EDA Part 2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Exploratory Data Analysis - part 2</h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>1. Import Data </h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import libraries "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " load data and store in dataframe df:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>make</th>\n",
       "      <th>fuel-type</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>...</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>fuel-system</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>?</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>...</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111</td>\n",
       "      <td>5000</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>13495</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>?</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>convertible</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>...</td>\n",
       "      <td>130</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.47</td>\n",
       "      <td>2.68</td>\n",
       "      <td>9.0</td>\n",
       "      <td>111</td>\n",
       "      <td>5000</td>\n",
       "      <td>21</td>\n",
       "      <td>27</td>\n",
       "      <td>16500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>?</td>\n",
       "      <td>alfa-romero</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>two</td>\n",
       "      <td>hatchback</td>\n",
       "      <td>rwd</td>\n",
       "      <td>front</td>\n",
       "      <td>...</td>\n",
       "      <td>152</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>2.68</td>\n",
       "      <td>3.47</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154</td>\n",
       "      <td>5000</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>fwd</td>\n",
       "      <td>front</td>\n",
       "      <td>...</td>\n",
       "      <td>109</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102</td>\n",
       "      <td>5500</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>13950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>audi</td>\n",
       "      <td>gas</td>\n",
       "      <td>std</td>\n",
       "      <td>four</td>\n",
       "      <td>sedan</td>\n",
       "      <td>4wd</td>\n",
       "      <td>front</td>\n",
       "      <td>...</td>\n",
       "      <td>136</td>\n",
       "      <td>mpfi</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115</td>\n",
       "      <td>5500</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>17450</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 27 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  symboling normalized-losses         make fuel-type aspiration  \\\n",
       "0           0          3                 ?  alfa-romero       gas        std   \n",
       "1           1          3                 ?  alfa-romero       gas        std   \n",
       "2           2          1                 ?  alfa-romero       gas        std   \n",
       "3           3          2               164         audi       gas        std   \n",
       "4           4          2               164         audi       gas        std   \n",
       "\n",
       "  num-of-doors   body-style drive-wheels engine-location  ...  engine-size  \\\n",
       "0          two  convertible          rwd           front  ...          130   \n",
       "1          two  convertible          rwd           front  ...          130   \n",
       "2          two    hatchback          rwd           front  ...          152   \n",
       "3         four        sedan          fwd           front  ...          109   \n",
       "4         four        sedan          4wd           front  ...          136   \n",
       "\n",
       "   fuel-system  bore  stroke  compression-ratio horsepower peak-rpm  city-mpg  \\\n",
       "0         mpfi  3.47    2.68                9.0        111     5000        21   \n",
       "1         mpfi  3.47    2.68                9.0        111     5000        21   \n",
       "2         mpfi  2.68    3.47                9.0        154     5000        19   \n",
       "3         mpfi  3.19    3.40               10.0        102     5500        24   \n",
       "4         mpfi  3.19    3.40                8.0        115     5500        18   \n",
       "\n",
       "  highway-mpg  price  \n",
       "0          27  13495  \n",
       "1          27  16500  \n",
       "2          26  16500  \n",
       "3          30  13950  \n",
       "4          22  17450  \n",
       "\n",
       "[5 rows x 27 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path='car.csv'\n",
    "df = pd.read_csv(path)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> To first understand what type of variable are in the dataset. </p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unnamed: 0             int64\n",
      "symboling              int64\n",
      "normalized-losses     object\n",
      "make                  object\n",
      "fuel-type             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             int64\n",
      "peak-rpm              object\n",
      "city-mpg               int64\n",
      "highway-mpg            int64\n",
      "price                  int64\n",
      "dtype: object\n"
     ]
    }
   ],
   "source": [
    "# list the data types for each column\n",
    "print(df.dtypes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 >2. Analyzing some variables using Visualization</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Import visualization package\n",
