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exploratory-data-analysis.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
" <a href=\"https://cocl.us/corsera_da0101en_notebook_top\">\n",
" <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/TopAd.png\" width=\"750\" align=\"center\">\n",
" </a>\n",
"</div>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/CCLog.png\" width = 300, align = \"center\"></a>\n",
"\n",
"<h1 align=center><font size = 5>Data Analysis with Python</font></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exploratory Data Analysis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Welcome!</h3>\n",
"In this section, we will explore several methods to see if certain characteristics or features can be used to predict car price. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Table of content</h2>\n",
"\n",
"<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
"<ol>\n",
" <li><a href=\"#import_data\">Import Data from Module</a></li>\n",
" <li><a href=\"#pattern_visualization\">Analyzing Individual Feature Patterns using Visualization</a></li>\n",
" <li><a href=\"#discriptive_statistics\">Descriptive Statistical Analysis</a></li>\n",
" <li><a href=\"#basic_grouping\">Basics of Grouping</a></li>\n",
" <li><a href=\"#correlation_causation\">Correlation and Causation</a></li>\n",
" <li><a href=\"#anova\">ANOVA</a></li>\n",
"</ol>\n",
" \n",
"Estimated Time Needed: <strong>30 min</strong>\n",
"</div>\n",
" \n",
"<hr>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>What are the main characteristics which have the most impact on the car price?</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"import_data\">1. Import Data from Module 2</h2>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Setup</h4>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Import libraries "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"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": "markdown",
"metadata": {},
"source": [
"This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>symboling</th>\n",
" <th>normalized-losses</th>\n",
" <th>make</th>\n",
" <th>aspiration</th>\n",
" <th>num-of-doors</th>\n",
" <th>body-style</th>\n",
" <th>drive-wheels</th>\n",
" <th>engine-location</th>\n",
" <th>wheel-base</th>\n",
" <th>length</th>\n",
" <th>...</th>\n",
" <th>compression-ratio</th>\n",
" <th>horsepower</th>\n",
" <th>peak-rpm</th>\n",
" <th>city-mpg</th>\n",
" <th>highway-mpg</th>\n",
" <th>price</th>\n",
" <th>city-L/100km</th>\n",
" <th>horsepower-binned</th>\n",
" <th>diesel</th>\n",
" <th>gas</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>3</td>\n",
" <td>122</td>\n",
" <td>alfa-romero</td>\n",
" <td>std</td>\n",
" <td>two</td>\n",
" <td>convertible</td>\n",
" <td>rwd</td>\n",
" <td>front</td>\n",
" <td>88.6</td>\n",
" <td>0.811148</td>\n",
" <td>...</td>\n",
" <td>9.0</td>\n",
" <td>111.0</td>\n",
" <td>5000.0</td>\n",
" <td>21</td>\n",
" <td>27</td>\n",
" <td>13495.0</td>\n",
" <td>11.190476</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>3</td>\n",
" <td>122</td>\n",
" <td>alfa-romero</td>\n",
" <td>std</td>\n",
" <td>two</td>\n",
" <td>convertible</td>\n",
" <td>rwd</td>\n",
" <td>front</td>\n",
" <td>88.6</td>\n",
" <td>0.811148</td>\n",
" <td>...</td>\n",
" <td>9.0</td>\n",
" <td>111.0</td>\n",
" <td>5000.0</td>\n",
" <td>21</td>\n",
" <td>27</td>\n",
" <td>16500.0</td>\n",
" <td>11.190476</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1</td>\n",
" <td>122</td>\n",
" <td>alfa-romero</td>\n",
" <td>std</td>\n",
" <td>two</td>\n",
" <td>hatchback</td>\n",
" <td>rwd</td>\n",
" <td>front</td>\n",
" <td>94.5</td>\n",
" <td>0.822681</td>\n",
" <td>...</td>\n",
" <td>9.0</td>\n",
" <td>154.0</td>\n",
" <td>5000.0</td>\n",
" <td>19</td>\n",
" <td>26</td>\n",
" <td>16500.0</td>\n",
" <td>12.368421</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>2</td>\n",
" <td>164</td>\n",
" <td>audi</td>\n",
" <td>std</td>\n",
" <td>four</td>\n",
" <td>sedan</td>\n",
" <td>fwd</td>\n",
" <td>front</td>\n",
" <td>99.8</td>\n",
" <td>0.848630</td>\n",
" <td>...</td>\n",
" <td>10.0</td>\n",
" <td>102.0</td>\n",
" <td>5500.0</td>\n",
" <td>24</td>\n",
" <td>30</td>\n",
" <td>13950.0</td>\n",
" <td>9.791667</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>2</td>\n",
" <td>164</td>\n",
" <td>audi</td>\n",
" <td>std</td>\n",
" <td>four</td>\n",
" <td>sedan</td>\n",
" <td>4wd</td>\n",
" <td>front</td>\n",
" <td>99.4</td>\n",
" <td>0.848630</td>\n",
" <td>...</td>\n",
" <td>8.0</td>\n",
" <td>115.0</td>\n",
" <td>5500.0</td>\n",
" <td>18</td>\n",
" <td>22</td>\n",
" <td>17450.0</td>\n",
" <td>13.055556</td>\n",
" <td>Medium</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 29 columns</p>\n",
"</div>"
],
"text/plain": [
" symboling normalized-losses make aspiration num-of-doors \\\n",
"0 3 122 alfa-romero std two \n",
"1 3 122 alfa-romero std two \n",
"2 1 122 alfa-romero std two \n",
"3 2 164 audi std four \n",
"4 2 164 audi std four \n",
"\n",
" body-style drive-wheels engine-location wheel-base length ... \\\n",
"0 convertible rwd front 88.6 0.811148 ... \n",
"1 convertible rwd front 88.6 0.811148 ... \n",
"2 hatchback rwd front 94.5 0.822681 ... \n",
"3 sedan fwd front 99.8 0.848630 ... \n",
"4 sedan 4wd front 99.4 0.848630 ... \n",
"\n",
" compression-ratio horsepower peak-rpm city-mpg highway-mpg price \\\n",
"0 9.0 111.0 5000.0 21 27 13495.0 \n",
"1 9.0 111.0 5000.0 21 27 16500.0 \n",
"2 9.0 154.0 5000.0 19 26 16500.0 \n",
"3 10.0 102.0 5500.0 24 30 13950.0 \n",
"4 8.0 115.0 5500.0 18 22 17450.0 \n",
"\n",
" city-L/100km horsepower-binned diesel gas \n",
"0 11.190476 Medium 0 1 \n",
"1 11.190476 Medium 0 1 \n",
"2 12.368421 Medium 0 1 \n",
"3 9.791667 Medium 0 1 \n",
"4 13.055556 Medium 0 1 \n",
"\n",
"[5 rows x 29 columns]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"path='https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
"df = pd.read_csv(path)\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"pattern_visualization\">2. Analyzing Individual Feature Patterns using Visualization</h2>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To install seaborn we use the pip which is the python package manager."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"%%capture\n",
