\ Variable\\\\\n",
    " X: Predictor \\ Variables\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " <b>Linear function:</b>\n",
    "$$\n",
    "Yhat = a + b  X\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<ul>\n",
    "    <li>a refers to the <b>intercept</b> of the regression 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": 23,
   "metadata": {},
   "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": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 24,
     "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": 25,
   "metadata": {},
   "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": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 26,
     "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": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
       "       20345.17153508])"
      ]
     },
     "execution_count": 27,
     "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": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38423.3058581574"
      ]
     },
     "execution_count": 28,
     "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": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-821.73337832])"
      ]
     },
     "execution_count": 29,
     "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": [
    "<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": 30,
   "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": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 31,
     "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": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-15806.62462632922"
      ]
     },
     "execution_count": 32,
     "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": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([53.49574423,  4.70770099, 81.53026382, 36.05748882])"
      ]
     },
     "execution_count": 33,
     "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": [
    "<h3>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": 34,
   "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": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 48270.37765401766)"
      ]
     },
     "execution_count": 35,
     "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": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 47422.919330307624)"
      ]
     },
     "execution_count": 36,
     "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": [
    "<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": 37,
   "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>"
   ]
  },
  {
   "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": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_hat = lm.predict(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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": [
    "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>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": "code",
   "execution_count": 40,
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "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": 43,
   "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": [
    "PlotPolly(p, x, y, 'highway-mpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.55663829e+00,  2.04754306e+02, -8.96543312e+03,  1.37923594e+05])"
      ]
     },
     "execution_count": 44,
     "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": [
    "<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": 45,
   "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": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr=PolynomialFeatures(degree=2)\n",
    "pr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 4)"
      ]
     },
     "execution_count": 48,
     "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": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(201, 15)"
      ]
     },
     "execution_count": 49,
     "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": 50,
   "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": 51,
   "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 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "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": 52,
     "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": 53,
   "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"
     ]
    },
    {
     "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": 53,
     "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": 54,
   "metadata": {},
   "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": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ypipe=pipe.predict(Z)\n",
    "ypipe[0:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Measures for In-Sample Evaluation</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
    "\n",
    "<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
    "<ul>\n",
    "    <li><b>R^2 / R-squared</b></li>\n",
    "    <li><b>Mean Squared Error (MSE)</b></li>\n",
    "</ul>\n",
    "    \n",
    "<b>R-squared</b>\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": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The R-square is:  0.4965911884339176\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": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output of the first four predicted value is:  [16236.50464347 16236.50464347 17058.23802179 13771.3045085 ]\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": 57,
   "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": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean square error of price and predicted value is:  31635042.944639888\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": 59,
   "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\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate the MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " we produce a prediction "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "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": 61,
   "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>"
   ]
  },
  {
   "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": 62,
   "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": 63,
   "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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>MSE</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the MSE:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20474146.426361218"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(df['price'], p(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Prediction and Decision Making</h2>\n",
    "<h3>Prediction</h3>\n",
    "\n",
    "<p>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": 65,
   "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": 66,
   "metadata": {},
   "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": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 67,
     "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([37601.57247984, 36779.83910151, 35958.10572319, 35136.37234487,\n",
       "       34314.63896655])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat=lm.predict(new_input)\n",
    "yhat[0:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can plot the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "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>"
   ]
  },
  {
   "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.<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>"
   ]
  }
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