    "\n",
    "Seaborn \n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import seaborn as sns\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>1) We can calculate the correlation between numeric attributes (type int64 or float64) using the method corr()</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <td>0.015940</td>\n",
       "      <td>0.011255</td>\n",
       "      <td>-0.116555</td>\n",
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       "      <th>symboling</th>\n",
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       "      <td>-0.357612</td>\n",
       "      <td>-0.232919</td>\n",
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       "      <td>-0.105790</td>\n",
       "      <td>-0.134205</td>\n",
       "      <td>-0.008965</td>\n",
       "      <td>-0.178515</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>-0.035823</td>\n",
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       "      <td>-0.082201</td>\n",
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       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>0.129729</td>\n",
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       "      <td>1.000000</td>\n",
       "      <td>0.874587</td>\n",
       "      <td>0.795144</td>\n",
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       "      <td>0.161477</td>\n",
       "      <td>0.249786</td>\n",
       "      <td>0.351985</td>\n",
       "      <td>-0.470414</td>\n",
       "      <td>-0.544082</td>\n",
       "      <td>0.583168</td>\n",
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       "      <th>length</th>\n",
       "      <td>0.170636</td>\n",
       "      <td>-0.357612</td>\n",
       "      <td>0.874587</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.841118</td>\n",
       "      <td>0.491029</td>\n",
       "      <td>0.877728</td>\n",
       "      <td>0.683360</td>\n",
       "      <td>0.607480</td>\n",
       "      <td>0.129739</td>\n",
       "      <td>0.158414</td>\n",
       "      <td>0.554408</td>\n",
       "      <td>-0.670909</td>\n",
       "      <td>-0.704662</td>\n",
       "      <td>0.682986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>0.052387</td>\n",
       "      <td>-0.232919</td>\n",
       "      <td>0.795144</td>\n",
       "      <td>0.841118</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.279210</td>\n",
       "      <td>0.867032</td>\n",
       "      <td>0.735433</td>\n",
       "      <td>0.559204</td>\n",
       "      <td>0.182956</td>\n",
       "      <td>0.181129</td>\n",
       "      <td>0.642176</td>\n",
       "      <td>-0.642704</td>\n",
       "      <td>-0.677218</td>\n",
       "      <td>0.728699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>0.255960</td>\n",
       "      <td>-0.541038</td>\n",
       "      <td>0.589435</td>\n",
       "      <td>0.491029</td>\n",
       "      <td>0.279210</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.295572</td>\n",
       "      <td>0.067149</td>\n",
       "      <td>0.176195</td>\n",
       "      <td>-0.056999</td>\n",
       "      <td>0.261214</td>\n",
       "      <td>-0.110114</td>\n",
       "      <td>-0.048640</td>\n",
       "      <td>-0.107358</td>\n",
       "      <td>0.134388</td>\n",
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       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>0.071962</td>\n",
       "      <td>-0.227691</td>\n",
       "      <td>0.776386</td>\n",
       "      <td>0.877728</td>\n",
       "      <td>0.867032</td>\n",
       "      <td>0.295572</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.850594</td>\n",
       "      <td>0.649045</td>\n",
       "      <td>0.168929</td>\n",
       "      <td>0.151362</td>\n",
       "      <td>0.750973</td>\n",
       "      <td>-0.757414</td>\n",
       "      <td>-0.797465</td>\n",
       "      <td>0.820825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.033930</td>\n",
       "      <td>-0.105790</td>\n",
       "      <td>0.569329</td>\n",
       "      <td>0.683360</td>\n",
       "      <td>0.735433</td>\n",
       "      <td>0.067149</td>\n",
       "      <td>0.850594</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.594090</td>\n",
       "      <td>0.206675</td>\n",
       "      <td>0.028971</td>\n",
       "      <td>0.810705</td>\n",
       "      <td>-0.653658</td>\n",
       "      <td>-0.677470</td>\n",
       "      <td>0.861752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>0.261622</td>\n",
       "      <td>-0.134205</td>\n",
       "      <td>0.490378</td>\n",
       "      <td>0.607480</td>\n",
       "      <td>0.559204</td>\n",
       "      <td>0.176195</td>\n",
       "      <td>0.649045</td>\n",
       "      <td>0.594090</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055909</td>\n",
       "      <td>0.005203</td>\n",
       "      <td>0.576594</td>\n",
       "      <td>-0.594584</td>\n",
       "      <td>-0.594572</td>\n",
       "      <td>0.532577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.161799</td>\n",
       "      <td>-0.008965</td>\n",
       "      <td>0.161477</td>\n",
       "      <td>0.129739</td>\n",
       "      <td>0.182956</td>\n",
       "      <td>-0.056999</td>\n",
       "      <td>0.168929</td>\n",
       "      <td>0.206675</td>\n",
       "      <td>-0.055909</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.186170</td>\n",
       "      <td>0.088269</td>\n",
       "      <td>-0.042906</td>\n",
       "      <td>-0.044528</td>\n",
       "      <td>0.082138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.150276</td>\n",
       "      <td>-0.178515</td>\n",
       "      <td>0.249786</td>\n",
       "      <td>0.158414</td>\n",
       "      <td>0.181129</td>\n",
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       "      <td>0.151362</td>\n",
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       "      <td>1.000000</td>\n",
       "      <td>-0.205717</td>\n",
       "      <td>0.324701</td>\n",
       "      <td>0.265201</td>\n",
       "      <td>0.070990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>-0.013346</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.351985</td>\n",
       "      <td>0.554408</td>\n",
       "      <td>0.642176</td>\n",
       "      <td>-0.110114</td>\n",
       "      <td>0.750973</td>\n",
       "      <td>0.810705</td>\n",
       "      <td>0.576594</td>\n",
       "      <td>0.088269</td>\n",
       "      <td>-0.205717</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.803140</td>\n",
       "      <td>-0.770905</td>\n",
       "      <td>0.757946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>0.015940</td>\n",
       "      <td>-0.035823</td>\n",
       "      <td>-0.470414</td>\n",
       "      <td>-0.670909</td>\n",
       "      <td>-0.642704</td>\n",
       "      <td>-0.048640</td>\n",
       "      <td>-0.757414</td>\n",
       "      <td>-0.653658</td>\n",
       "      <td>-0.594584</td>\n",
       "      <td>-0.042906</td>\n",
       "      <td>0.324701</td>\n",
       "      <td>-0.803140</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.971337</td>\n",
       "      <td>-0.667449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.011255</td>\n",
       "      <td>0.034606</td>\n",
       "      <td>-0.544082</td>\n",
       "      <td>-0.704662</td>\n",
       "      <td>-0.677218</td>\n",
       "      <td>-0.107358</td>\n",
       "      <td>-0.797465</td>\n",
       "      <td>-0.677470</td>\n",
       "      <td>-0.594572</td>\n",
       "      <td>-0.044528</td>\n",
       "      <td>0.265201</td>\n",
       "      <td>-0.770905</td>\n",
       "      <td>0.971337</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.690526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.116555</td>\n",
       "      <td>-0.082201</td>\n",
       "      <td>0.583168</td>\n",
       "      <td>0.682986</td>\n",
       "      <td>0.728699</td>\n",
       "      <td>0.134388</td>\n",
       "      <td>0.820825</td>\n",
       "      <td>0.861752</td>\n",
       "      <td>0.532577</td>\n",
       "      <td>0.082138</td>\n",
       "      <td>0.070990</td>\n",
       "      <td>0.757946</td>\n",
       "      <td>-0.667449</td>\n",
       "      <td>-0.690526</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Unnamed: 0  symboling  wheel-base    length     width  \\\n",
       "Unnamed: 0           1.000000  -0.151621    0.129729  0.170636  0.052387   \n",
       "symboling           -0.151621   1.000000   -0.531954 -0.357612 -0.232919   \n",
       "wheel-base           0.129729  -0.531954    1.000000  0.874587  0.795144   \n",
       "length               0.170636  -0.357612    0.874587  1.000000  0.841118   \n",
       "width                0.052387  -0.232919    0.795144  0.841118  1.000000   \n",
       "height               0.255960  -0.541038    0.589435  0.491029  0.279210   \n",
       "curb-weight          0.071962  -0.227691    0.776386  0.877728  0.867032   \n",
       "engine-size         -0.033930  -0.105790    0.569329  0.683360  0.735433   \n",
       "bore                 0.261622  -0.134205    0.490378  0.607480  0.559204   \n",
       "stroke              -0.161799  -0.008965    0.161477  0.129739  0.182956   \n",
       "compression-ratio    0.150276  -0.178515    0.249786  0.158414  0.181129   \n",
       "horsepower          -0.013346   0.071380    0.351985  0.554408  0.642176   \n",
       "city-mpg             0.015940  -0.035823   -0.470414 -0.670909 -0.642704   \n",
       "highway-mpg          0.011255   0.034606   -0.544082 -0.704662 -0.677218   \n",
       "price               -0.116555  -0.082201    0.583168  0.682986  0.728699   \n",
       "\n",
       "                     height  curb-weight  engine-size      bore    stroke  \\\n",
       "Unnamed: 0         0.255960     0.071962    -0.033930  0.261622 -0.161799   \n",
       "symboling         -0.541038    -0.227691    -0.105790 -0.134205 -0.008965   \n",
       "wheel-base         0.589435     0.776386     0.569329  0.490378  0.161477   \n",
       "length             0.491029     0.877728     0.683360  0.607480  0.129739   \n",
       "width              0.279210     0.867032     0.735433  0.559204  0.182956   \n",
       "height             1.000000     0.295572     0.067149  0.176195 -0.056999   \n",
       "curb-weight        0.295572     1.000000     0.850594  0.649045  0.168929   \n",
       "engine-size        0.067149     0.850594     1.000000  0.594090  0.206675   \n",
       "bore               0.176195     0.649045     0.594090  1.000000 -0.055909   \n",
       "stroke            -0.056999     0.168929     0.206675 -0.055909  1.000000   \n",
       "compression-ratio  0.261214     0.151362     0.028971  0.005203  0.186170   \n",
       "horsepower        -0.110114     0.750973     0.810705  0.576594  0.088269   \n",
       "city-mpg          -0.048640    -0.757414    -0.653658 -0.594584 -0.042906   \n",
       "highway-mpg       -0.107358    -0.797465    -0.677470 -0.594572 -0.044528   \n",
       "price              0.134388     0.820825     0.861752  0.532577  0.082138   \n",
       "\n",