"! pip install seaborn"
]
},
{
"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": 4,
"metadata": {
"collapsed": 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": 5,
"metadata": {
"collapsed": 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": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h3>Question #1:</h3>\n",
"\n",
"<b>What is the data type of the column \"peak-rpm\"? </b>\n",
"<p>float64</p>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"float64\n",
"\n",
"-->"
]
},
{
"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": 6,
"metadata": {
"collapsed": 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",
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" .dataframe thead th {\n",
" text-align: right;\n",
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"</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",
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" <td>-0.110581</td>\n",
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" <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": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.corr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The diagonal elements are always one; we will study correlation more precisely Pearson correlation in-depth at the end of the notebook."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1> Question #2: </h1>\n",
"\n",
"<p>Find the correlation between the following columns: bore, stroke,compression-ratio , and horsepower.</p>\n",
"<p>Hint: if you would like to select those columns use the following syntax: df[['bore','stroke' ,'compression-ratio','horsepower']]</p>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"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>-0.055390</td>\n",
" <td>0.001263</td>\n",
" <td>0.566936</td>\n",
" </tr>\n",
" <tr>\n",
" <th>stroke</th>\n",
" <td>-0.055390</td>\n",
" <td>1.000000</td>\n",
" <td>0.187923</td>\n",
" <td>0.098462</td>\n",
" </tr>\n",
" <tr>\n",
" <th>compression-ratio</th>\n",
" <td>0.001263</td>\n",
" <td>0.187923</td>\n",
" <td>1.000000</td>\n",
" <td>-0.214514</td>\n",
" </tr>\n",
" <tr>\n",
" <th>horsepower</th>\n",
" <td>0.566936</td>\n",
" <td>0.098462</td>\n",
" <td>-0.214514</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 -0.055390 0.001263 0.566936\n",
"stroke -0.055390 1.000000 0.187923 0.098462\n",
"compression-ratio 0.001263 0.187923 1.000000 -0.214514\n",
"horsepower 0.566936 0.098462 -0.214514 1.000000"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"df[['bore', 'stroke', 'compression-ratio', 'horsepower']].corr() \n",
"\n",
"-->"
]
},
{
"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": 8,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
" return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
]
},
{
"data": {
"text/plain": [
"(0, 56457.01882359609)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\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": 9,
"metadata": {
"collapsed": 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": 9,
"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": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7fe5880f77f0>"
]
},
"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=\"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": 11,
"metadata": {
"collapsed": 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": 11,
"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": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7fe593df97b8>"
]
},
"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 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": 13,
"metadata": {
"collapsed": 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": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df[['peak-rpm','price']].corr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" <div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1> Question 3 a): </h1>\n",
"\n",
"<p>Find the correlation between x=\"stroke\", y=\"price\".</p>\n",
"<p>Hint: if you would like to select those columns use the following syntax: df[[\"stroke\",\"price\"]] </p>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": 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>stroke</th>\n",
" <th>price</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>stroke</th>\n",
" <td>1.00000</td>\n",
" <td>0.08231</td>\n",
" </tr>\n",
" <tr>\n",
" <th>price</th>\n",
" <td>0.08231</td>\n",
" <td>1.00000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" stroke price\n",
"stroke 1.00000 0.08231\n",
"price 0.08231 1.00000"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute\n",
"df[['stroke', 'price']].corr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"#The correlation is 0.0823, the non-diagonal elements of the table.\n",
"#code:\n",
"df[[\"stroke\",\"price\"]].corr() \n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question 3 b):</h1>\n",
"\n",
"<p>Given the correlation results between \"price\" and \"stroke\" do you expect a linear relationship?</p> \n",
"<p>Verify your results using the function \"regplot()\".</p>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7fe57cf9db00>"
]
},
"execution_count": 16,
"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": [
"# Write your code below and press Shift+Enter to execute \n",
"#Weak correlation\n",
"sns.regplot(x=\"stroke\", y=\"price\", data=df)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"#There is a weak correlation between the variable 'stroke' and 'price.' as such regression will not work well. We #can see this use \"regplot\" to demonstrate this.\n",
"\n",
"#Code: \n",
"sns.regplot(x=\"stroke\", y=\"price\", data=df)\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Categorical variables</h3>\n",
"\n",
"<p>These are variables that describe a 'characteristic' of a data unit, and are selected from a small group of categories. The categorical variables can have the type \"object\" or \"int64\". A good way to visualize categorical variables is by using boxplots.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's look at the relationship between \"body-style\" and \"price\"."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7fe57ceeb160>"
]
},
"execution_count": 17,
"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.boxplot(x=\"body-style\", y=\"price\", data=df)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We see that the distributions of price between the different body-style categories have a significant overlap, and so body-style would not be a good predictor of price. Let's examine engine \"engine-location\" and \"price\":</p>"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7fe57cefef28>"
]
},
"execution_count": 18,
"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.boxplot(x=\"engine-location\", y=\"price\", data=df)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Here we see that the distribution of price between these two engine-location categories, front and rear, are distinct enough to take engine-location as a potential good predictor of price.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's examine \"drive-wheels\" and \"price\"."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7fe5889a6978>"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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N/PUREcANwEfT/hXg6gmet9mU0tnZSW9vL52dnWVXxWyPjHtPJbUoztiNYx8L/DFw3Ijuw/9T0t2SeoH3A/8tfc69wFXAfcC/AqenFs3O9PkbgfuBq1JZgHOAs9NN/XlkScysrgwODtLV1UVE0NXV5daK1bWJ9v7qlvQp4Ergl8PBiNg+2g4R8UNq3/fYMMY+FwAX1IhvqLVf6hF29Mi4WT3p7Owka3jD0NAQnZ2dnH322SXXymz3TPQ5lT8h6/X1A6Cn6mVme6i7u5sdO3YAsGPHDjZt2lRyjcx230STyhFkDyDeBWwBLiJ7SNHM9tCyZctobGwEoLGxkfb29pJrZLb7JppUOoHDgTVkCeXwFDOzPVSpVMj6tUBDQwOVSqXkGpntvokmlbdFxH+NiBvSaxXwtiIrZjZTNDU10dHRgSQ6OjqYN29e2VUy220TTSp3Slo6vCLpGODfiqmS2cxTqVRYvHixWylW9zTc62TMQtk4W28DfpZCh5B17x0CIiIWF1bDnLW1tUVPz/h9DNasWUNfX98k1Cg/W7duBaC1tbXkmkzcokWLWL16ddnVMLNxSNocEW3jlZtol+Lle1ifutPX18edd9/H0BsOKLsqE6aXsh8Im3/y85JrMjENz43aI93M6tSEkkpE/LToikxFQ284gBeOGHc0GttN+953TdlVMLOcTfSeipmZ2bicVMzMLDdOKmZmlhsnFTMzy42TipmZ5cZJxczMcuOkYmZmuSksqUg6WNINku6XdK+ks1L8AEndkram97kpLklrJPVJ6pX0rqpjVVL5rZIqVfGj0oRffWnfWvO3mJnZJCmypbIT+POIOBxYCpwu6QjgXOC6iGgFrkvrAB1kUwi3AquAiyFLQsD5wDFkE3KdP5yIUplVVfvNuCf/zcymksKSSkRsi4gfpeVnyMYKWwCs5NVh8zuBE9PySuCKyNwKzEnz2Z8AdEfE9oh4EugGlqdt+0fELWm++iuqjmVmZiWYlHsqkhYC7wRuA+ZHxDbIEg/w5lRsAfBI1W79KTZWvL9G3MzMSlJ4UpG0H/A94JMR8YuxitaIxW7Ea9VhlaQeST0DAwPjVdnMzHZToUlFUiNZQvlORHw/hR9Ll65I74+neD9wcNXuLcCj48RbasRfJyIujYi2iGhrbm7es5MyK8Dg4CBnnnkmTzzxRNlVMdsjRfb+EnA5cH9EfLlq03pguAdXBbi6Kn5y6gW2FHg6XR7bCLRLmptu0LcDG9O2ZyQtTZ91ctWxzOpKZ2cnvb29dHZ6lm6rb0W2VI4F/hg4TtKW9FoBfBFYJmkrsCytA2wAHgT6gK8DfwYQEduBzwN3pNfnUgzgE8BlaZ+fAF0Fno9ZIQYHB9mwYQMRwYYNG9xasbo20Um6dllE/JDa9z0APlCjfACnj3KstcDaGvEe4Mg9qKZZ6To7O9m5cycAO3bsoLOzk7PPPrvkWpntHj9Rb1ayTZs2MTytd0SwcePGkmtktvucVMxKNn/+/DHXzeqJk4pZyX7+85+PuW5WT5xUzEp24IEHjrluU5+7hL/KScWsZG6p1D93CX+Vk4pZydxSqW+Dg4N0dXUREXR1dc341oqTilnJHnvssTHXbWrr7Ox8pffe0NDQjG+tOKmYlay9vZ3hqYAkccIJJ5RcI9sV3d3d7NixA8ieM9q0aVPJNSqXk4pZySqVCnvtlT2H3NjYSKVSGWcPm0qWLVtGY2MjkH1/7e3tJdeoXIU9UV/v+vv7aXjuafa975qyqzJtNTz3BP39O8uuRumamppYsWIF69evZ8WKFcybN6/sKtkuqFQqdHVlI0Q1NDTM+B8FbqmYTQGVSoXFixfP+D9I9aipqYmOjg4k0dHRMeN/FLilMoqWlhYee3EvXjjig2VXZdra975raGlxTyfI/jBddNFFZVfDdlOlUuHhhx/2jwKcVMzM9ph/FLzKl7/MpgA/kW3ThZOK2RTgJ7JtunBSMSuZn8i26aTI6YTXSnpc0j1Vsc9I+o8RM0EObztPUp+kBySdUBVfnmJ9ks6tih8q6TZJWyVdKWnvos7FrEh+ItumkyJv1H8T+DvgihHxCyPif1cHJB0BnAS8A3gLcK2kt6bNXyGbdrgfuEPS+oi4D/hSOtY6SV8DTgUuLupkzADWrFlDX19frsfs7e1laGgIyJ7IXr9+PQ8//HBux1+0aBGrV6/O7XhmYymspRIRNwHbxy2YWQmsi4gXI+Ihsjnnj06vvoh4MCJeAtYBK5WNaXEc8N20fydwYq4nYDZJ5s6dO+a6WT0po0vxGZJOBnqAP4+IJ4EFwK1VZfpTDOCREfFjgHnAUxGxs0b515G0ClgFcMghh+RxDjZDFfGLf3BwkI985CNEBPvssw+XXXbZjH+AzurXZN+ovxg4DFgCbAP+JsVVo2zsRrymiLg0Itoioq25uXnXamxWsKamJg444AAAP5FtdW9SWyoR8cqY3pK+DgwPrNUPHFxVtAV4NC3Xig8CcyTtlVor1eXN6s6BBx7ICy+84Ceyre5NaktF0kFVq78LDPcMWw+cJGkfSYcCrcDtwB1Aa+rptTfZzfz1kXWVuQH4aNq/Alw9GedgVoTGxkZaW1vdSrG6V1hLRdI/AO8DmiT1A+cD75O0hOxS1cPAaQARca+kq4D7gJ3A6RHxcjrOGcBGYBawNiLuTR9xDrBO0heAO4HLizoXMzObmMKSSkR8rEZ41D/8EXEBcEGN+AZgQ434g2S9w8zMbIrwE/VmZpYbj1I8hobnttfVJF164RcAxL77l1yTiWl4bjvgoe/NphMnlVEsWrSo7Crssq1bnwGg9bB6+UN9YF3+dzaz0TmpjKIeh7UYrvOaNWtKromZzVS+p2JmZrlxUjEzs9w4qZiZWW6cVMzMLDdOKmZmlhsnFTMzy427FJvZjFDErJ3D+vv7AWhpacn92PU2c6eTiplNKUX98e/v7+f555/P/bjAK8ct4vj9/f2F/PcoKlk5qZjZlNLX18ed994Jc3I+sIA35HzMYUPZ27NveDb3Qz/Lswz8x0C+B30q38NVc1Ixs6lnDgy9b6jsWkxbDTcWdzvdN+rNzCw3hSUVSWslPS7pnqrYAZK6JW1N73NTXJLWSOqT1CvpXVX7VFL5rZIqVfGjJN2d9lkjqda89WZmNomKvPz1TeDvgCuqYucC10XEFyWdm9bPATrIphBuBY4BLgaOkXQA2YyRbWSzRW6WtD4inkxlVgG3kk3itRzoKvB8rE4U2cunKFu3bgXqbyDTeuuZZMUrcubHmyQtHBFeSTbFMEAncCNZUlkJXJHmnr9V0pw0n/37gO6I2A4gqRtYLulGYP+IuCXFrwBOxEnFyG70/vs9P+KQ/V4uuyoTtveO7KLBCw/fUXJNJu5nz84quwo2BU32jfr5EbENICK2SXpzii8AHqkq159iY8X7a8TNADhkv5f5q7b8e+LYq77Qs1/ZVbApaKrcqK91PyR2I1774NIqST2SegYGcu6aZ2Zmr5jspPJYuqxFen88xfuBg6vKtQCPjhNvqRGvKSIujYi2iGhrbm7e45MwM7PaJjuprAeGe3BVgKur4ienXmBLgafTZbKNQLukuamnWDuwMW17RtLS1Ovr5KpjmZlZSQq7pyLpH8hutDdJ6ifrxfVF4CpJpwI/A34/Fd8ArAD6gOeAUwAiYrukzwPDdy8/N3zTHvgEWQ+z2WQ36H2T3sysZEX2/vrYKJs+UKNsAKePcpy1wNoa8R7gyD2po5lNPf39/fB0sU99z3hPQX/0j19uN/hbMzOz3HjsLzObUlpaWhjQgMf+KlDDjQ20LMh/mH5wS8XMzHLklopNO/39/fzymVl+OK9gP31mFm/sL+a6vNUvJxUzm3qeqrMb9cODN9TL75inKGwMEicVm3ZaWlp4Yec2D9NSsC/07Me+BU2fW2+GBwRtXdBack0maEFx/52dVMxsSilq1ON6HL0a6m8kaCcVM7M9NHv27LKrMGU4qZjZjFBPv/brmZOKTUs/e7a+en899lx2U3r+G+rn2YyfPTuLt5ZdCZtynFQmWZHXdYucPbCeruvW443el9J3t+/COrnRC7yV+vxvbcVyUplGfF03Uy/Jr9pwndesWVNyTcz2jJPKJKvHP3hmZhNVR08XmZnZVOekYmZmuXFSMTOz3JSSVCQ9LOluSVsk9aTYAZK6JW1N73NTXJLWSOqT1CvpXVXHqaTyWyVVRvs8MzObHGW2VN4fEUsioi2tnwtcFxGtwHVpHaADaE2vVcDFkCUhsimKjwGOBs4fTkRmZlaOqdT7ayXZnPYAncCNwDkpfkWacvhWSXMkHZTKdg/PWS+pG1gO/MPkVttmkqKeM/IzRjZdlNVSCWCTpM2SVqXY/IjYBpDe35ziC4BHqvbtT7HR4q8jaZWkHkk9AwMDOZ6GWT5mz57t54xsWiirpXJsRDwq6c1At6Qfj1FWNWIxRvz1wYhLgUsB2traapYxmwj/4jcbWyktlYh4NL0/DvwT2T2Rx9JlLdL746l4P3Bw1e4twKNjxM3MrCSTnlQkvVHSrwwvA+3APcB6YLgHVwW4Oi2vB05OvcCWAk+ny2MbgXZJc9MN+vYUMzOzkpRx+Ws+8E+Shj//7yPiXyXdAVwl6VTgZ8Dvp/IbgBVAH/AccApARGyX9HngjlTuc8M37c3MrBzKOlXNHG1tbdHT01N2NczM6oqkzVWPgIzKT9SbmVlunFTMzCw3TipmZpYbJxUzM8vNjLtRL2kA+GnZ9ShQEzBYdiVst/i7q2/T/fv71YhoHq/QjEsq052knon00LCpx99dffP3l/HlLzMzy42TipmZ5cZJZfq5tOwK2G7zd1ff/P3heypmZpYjt1TMzCw3TiozhKT3Sbqm7HrMZJJWS7pf0nd2cb8bJc34XkVlkzRL0p278+9I0kJJ9xRRr6lmKk0nbLtA2TDPioihsutiE/ZnQEdEPFR2RWy3nAXcD+xfdkWmMrdU6kj6tXO/pK8CDwKXp/hZkh5My4dJ+mFaXi7px2n990qruCHpa8CvAeslPSNpTpoj6AlJJ6cy35J0vKTZktZJ6pV0JeB5hksmqQX4HeCytH60pO+n5ZWSnpe0t6R9q/4tHiXpLkm3AKeXVvlJ5qRSf94GXAG8Bzgyxd4LPCFpAfCbwM2S9gW+DnwobT+whLpaEhEfJ5uZ9P3Ad4BjgXeQ/Th4byq2FLgV+ATwXEQsBi4Ajpr0CttIfwt8Ghi+MvAj4J1p+b1kEw2+GzgGuC3FvwGsjoj3TGI9S+ekUn9+GhG3RsTPgf3SLJoHA38P/BbZ/+A3A28HHoqIrZF18ft2aTW2kW4m+65+C7gY+PX0g2B7RDyb4t8GiIheoLesihpI+iDweERsHo5FxE6gT9LhZNOhf5mqf3+S3gTMiYgfpF2+NcnVLo2TSv35ZdXyLWQzYT5A9ofqvWQtmH9L291ffGq6iey7ei9wIzAAfJTsOxzm727qOBb4sKSHgXXAcZK+TfZ9dQA7gGvJrhL8Jtn3K2bod+ikUt9uAj6V3u8ku7TyYkQ8DfwYOFTSYansx8qpoo0UEY+QDT7YGhEPAj8k+x6Hk8pNwB8CSDoSWFxGPS0TEedFREtELAROAq6PiD8i+54+CdwSEQPAPLIrBPdGxFPA05J+Mx3mD0uoeimcVOrbzWSXvm6KiJeBR8j+QBERLwCrgH9JN+qn88jM9eg24N/T8s3AAtJ3R3ZJbD9JvWTX8W+f/OrZBNwGzCdLLpBdpuyNV58oPwX4SrpR/3wJ9SuFn6g3M7PcuKViZma5cVIxM7PcOKmYmVlunFTMzCw3TipmZpYbJxWzMUj6jKRP1Yh/fHjMrkmow7M5HccjVVvhPEqx2S6StFdEfK3sephNRW6pmI0g6S8lPSDpWrIBPIfnNPlrST8AzhpuwUg6XNLtVfsuTA8tDo9S+wNJmyVtlHRQjc/6tKTVaflCSden5Q+koUCGy12QRry9VdL8FGuW9D1Jd6TXsSn+RklrU+xOSStrfO5vS9qSXnemMeTM9piTilkVSUeRDcXxTrLpAt5dtXlORPx2RPzNcCAi7gf2lvRrKfQHwFWSGoGLgI9GxFHAWrIRh0caHgcMoI3sSfpG0mjTKf5G4NaI+I38gmdJAAAB/ElEQVRU/k9T/P8AF0bEu4GPkIZlB/6SbCiRd5MN3fO/JL1xxOd+Cjg9Ipakz58xT3xbsXz5y+y13gv8U0Q8ByBpfdW2K0fZ5yrgPwNfJEsqf0DWwjkS6M7mU2MWsK3GvpuBo1JL4UWyIdXbUj1WpzIvAddUlV+Wlo8HjkjHB9g/HaedbADE4XtB+wKHjPjcfwO+nGah/H5E9I9ybma7xEnF7PVGG7vol6PErwT+MU3aFBGxVdKvkw0s+Jq5NCQdDPxzWv1aRHwtjX57CvD/yMaPej9wGNksgwA7qsaTeplX/902AO+JiNe0MtKsoB+JiAdGxOe/coIRX5T0L8AK4FZJx0fEj0c5P7MJ8+Uvs9e6CfjdNPvir5BNcjamiPgJ2R/7/8GrrZkHgGZJ7wGQ1CjpHRHxSEQsSa/hm/3Vo03fDHwc2BLjD8y3CThjeEXSkrS4ETgzJRckvXPkjpIOi4i7I+JLQA/Z6Lpme8xJxaxKRPyILDFsAb7Ha+c4GcuVwB+RXQojIl4imyPlS5LuSsf7T6PsezNwENkQ6o8BL0zwc1cDbWna4fvIkhHA54FGoFfSPWl9pE9KuifV7XmgawKfZzYuj1JsZma5cUvFzMxy46RiZma5cVIxM7PcOKmYmVlunFTMzCw3TipmZpYbJxUzM8uNk4qZmeXm/wOJ4wILNo1GjAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# drive-wheels\n",
"sns.boxplot(x=\"drive-wheels\", y=\"price\", data=df)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Here we see that the distribution of price between the different drive-wheels categories differs; as such drive-wheels could potentially be a predictor of price.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"discriptive_statistics\">3. Descriptive Statistical Analysis</h2>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Let's first take a look at the variables by utilizing a description method.</p>\n",
"\n",
"<p>The <b>describe</b> function automatically computes basic statistics for all continuous variables. Any NaN values are automatically skipped in these statistics.</p>\n",
"\n",
"This will show:\n",
"<ul>\n",
" <li>the count of that variable</li>\n",
" <li>the mean</li>\n",
" <li>the standard deviation (std)</li> \n",
" <li>the minimum value</li>\n",
" <li>the IQR (Interquartile Range: 25%, 50% and 75%)</li>\n",
" <li>the maximum value</li>\n",
"<ul>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" We can apply the method \"describe\" as follows:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": 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>count</th>\n",
" <td>201.000000</td>\n",
" <td>201.00000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>197.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" <td>201.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td>0.840796</td>\n",
" <td>122.00000</td>\n",
" <td>98.797015</td>\n",
" <td>0.837102</td>\n",
" <td>0.915126</td>\n",
" <td>53.766667</td>\n",
" <td>2555.666667</td>\n",
" <td>126.875622</td>\n",
" <td>3.330692</td>\n",
" <td>3.256904</td>\n",
" <td>10.164279</td>\n",
" <td>103.405534</td>\n",
" <td>5117.665368</td>\n",
" <td>25.179104</td>\n",
" <td>30.686567</td>\n",
" <td>13207.129353</td>\n",
" <td>9.944145</td>\n",
" <td>0.099502</td>\n",
" <td>0.900498</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td>1.254802</td>\n",
" <td>31.99625</td>\n",
" <td>6.066366</td>\n",
" <td>0.059213</td>\n",
" <td>0.029187</td>\n",
" <td>2.447822</td>\n",
" <td>517.296727</td>\n",
" <td>41.546834</td>\n",
" <td>0.268072</td>\n",
" <td>0.319256</td>\n",
" <td>4.004965</td>\n",
" <td>37.365700</td>\n",
" <td>478.113805</td>\n",
" <td>6.423220</td>\n",
" <td>6.815150</td>\n",
" <td>7947.066342</td>\n",
" <td>2.534599</td>\n",
" <td>0.300083</td>\n",
" <td>0.300083</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td>-2.000000</td>\n",
" <td>65.00000</td>\n",
" <td>86.600000</td>\n",
" <td>0.678039</td>\n",
" <td>0.837500</td>\n",
" <td>47.800000</td>\n",
" <td>1488.000000</td>\n",
" <td>61.000000</td>\n",
" <td>2.540000</td>\n",
" <td>2.070000</td>\n",
" <td>7.000000</td>\n",
" <td>48.000000</td>\n",
" <td>4150.000000</td>\n",
" <td>13.000000</td>\n",
" <td>16.000000</td>\n",
" <td>5118.000000</td>\n",
" <td>4.795918</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td>0.000000</td>\n",
" <td>101.00000</td>\n",
" <td>94.500000</td>\n",
" <td>0.801538</td>\n",
" <td>0.890278</td>\n",
" <td>52.000000</td>\n",
" <td>2169.000000</td>\n",
" <td>98.000000</td>\n",
" <td>3.150000</td>\n",
" <td>3.110000</td>\n",
" <td>8.600000</td>\n",
" <td>70.000000</td>\n",
" <td>4800.000000</td>\n",
" <td>19.000000</td>\n",
" <td>25.000000</td>\n",
" <td>7775.000000</td>\n",
" <td>7.833333</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td>1.000000</td>\n",
" <td>122.00000</td>\n",
" <td>97.000000</td>\n",
" <td>0.832292</td>\n",
" <td>0.909722</td>\n",
" <td>54.100000</td>\n",
" <td>2414.000000</td>\n",
" <td>120.000000</td>\n",
" <td>3.310000</td>\n",
" <td>3.290000</td>\n",
" <td>9.000000</td>\n",
" <td>95.000000</td>\n",
" <td>5125.369458</td>\n",
" <td>24.000000</td>\n",
" <td>30.000000</td>\n",
" <td>10295.000000</td>\n",
" <td>9.791667</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td>2.000000</td>\n",
" <td>137.00000</td>\n",
" <td>102.400000</td>\n",
" <td>0.881788</td>\n",
" <td>0.925000</td>\n",
" <td>55.500000</td>\n",
" <td>2926.000000</td>\n",
" <td>141.000000</td>\n",
" <td>3.580000</td>\n",
" <td>3.410000</td>\n",
" <td>9.400000</td>\n",
" <td>116.000000</td>\n",
" <td>5500.000000</td>\n",
" <td>30.000000</td>\n",