       "                   compression-ratio  horsepower  city-mpg  highway-mpg  \\\n",
       "Unnamed: 0                  0.150276   -0.013346  0.015940     0.011255   \n",
       "symboling                  -0.178515    0.071380 -0.035823     0.034606   \n",
       "wheel-base                  0.249786    0.351985 -0.470414    -0.544082   \n",
       "length                      0.158414    0.554408 -0.670909    -0.704662   \n",
       "width                       0.181129    0.642176 -0.642704    -0.677218   \n",
       "height                      0.261214   -0.110114 -0.048640    -0.107358   \n",
       "curb-weight                 0.151362    0.750973 -0.757414    -0.797465   \n",
       "engine-size                 0.028971    0.810705 -0.653658    -0.677470   \n",
       "bore                        0.005203    0.576594 -0.594584    -0.594572   \n",
       "stroke                      0.186170    0.088269 -0.042906    -0.044528   \n",
       "compression-ratio           1.000000   -0.205717  0.324701     0.265201   \n",
       "horsepower                 -0.205717    1.000000 -0.803140    -0.770905   \n",
       "city-mpg                    0.324701   -0.803140  1.000000     0.971337   \n",
       "highway-mpg                 0.265201   -0.770905  0.971337     1.000000   \n",
       "price                       0.070990    0.757946 -0.667449    -0.690526   \n",
       "\n",
       "                      price  \n",
       "Unnamed: 0        -0.116555  \n",
       "symboling         -0.082201  \n",
       "wheel-base         0.583168  \n",
       "length             0.682986  \n",
       "width              0.728699  \n",
       "height             0.134388  \n",
       "curb-weight        0.820825  \n",
       "engine-size        0.861752  \n",
       "bore               0.532577  \n",
       "stroke             0.082138  \n",
       "compression-ratio  0.070990  \n",
       "horsepower         0.757946  \n",
       "city-mpg          -0.667449  \n",
       "highway-mpg       -0.690526  \n",
       "price              1.000000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The diagonal elements are always one as it is the correleation of that attribute itself.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> To find the correlation between the following columns: \n",
    "    bore, stroke,compression-ratio , and horsepower.</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>bore</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055909</td>\n",
       "      <td>0.005203</td>\n",
       "      <td>0.576594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.055909</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.186170</td>\n",
       "      <td>0.088269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.005203</td>\n",
       "      <td>0.186170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.205717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>0.576594</td>\n",
       "      <td>0.088269</td>\n",
       "      <td>-0.205717</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       bore    stroke  compression-ratio  horsepower\n",
       "bore               1.000000 -0.055909           0.005203    0.576594\n",
       "stroke            -0.055909  1.000000           0.186170    0.088269\n",
       "compression-ratio  0.005203  0.186170           1.000000   -0.205717\n",
       "horsepower         0.576594  0.088269          -0.205717    1.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Continuous numerical variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Continuous numerical attributes - contain any value within some range. \n",
    "\n",
    "Continuous numerical attributes - type \"int64\" or \"float64\". \n",
    "\n",
    "To visualize these variables we use scatterplots with fitted lines.\n",
    "\n",
    "To understand the relationship between an individual variable and the price, We use \"regplot\" and plots the scatterplot plus along with fitted regression line for the data.\n",
    "\n",
    "Let's see some examples of different linear relationships:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>2. Positive linear relationship</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Scatterplot of \"engine-size\" and \"price\"</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='engine-size', ylabel='price'>"
      ]
     },
     "execution_count": 7,
     "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": [
    "# Engine size vs price\n",
    "sns.regplot(x=\"engine-size\", y=\"price\", data=df)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see as the engine-size goes up, the price goes up\n",
    "    \n",
    "    This indicates a positive correlation between engine size and price. \n",
    "    \n",
    "    If this is between two independent attributes, then we can remove either one of the attribute from dataset as redundency\n",
    "    \n",
    "    But here it is between independent attribute(Engine Size)  and target attrbute(Price).\n",
    "    \n",
    "    Therefore Engine size is a good predictor of price ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation between 'engine-size' and 'price' and is nearly  0.87"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>0.861752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.861752</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             engine-size     price\n",
       "engine-size     1.000000  0.861752\n",
       "price           0.861752  1.000000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"engine-size\", \"price\"]].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>3. Negative linear relationship</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Highway mpg is a potential predictor variable of price</h3> \n",