" <td>34.000000</td>\n",
" <td>16500.000000</td>\n",
" <td>12.368421</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td>3.000000</td>\n",
" <td>256.00000</td>\n",
" <td>120.900000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" <td>59.800000</td>\n",
" <td>4066.000000</td>\n",
" <td>326.000000</td>\n",
" <td>3.940000</td>\n",
" <td>4.170000</td>\n",
" <td>23.000000</td>\n",
" <td>262.000000</td>\n",
" <td>6600.000000</td>\n",
" <td>49.000000</td>\n",
" <td>54.000000</td>\n",
" <td>45400.000000</td>\n",
" <td>18.076923</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 width \\\n",
"count 201.000000 201.00000 201.000000 201.000000 201.000000 \n",
"mean 0.840796 122.00000 98.797015 0.837102 0.915126 \n",
"std 1.254802 31.99625 6.066366 0.059213 0.029187 \n",
"min -2.000000 65.00000 86.600000 0.678039 0.837500 \n",
"25% 0.000000 101.00000 94.500000 0.801538 0.890278 \n",
"50% 1.000000 122.00000 97.000000 0.832292 0.909722 \n",
"75% 2.000000 137.00000 102.400000 0.881788 0.925000 \n",
"max 3.000000 256.00000 120.900000 1.000000 1.000000 \n",
"\n",
" height curb-weight engine-size bore stroke \\\n",
"count 201.000000 201.000000 201.000000 201.000000 197.000000 \n",
"mean 53.766667 2555.666667 126.875622 3.330692 3.256904 \n",
"std 2.447822 517.296727 41.546834 0.268072 0.319256 \n",
"min 47.800000 1488.000000 61.000000 2.540000 2.070000 \n",
"25% 52.000000 2169.000000 98.000000 3.150000 3.110000 \n",
"50% 54.100000 2414.000000 120.000000 3.310000 3.290000 \n",
"75% 55.500000 2926.000000 141.000000 3.580000 3.410000 \n",
"max 59.800000 4066.000000 326.000000 3.940000 4.170000 \n",
"\n",
" compression-ratio horsepower peak-rpm city-mpg highway-mpg \\\n",
"count 201.000000 201.000000 201.000000 201.000000 201.000000 \n",
"mean 10.164279 103.405534 5117.665368 25.179104 30.686567 \n",
"std 4.004965 37.365700 478.113805 6.423220 6.815150 \n",
"min 7.000000 48.000000 4150.000000 13.000000 16.000000 \n",
"25% 8.600000 70.000000 4800.000000 19.000000 25.000000 \n",
"50% 9.000000 95.000000 5125.369458 24.000000 30.000000 \n",
"75% 9.400000 116.000000 5500.000000 30.000000 34.000000 \n",
"max 23.000000 262.000000 6600.000000 49.000000 54.000000 \n",
"\n",
" price city-L/100km diesel gas \n",
"count 201.000000 201.000000 201.000000 201.000000 \n",
"mean 13207.129353 9.944145 0.099502 0.900498 \n",
"std 7947.066342 2.534599 0.300083 0.300083 \n",
"min 5118.000000 4.795918 0.000000 0.000000 \n",
"25% 7775.000000 7.833333 0.000000 1.000000 \n",
"50% 10295.000000 9.791667 0.000000 1.000000 \n",
"75% 16500.000000 12.368421 0.000000 1.000000 \n",
"max 45400.000000 18.076923 1.000000 1.000000 "
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.describe()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" The default setting of \"describe\" skips variables of type object. We can apply the method \"describe\" on the variables of type 'object' as follows:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false,
"scrolled": true
},
"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>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>engine-type</th>\n",
" <th>num-of-cylinders</th>\n",
" <th>fuel-system</th>\n",
" <th>horsepower-binned</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td>201</td>\n",
" <td>201</td>\n",
" <td>201</td>\n",
" <td>201</td>\n",
" <td>201</td>\n",
" <td>201</td>\n",
" <td>201</td>\n",
" <td>201</td>\n",
" <td>201</td>\n",
" <td>200</td>\n",
" </tr>\n",
" <tr>\n",
" <th>unique</th>\n",
" <td>22</td>\n",
" <td>2</td>\n",
" <td>2</td>\n",
" <td>5</td>\n",
" <td>3</td>\n",
" <td>2</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" <td>8</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>top</th>\n",
" <td>toyota</td>\n",
" <td>std</td>\n",
" <td>four</td>\n",
" <td>sedan</td>\n",
" <td>fwd</td>\n",
" <td>front</td>\n",
" <td>ohc</td>\n",
" <td>four</td>\n",
" <td>mpfi</td>\n",
" <td>Low</td>\n",
" </tr>\n",
" <tr>\n",
" <th>freq</th>\n",
" <td>32</td>\n",
" <td>165</td>\n",
" <td>115</td>\n",
" <td>94</td>\n",
" <td>118</td>\n",
" <td>198</td>\n",
" <td>145</td>\n",
" <td>157</td>\n",
" <td>92</td>\n",
" <td>115</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" make aspiration num-of-doors body-style drive-wheels \\\n",
"count 201 201 201 201 201 \n",
"unique 22 2 2 5 3 \n",
"top toyota std four sedan fwd \n",
"freq 32 165 115 94 118 \n",
"\n",
" engine-location engine-type num-of-cylinders fuel-system \\\n",
"count 201 201 201 201 \n",
"unique 2 6 7 8 \n",
"top front ohc four mpfi \n",
"freq 198 145 157 92 \n",
"\n",
" horsepower-binned \n",
"count 200 \n",
"unique 3 \n",
"top Low \n",
"freq 115 "
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.describe(include=['object'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Value Counts</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Value-counts is a good way of understanding how many units of each characteristic/variable we have. We can apply the \"value_counts\" method on the column 'drive-wheels'. Don’t forget the method \"value_counts\" only works on Pandas series, not Pandas Dataframes. As a result, we only include one bracket \"df['drive-wheels']\" not two brackets \"df[['drive-wheels']]\".</p>"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"fwd 118\n",
"rwd 75\n",
"4wd 8\n",
"Name: drive-wheels, dtype: int64"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df['drive-wheels'].value_counts()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can convert the series to a Dataframe as follows :"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": 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>drive-wheels</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>fwd</th>\n",
" <td>118</td>\n",
" </tr>\n",
" <tr>\n",
" <th>rwd</th>\n",
" <td>75</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4wd</th>\n",
" <td>8</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" drive-wheels\n",
"fwd 118\n",
"rwd 75\n",
"4wd 8"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df['drive-wheels'].value_counts().to_frame()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's repeat the above steps but save the results to the dataframe \"drive_wheels_counts\" and rename the column 'drive-wheels' to 'value_counts'."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": 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>value_counts</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>fwd</th>\n",
" <td>118</td>\n",
" </tr>\n",
" <tr>\n",
" <th>rwd</th>\n",
" <td>75</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4wd</th>\n",
" <td>8</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" value_counts\n",
"fwd 118\n",
"rwd 75\n",
"4wd 8"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"drive_wheels_counts = df['drive-wheels'].value_counts().to_frame()\n",
"drive_wheels_counts.rename(columns={'drive-wheels': 'value_counts'}, inplace=True)\n",
"drive_wheels_counts"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Now let's rename the index to 'drive-wheels':"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": 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>value_counts</th>\n",
" </tr>\n",
" <tr>\n",
" <th>drive-wheels</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>fwd</th>\n",
" <td>118</td>\n",
" </tr>\n",
" <tr>\n",
" <th>rwd</th>\n",
" <td>75</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4wd</th>\n",
" <td>8</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" value_counts\n",
"drive-wheels \n",
"fwd 118\n",
"rwd 75\n",
"4wd 8"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"drive_wheels_counts.index.name = 'drive-wheels'\n",
"drive_wheels_counts"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can repeat the above process for the variable 'engine-location'."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": 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>value_counts</th>\n",
" </tr>\n",
" <tr>\n",
" <th>engine-location</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>front</th>\n",
" <td>198</td>\n",
" </tr>\n",
" <tr>\n",
" <th>rear</th>\n",
" <td>3</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" value_counts\n",
"engine-location \n",
"front 198\n",
"rear 3"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# engine-location as variable\n",
"engine_loc_counts = df['engine-location'].value_counts().to_frame()\n",
"engine_loc_counts.rename(columns={'engine-location': 'value_counts'}, inplace=True)\n",
"engine_loc_counts.index.name = 'engine-location'\n",
"engine_loc_counts.head(10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Examining the value counts of the engine location would not be a good predictor variable for the price. This is because we only have three cars with a rear engine and 198 with an engine in the front, this result is skewed. Thus, we are not able to draw any conclusions about the engine location.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"basic_grouping\">4. Basics of Grouping</h2>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>The \"groupby\" method groups data by different categories. The data is grouped based on one or several variables and analysis is performed on the individual groups.</p>\n",
"\n",
"<p>For example, let's group by the variable \"drive-wheels\". We see that there are 3 different categories of drive wheels.</p>"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array(['rwd', 'fwd', '4wd'], dtype=object)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df['drive-wheels'].unique()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>If we want to know, on average, which type of drive wheel is most valuable, we can group \"drive-wheels\" and then average them.</p>\n",
"\n",
"<p>We can select the columns 'drive-wheels', 'body-style' and 'price', then assign it to the variable \"df_group_one\".</p>"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_group_one = df[['drive-wheels','body-style','price']]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can then calculate the average price for each of the different categories of data."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": 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>drive-wheels</th>\n",
" <th>price</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>4wd</td>\n",
" <td>10241.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>fwd</td>\n",
" <td>9244.779661</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>rwd</td>\n",
" <td>19757.613333</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" drive-wheels price\n",
"0 4wd 10241.000000\n",
"1 fwd 9244.779661\n",
"2 rwd 19757.613333"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# grouping results\n",
"df_group_one = df_group_one.groupby(['drive-wheels'],as_index=False).mean()\n",
"df_group_one"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>From our data, it seems rear-wheel drive vehicles are, on average, the most expensive, while 4-wheel and front-wheel are approximately the same in price.</p>\n",
"\n",
"<p>You can also group with multiple variables. For example, let's group by both 'drive-wheels' and 'body-style'. This groups the dataframe by the unique combinations 'drive-wheels' and 'body-style'. We can store the results in the variable 'grouped_test1'.</p>"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": 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>drive-wheels</th>\n",
" <th>body-style</th>\n",
" <th>price</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>4wd</td>\n",
" <td>hatchback</td>\n",
" <td>7603.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>4wd</td>\n",
" <td>sedan</td>\n",
" <td>12647.333333</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>4wd</td>\n",
" <td>wagon</td>\n",
" <td>9095.750000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>fwd</td>\n",
" <td>convertible</td>\n",
" <td>11595.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>fwd</td>\n",
" <td>hardtop</td>\n",
" <td>8249.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>8396.387755</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>9811.800000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>fwd</td>\n",
" <td>wagon</td>\n",
" <td>9997.333333</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>rwd</td>\n",
" <td>convertible</td>\n",