    "\n",
    "Some decision we can get from the domain knowledge.\n",
    "\n",
    "Let us understand.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='highway-mpg', ylabel='price'>"
      ]
     },
     "execution_count": 9,
     "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>Here we can see, as the highway-mpg goes up, the price goes down\n",
    "    \n",
    "    This indicates an Negative relationship between these two variables. \n",
    "    \n",
    "    Therefore Highway mpg also be a  potential predictor of price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation between 'highway-mpg' and 'price' is  -0.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.690526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.690526</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             highway-mpg     price\n",
       "highway-mpg     1.000000 -0.690526\n",
       "price          -0.690526  1.000000"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['highway-mpg', 'price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>4. Some examples on Weak Linear Relationship</h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>\"Peak-rpm\" can be a predictor variable of \"price\"???</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "peakRpm = df['peak-rpm'].loc[df['peak-rpm'] != '?']\n",
    "prmean = peakRpm.astype(str).astype(int).mean()\n",
    "df['peak-rpm'] = df['peak-rpm'].replace('?',prmean).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='peak-rpm', ylabel='price'>"
      ]
     },
     "execution_count": 12,
     "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 is not a good predictor of price as the data points are very scattered and far from the fitted line. \n",
    "    \n",
    "    Therefore it is not a reliable attribute to predict the price.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation between 'peak-rpm' and 'price' and see is nearly -0.1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.100851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.100851</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          peak-rpm     price\n",
       "peak-rpm  1.000000 -0.100851\n",
       "price    -0.100851  1.000000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[['peak-rpm','price']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>\"stroke\" can be a predictor variable of \"price\"???</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>stroke</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.082138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.082138</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          stroke     price\n",
       "stroke  1.000000  0.082138\n",
       "price   0.082138  1.000000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "df[[\"stroke\",\"price\"]].corr() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='stroke', ylabel='price'>"
      ]
     },
     "execution_count": 15,
     "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": [
    "\n",
    "sns.regplot(x=\"stroke\", y=\"price\", data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "<h3>5. Pearson Correlation Coefficient and P-Value</h3>\n",
    "<p>The Pearson Correlation measures the linear dependence between two Attributes.</p>\n",
    "<p>The value ranges from -1 to 1 </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": [
    "We can Caluculate Pearson Correlation using the function \"corr\". "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>symboling</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.151621</td>\n",
       "      <td>0.129729</td>\n",
       "      <td>0.170636</td>\n",
       "      <td>0.052387</td>\n",
       "      <td>0.255960</td>\n",
       "      <td>0.071962</td>\n",
       "      <td>-0.033930</td>\n",
       "      <td>0.261622</td>\n",
       "      <td>-0.161799</td>\n",
       "      <td>0.150276</td>\n",
       "      <td>-0.013346</td>\n",
       "      <td>-0.203545</td>\n",
       "      <td>0.015940</td>\n",
       "      <td>0.011255</td>\n",
       "      <td>-0.116555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>symboling</th>\n",
       "      <td>-0.151621</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.531954</td>\n",
       "      <td>-0.357612</td>\n",
       "      <td>-0.232919</td>\n",
       "      <td>-0.541038</td>\n",
       "      <td>-0.227691</td>\n",
       "      <td>-0.105790</td>\n",
       "      <td>-0.134205</td>\n",
       "      <td>-0.008965</td>\n",
       "      <td>-0.178515</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.273678</td>\n",
       "      <td>-0.035823</td>\n",
       "      <td>0.034606</td>\n",
       "      <td>-0.082201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wheel-base</th>\n",
       "      <td>0.129729</td>\n",
       "      <td>-0.531954</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.874587</td>\n",
       "      <td>0.795144</td>\n",
       "      <td>0.589435</td>\n",
       "      <td>0.776386</td>\n",
       "      <td>0.569329</td>\n",
       "      <td>0.490378</td>\n",
       "      <td>0.161477</td>\n",
       "      <td>0.249786</td>\n",
       "      <td>0.351985</td>\n",
       "      <td>-0.360700</td>\n",
       "      <td>-0.470414</td>\n",
       "      <td>-0.544082</td>\n",
       "      <td>0.583168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>length</th>\n",
       "      <td>0.170636</td>\n",