" <td>23949.600000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>rwd</td>\n",
" <td>hardtop</td>\n",
" <td>24202.714286</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>rwd</td>\n",
" <td>hatchback</td>\n",
" <td>14337.777778</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>21711.833333</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>rwd</td>\n",
" <td>wagon</td>\n",
" <td>16994.222222</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" drive-wheels body-style price\n",
"0 4wd hatchback 7603.000000\n",
"1 4wd sedan 12647.333333\n",
"2 4wd wagon 9095.750000\n",
"3 fwd convertible 11595.000000\n",
"4 fwd hardtop 8249.000000\n",
"5 fwd hatchback 8396.387755\n",
"6 fwd sedan 9811.800000\n",
"7 fwd wagon 9997.333333\n",
"8 rwd convertible 23949.600000\n",
"9 rwd hardtop 24202.714286\n",
"10 rwd hatchback 14337.777778\n",
"11 rwd sedan 21711.833333\n",
"12 rwd wagon 16994.222222"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# grouping results\n",
"df_gptest = df[['drive-wheels','body-style','price']]\n",
"grouped_test1 = df_gptest.groupby(['drive-wheels','body-style'],as_index=False).mean()\n",
"grouped_test1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>This grouped data is much easier to visualize when it is made into a pivot table. A pivot table is like an Excel spreadsheet, with one variable along the column and another along the row. We can convert the dataframe to a pivot table using the method \"pivot \" to create a pivot table from the groups.</p>\n",
"\n",
"<p>In this case, we will leave the drive-wheel variable as the rows of the table, and pivot body-style to become the columns of the table:</p>"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": 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 tr th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe thead tr:last-of-type th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr>\n",
" <th></th>\n",
" <th colspan=\"5\" halign=\"left\">price</th>\n",
" </tr>\n",
" <tr>\n",
" <th>body-style</th>\n",
" <th>convertible</th>\n",
" <th>hardtop</th>\n",
" <th>hatchback</th>\n",
" <th>sedan</th>\n",
" <th>wagon</th>\n",
" </tr>\n",
" <tr>\n",
" <th>drive-wheels</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>4wd</th>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>7603.000000</td>\n",
" <td>12647.333333</td>\n",
" <td>9095.750000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>fwd</th>\n",
" <td>11595.0</td>\n",
" <td>8249.000000</td>\n",
" <td>8396.387755</td>\n",
" <td>9811.800000</td>\n",
" <td>9997.333333</td>\n",
" </tr>\n",
" <tr>\n",
" <th>rwd</th>\n",
" <td>23949.6</td>\n",
" <td>24202.714286</td>\n",
" <td>14337.777778</td>\n",
" <td>21711.833333</td>\n",
" <td>16994.222222</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" price \\\n",
"body-style convertible hardtop hatchback sedan \n",
"drive-wheels \n",
"4wd NaN NaN 7603.000000 12647.333333 \n",
"fwd 11595.0 8249.000000 8396.387755 9811.800000 \n",
"rwd 23949.6 24202.714286 14337.777778 21711.833333 \n",
"\n",
" \n",
"body-style wagon \n",
"drive-wheels \n",
"4wd 9095.750000 \n",
"fwd 9997.333333 \n",
"rwd 16994.222222 "
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"grouped_pivot = grouped_test1.pivot(index='drive-wheels',columns='body-style')\n",
"grouped_pivot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Often, we won't have data for some of the pivot cells. We can fill these missing cells with the value 0, but any other value could potentially be used as well. It should be mentioned that missing data is quite a complex subject and is an entire course on its own.</p>"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false,
"scrolled": true
},
"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 tr th {\n",
" text-align: left;\n",
" }\n",
"\n",
" .dataframe thead tr:last-of-type th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr>\n",
" <th></th>\n",
" <th colspan=\"5\" halign=\"left\">price</th>\n",
" </tr>\n",
" <tr>\n",
" <th>body-style</th>\n",
" <th>convertible</th>\n",
" <th>hardtop</th>\n",
" <th>hatchback</th>\n",
" <th>sedan</th>\n",
" <th>wagon</th>\n",
" </tr>\n",
" <tr>\n",
" <th>drive-wheels</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>4wd</th>\n",
" <td>0.0</td>\n",
" <td>0.000000</td>\n",
" <td>7603.000000</td>\n",
" <td>12647.333333</td>\n",
" <td>9095.750000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>fwd</th>\n",
" <td>11595.0</td>\n",
" <td>8249.000000</td>\n",
" <td>8396.387755</td>\n",
" <td>9811.800000</td>\n",
" <td>9997.333333</td>\n",
" </tr>\n",
" <tr>\n",
" <th>rwd</th>\n",
" <td>23949.6</td>\n",
" <td>24202.714286</td>\n",
" <td>14337.777778</td>\n",
" <td>21711.833333</td>\n",
" <td>16994.222222</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" price \\\n",
"body-style convertible hardtop hatchback sedan \n",
"drive-wheels \n",
"4wd 0.0 0.000000 7603.000000 12647.333333 \n",
"fwd 11595.0 8249.000000 8396.387755 9811.800000 \n",
"rwd 23949.6 24202.714286 14337.777778 21711.833333 \n",
"\n",
" \n",
"body-style wagon \n",
"drive-wheels \n",
"4wd 9095.750000 \n",
"fwd 9997.333333 \n",
"rwd 16994.222222 "
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"grouped_pivot = grouped_pivot.fillna(0) #fill missing values with 0\n",
"grouped_pivot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question 4:</h1>\n",
"\n",
"<p>Use the \"groupby\" function to find the average \"price\" of each car based on \"body-style\" ? </p>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": 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>body-style</th>\n",
" <th>price</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>convertible</td>\n",
" <td>21890.500000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>hardtop</td>\n",
" <td>22208.500000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>hatchback</td>\n",
" <td>9957.441176</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>sedan</td>\n",
" <td>14459.755319</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>wagon</td>\n",
" <td>12371.960000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" body-style price\n",
"0 convertible 21890.500000\n",