       "      <td>-0.357612</td>\n",
       "      <td>0.874587</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.841118</td>\n",
       "      <td>0.491029</td>\n",
       "      <td>0.877728</td>\n",
       "      <td>0.683360</td>\n",
       "      <td>0.607480</td>\n",
       "      <td>0.129739</td>\n",
       "      <td>0.158414</td>\n",
       "      <td>0.554408</td>\n",
       "      <td>-0.287034</td>\n",
       "      <td>-0.670909</td>\n",
       "      <td>-0.704662</td>\n",
       "      <td>0.682986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>width</th>\n",
       "      <td>0.052387</td>\n",
       "      <td>-0.232919</td>\n",
       "      <td>0.795144</td>\n",
       "      <td>0.841118</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.279210</td>\n",
       "      <td>0.867032</td>\n",
       "      <td>0.735433</td>\n",
       "      <td>0.559204</td>\n",
       "      <td>0.182956</td>\n",
       "      <td>0.181129</td>\n",
       "      <td>0.642176</td>\n",
       "      <td>-0.219861</td>\n",
       "      <td>-0.642704</td>\n",
       "      <td>-0.677218</td>\n",
       "      <td>0.728699</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <td>0.255960</td>\n",
       "      <td>-0.541038</td>\n",
       "      <td>0.589435</td>\n",
       "      <td>0.491029</td>\n",
       "      <td>0.279210</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.295572</td>\n",
       "      <td>0.067149</td>\n",
       "      <td>0.176195</td>\n",
       "      <td>-0.056999</td>\n",
       "      <td>0.261214</td>\n",
       "      <td>-0.110114</td>\n",
       "      <td>-0.320599</td>\n",
       "      <td>-0.048640</td>\n",
       "      <td>-0.107358</td>\n",
       "      <td>0.134388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>curb-weight</th>\n",
       "      <td>0.071962</td>\n",
       "      <td>-0.227691</td>\n",
       "      <td>0.776386</td>\n",
       "      <td>0.877728</td>\n",
       "      <td>0.867032</td>\n",
       "      <td>0.295572</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.850594</td>\n",
       "      <td>0.649045</td>\n",
       "      <td>0.168929</td>\n",
       "      <td>0.151362</td>\n",
       "      <td>0.750973</td>\n",
       "      <td>-0.266282</td>\n",
       "      <td>-0.757414</td>\n",
       "      <td>-0.797465</td>\n",
       "      <td>0.820825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>engine-size</th>\n",
       "      <td>-0.033930</td>\n",
       "      <td>-0.105790</td>\n",
       "      <td>0.569329</td>\n",
       "      <td>0.683360</td>\n",
       "      <td>0.735433</td>\n",
       "      <td>0.067149</td>\n",
       "      <td>0.850594</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.594090</td>\n",
       "      <td>0.206675</td>\n",
       "      <td>0.028971</td>\n",
       "      <td>0.810705</td>\n",
       "      <td>-0.244600</td>\n",
       "      <td>-0.653658</td>\n",
       "      <td>-0.677470</td>\n",
       "      <td>0.861752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bore</th>\n",
       "      <td>0.261622</td>\n",
       "      <td>-0.134205</td>\n",
       "      <td>0.490378</td>\n",
       "      <td>0.607480</td>\n",
       "      <td>0.559204</td>\n",
       "      <td>0.176195</td>\n",
       "      <td>0.649045</td>\n",
       "      <td>0.594090</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055909</td>\n",
       "      <td>0.005203</td>\n",
       "      <td>0.576594</td>\n",
       "      <td>-0.263788</td>\n",
       "      <td>-0.594584</td>\n",
       "      <td>-0.594572</td>\n",
       "      <td>0.532577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>stroke</th>\n",
       "      <td>-0.161799</td>\n",
       "      <td>-0.008965</td>\n",
       "      <td>0.161477</td>\n",
       "      <td>0.129739</td>\n",
       "      <td>0.182956</td>\n",
       "      <td>-0.056999</td>\n",
       "      <td>0.168929</td>\n",
       "      <td>0.206675</td>\n",
       "      <td>-0.055909</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.186170</td>\n",
       "      <td>0.088269</td>\n",
       "      <td>-0.069228</td>\n",
       "      <td>-0.042906</td>\n",
       "      <td>-0.044528</td>\n",
       "      <td>0.082138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>compression-ratio</th>\n",
       "      <td>0.150276</td>\n",
       "      <td>-0.178515</td>\n",
       "      <td>0.249786</td>\n",
       "      <td>0.158414</td>\n",
       "      <td>0.181129</td>\n",
       "      <td>0.261214</td>\n",
       "      <td>0.151362</td>\n",
       "      <td>0.028971</td>\n",
       "      <td>0.005203</td>\n",
       "      <td>0.186170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.205717</td>\n",
       "      <td>-0.435933</td>\n",
       "      <td>0.324701</td>\n",
       "      <td>0.265201</td>\n",
       "      <td>0.070990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>-0.013346</td>\n",
       "      <td>0.071380</td>\n",
       "      <td>0.351985</td>\n",
       "      <td>0.554408</td>\n",
       "      <td>0.642176</td>\n",
       "      <td>-0.110114</td>\n",
       "      <td>0.750973</td>\n",
       "      <td>0.810705</td>\n",
       "      <td>0.576594</td>\n",
       "      <td>0.088269</td>\n",
       "      <td>-0.205717</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.130971</td>\n",
       "      <td>-0.803140</td>\n",
       "      <td>-0.770905</td>\n",
       "      <td>0.757946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>peak-rpm</th>\n",
       "      <td>-0.203545</td>\n",
       "      <td>0.273678</td>\n",
       "      <td>-0.360700</td>\n",
       "      <td>-0.287034</td>\n",
       "      <td>-0.219861</td>\n",
       "      <td>-0.320599</td>\n",
       "      <td>-0.266282</td>\n",
       "      <td>-0.244600</td>\n",
       "      <td>-0.263788</td>\n",
       "      <td>-0.069228</td>\n",
       "      <td>-0.435933</td>\n",
       "      <td>0.130971</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.113720</td>\n",
       "      <td>-0.054257</td>\n",
       "      <td>-0.100851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>city-mpg</th>\n",
       "      <td>0.015940</td>\n",
       "      <td>-0.035823</td>\n",
       "      <td>-0.470414</td>\n",
       "      <td>-0.670909</td>\n",
       "      <td>-0.642704</td>\n",
       "      <td>-0.048640</td>\n",
       "      <td>-0.757414</td>\n",
       "      <td>-0.653658</td>\n",
       "      <td>-0.594584</td>\n",
       "      <td>-0.042906</td>\n",
       "      <td>0.324701</td>\n",
       "      <td>-0.803140</td>\n",
       "      <td>-0.113720</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.971337</td>\n",
       "      <td>-0.667449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>highway-mpg</th>\n",
       "      <td>0.011255</td>\n",
       "      <td>0.034606</td>\n",
       "      <td>-0.544082</td>\n",
       "      <td>-0.704662</td>\n",
       "      <td>-0.677218</td>\n",
       "      <td>-0.107358</td>\n",
       "      <td>-0.797465</td>\n",
       "      <td>-0.677470</td>\n",
       "      <td>-0.594572</td>\n",
       "      <td>-0.044528</td>\n",
       "      <td>0.265201</td>\n",
       "      <td>-0.770905</td>\n",
       "      <td>-0.054257</td>\n",
       "      <td>0.971337</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.690526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>-0.116555</td>\n",
       "      <td>-0.082201</td>\n",
       "      <td>0.583168</td>\n",
       "      <td>0.682986</td>\n",
       "      <td>0.728699</td>\n",
       "      <td>0.134388</td>\n",
       "      <td>0.820825</td>\n",
       "      <td>0.861752</td>\n",
       "      <td>0.532577</td>\n",
       "      <td>0.082138</td>\n",
       "      <td>0.070990</td>\n",
       "      <td>0.757946</td>\n",
       "      <td>-0.100851</td>\n",
       "      <td>-0.667449</td>\n",
       "      <td>-0.690526</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Unnamed: 0  symboling  wheel-base    length     width  \\\n",
       "Unnamed: 0           1.000000  -0.151621    0.129729  0.170636  0.052387   \n",
       "symboling           -0.151621   1.000000   -0.531954 -0.357612 -0.232919   \n",
       "wheel-base           0.129729  -0.531954    1.000000  0.874587  0.795144   \n",
       "length               0.170636  -0.357612    0.874587  1.000000  0.841118   \n",
       "width                0.052387  -0.232919    0.795144  0.841118  1.000000   \n",
       "height               0.255960  -0.541038    0.589435  0.491029  0.279210   \n",
       "curb-weight          0.071962  -0.227691    0.776386  0.877728  0.867032   \n",
       "engine-size         -0.033930  -0.105790    0.569329  0.683360  0.735433   \n",
       "bore                 0.261622  -0.134205    0.490378  0.607480  0.559204   \n",
       "stroke              -0.161799  -0.008965    0.161477  0.129739  0.182956   \n",
       "compression-ratio    0.150276  -0.178515    0.249786  0.158414  0.181129   \n",
       "horsepower          -0.013346   0.071380    0.351985  0.554408  0.642176   \n",
       "peak-rpm            -0.203545   0.273678   -0.360700 -0.287034 -0.219861   \n",
       "city-mpg             0.015940  -0.035823   -0.470414 -0.670909 -0.642704   \n",
       "highway-mpg          0.011255   0.034606   -0.544082 -0.704662 -0.677218   \n",
       "price               -0.116555  -0.082201    0.583168  0.682986  0.728699   \n",
       "\n",
       "                     height  curb-weight  engine-size      bore    stroke  \\\n",
       "Unnamed: 0         0.255960     0.071962    -0.033930  0.261622 -0.161799   \n",
       "symboling         -0.541038    -0.227691    -0.105790 -0.134205 -0.008965   \n",
       "wheel-base         0.589435     0.776386     0.569329  0.490378  0.161477   \n",
       "length             0.491029     0.877728     0.683360  0.607480  0.129739   \n",
       "width              0.279210     0.867032     0.735433  0.559204  0.182956   \n",
       "height             1.000000     0.295572     0.067149  0.176195 -0.056999   \n",
       "curb-weight        0.295572     1.000000     0.850594  0.649045  0.168929   \n",
       "engine-size        0.067149     0.850594     1.000000  0.594090  0.206675   \n",
       "bore               0.176195     0.649045     0.594090  1.000000 -0.055909   \n",
       "stroke            -0.056999     0.168929     0.206675 -0.055909  1.000000   \n",
       "compression-ratio  0.261214     0.151362     0.028971  0.005203  0.186170   \n",
       "horsepower        -0.110114     0.750973     0.810705  0.576594  0.088269   \n",
       "peak-rpm          -0.320599    -0.266282    -0.244600 -0.263788 -0.069228   \n",
       "city-mpg          -0.048640    -0.757414    -0.653658 -0.594584 -0.042906   \n",
       "highway-mpg       -0.107358    -0.797465    -0.677470 -0.594572 -0.044528   \n",
       "price              0.134388     0.820825     0.861752  0.532577  0.082138   \n",
       "\n",
       "                   compression-ratio  horsepower  peak-rpm  city-mpg  \\\n",
       "Unnamed: 0                  0.150276   -0.013346 -0.203545  0.015940   \n",
       "symboling                  -0.178515    0.071380  0.273678 -0.035823   \n",
       "wheel-base                  0.249786    0.351985 -0.360700 -0.470414   \n",
       "length                      0.158414    0.554408 -0.287034 -0.670909   \n",
       "width                       0.181129    0.642176 -0.219861 -0.642704   \n",
       "height                      0.261214   -0.110114 -0.320599 -0.048640   \n",
       "curb-weight                 0.151362    0.750973 -0.266282 -0.757414   \n",
       "engine-size                 0.028971    0.810705 -0.244600 -0.653658   \n",
       "bore                        0.005203    0.576594 -0.263788 -0.594584   \n",
       "stroke                      0.186170    0.088269 -0.069228 -0.042906   \n",
       "compression-ratio           1.000000   -0.205717 -0.435933  0.324701   \n",
       "horsepower                 -0.205717    1.000000  0.130971 -0.803140   \n",
       "peak-rpm                   -0.435933    0.130971  1.000000 -0.113720   \n",
       "city-mpg                    0.324701   -0.803140 -0.113720  1.000000   \n",
       "highway-mpg                 0.265201   -0.770905 -0.054257  0.971337   \n",
       "price                       0.070990    0.757946 -0.100851 -0.667449   \n",
       "\n",
       "                   highway-mpg     price  \n",
       "Unnamed: 0            0.011255 -0.116555  \n",
       "symboling             0.034606 -0.082201  \n",
       "wheel-base           -0.544082  0.583168  \n",
       "length               -0.704662  0.682986  \n",
       "width                -0.677218  0.728699  \n",
       "height               -0.107358  0.134388  \n",
       "curb-weight          -0.797465  0.820825  \n",
       "engine-size          -0.677470  0.861752  \n",
       "bore                 -0.594572  0.532577  \n",
       "stroke               -0.044528  0.082138  \n",
       "compression-ratio     0.265201  0.070990  \n",
       "horsepower           -0.770905  0.757946  \n",
       "peak-rpm             -0.054257 -0.100851  \n",
       "city-mpg              0.971337 -0.667449  \n",
       "highway-mpg           1.000000 -0.690526  \n",
       "price                -0.690526  1.000000  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " But sometimes we want to know the significant of the correlation,  which means how much confident about the correlation. \n",
    " \n",
    " In that case we calculate P-Value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>P-value</b>: \n",
    "<p>What is this P-value? \n",
    "    \n",
    "    The P-value is the probability value that the correlation between these two variables is statistically significant. \n",
    "    \n",
    "    </p>\n",
    "\n",
    "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>\n",
    "\n",
    "<p>Normally, we choose a significance level of 0.05, which means that we are 95% confident that the correlation between attribute variables is significant.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us understand by calculating some of the P-Values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We use  \"stats\" module in the \"scipy\"  library to calculate P-Value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.5831682587228323  with a P-value of P = 4.527536401744334e-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, \n",
    "    \n",
    "    although the linear relationship isn't extremely strong (~0.585)</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Horsepower vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.6829864946320212  with a P-value of P =  1.649801455844585e-29\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, \n",
    "    \n",
    "    and the linear relationship is moderately strong (~0.691).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Width vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.7286986760208304  with a P-value of P = 3.2146646385520774e-35\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, \n",
    "\n",
    "and the linear relationship is quite strong (~0.751)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curb-weight vs Price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8208247364886393  with a P-value of P =  2.8663275083502043e-51\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, \n",
    "    \n",
    "    and the linear relationship is quite strong (~0.834).</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Engine-size vs Price</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is 0.8617522313557834  with a P-value of P = 9.669743096805981e-62\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, \n",
    "    \n",
    "    and the linear relationship is very strong (~0.872).</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": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6674493651999066  with a P-value of P =  8.463492369695295e-28\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,\n",
    "    \n",
    "    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": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pearson Correlation Coefficient is -0.6905258861803291  with a P-value of P =  2.23237596903188e-30\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, \n",
    "\n",
    "and the coefficient of ~ -0.705 shows that the relationship is negative and moderately strong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In next Video We will do more anaysis on this dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_csv('car.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Thank you</h1>"
   ]
  }
 ],
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