"1 hardtop 22208.500000\n",
"2 hatchback 9957.441176\n",
"3 sedan 14459.755319\n",
"4 wagon 12371.960000"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"df_group_two = df[['body-style', 'price']]\n",
"group_test_bodystyle = df_group_two.groupby(['body-style'], as_index=False).mean()\n",
"group_test_bodystyle"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"# grouping results\n",
"df_gptest2 = df[['body-style','price']]\n",
"grouped_test_bodystyle = df_gptest2.groupby(['body-style'],as_index= False).mean()\n",
"grouped_test_bodystyle\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you did not import \"pyplot\" let's do it again. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Variables: Drive Wheels and Body Style vs Price</h4>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's use a heat map to visualize the relationship between Body Style vs Price."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#use the grouped results\n",
"plt.pcolor(grouped_pivot, cmap='RdBu')\n",
"plt.colorbar()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>The heatmap plots the target variable (price) proportional to colour with respect to the variables 'drive-wheel' and 'body-style' in the vertical and horizontal axis respectively. This allows us to visualize how the price is related to 'drive-wheel' and 'body-style'.</p>\n",
"\n",
"<p>The default labels convey no useful information to us. Let's change that:</p>"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"im = ax.pcolor(grouped_pivot, cmap='RdBu')\n",
"\n",
"#label names\n",
"row_labels = grouped_pivot.columns.levels[1]\n",
"col_labels = grouped_pivot.index\n",
"\n",
"#move ticks and labels to the center\n",
"ax.set_xticks(np.arange(grouped_pivot.shape[1]) + 0.5, minor=False)\n",
"ax.set_yticks(np.arange(grouped_pivot.shape[0]) + 0.5, minor=False)\n",
"\n",
"#insert labels\n",
"ax.set_xticklabels(row_labels, minor=False)\n",
"ax.set_yticklabels(col_labels, minor=False)\n",
"\n",
"#rotate label if too long\n",
"plt.xticks(rotation=90)\n",
"\n",
"fig.colorbar(im)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Visualization is very important in data science, and Python visualization packages provide great freedom. We will go more in-depth in a separate Python Visualizations course.</p>\n",
"\n",
"<p>The main question we want to answer in this module, is \"What are the main characteristics which have the most impact on the car price?\".</p>\n",
"\n",
"<p>To get a better measure of the important characteristics, we look at the correlation of these variables with the car price, in other words: how is the car price dependent on this variable?</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"correlation_causation\">5. 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": 37,
"metadata": {
"collapsed": 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": 37,
"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": 38,
"metadata": {
"collapsed": true
},
"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": 39,
"metadata": {
"collapsed": 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": 40,
"metadata": {
"collapsed": 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": 41,
"metadata": {
"collapsed": 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": 42,
"metadata": {
"collapsed": 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": 43,
"metadata": {
"collapsed": 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": 44,
"metadata": {
"collapsed": 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": 46,
"metadata": {
"collapsed": 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": 48,
"metadata": {
"collapsed": 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": 49,
"metadata": {
"collapsed": 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": [
"<h2 id=\"anova\">6. ANOVA</h2>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>ANOVA: Analysis of Variance</h3>\n",
"<p>The Analysis of Variance (ANOVA) is a statistical method used to test whether there are significant differences between the means of two or more groups. ANOVA returns two parameters:</p>\n",
"\n",
"<p><b>F-test score</b>: ANOVA assumes the means of all groups are the same, calculates how much the actual means deviate from the assumption, and reports it as the F-test score. A larger score means there is a larger difference between the means.</p>\n",
"\n",
"<p><b>P-value</b>: P-value tells how statistically significant is our calculated score value.</p>\n",
"\n",
"<p>If our price variable is strongly correlated with the variable we are analyzing, expect ANOVA to return a sizeable F-test score and a small p-value.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Drive Wheels</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Since ANOVA analyzes the difference between different groups of the same variable, the groupby function will come in handy. Because the ANOVA algorithm averages the data automatically, we do not need to take the average before hand.</p>\n",
"\n",
"<p>Let's see if different types 'drive-wheels' impact 'price', we group the data.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's see if different types 'drive-wheels' impact 'price', we group the data."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>drive-wheels</th>\n",
" <th>price</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>rwd</td>\n",
" <td>13495.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>rwd</td>\n",
" <td>16500.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>fwd</td>\n",
" <td>13950.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>4wd</td>\n",
" <td>17450.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>fwd</td>\n",
" <td>15250.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>136</th>\n",
" <td>4wd</td>\n",
" <td>7603.0</td>\n",
" </tr>\n",
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"</table>\n",
"</div>"
],
"text/plain": [
" drive-wheels price\n",
"0 rwd 13495.0\n",
"1 rwd 16500.0\n",
"3 fwd 13950.0\n",
"4 4wd 17450.0\n",
"5 fwd 15250.0\n",
"136 4wd 7603.0"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"grouped_test2=df_gptest[['drive-wheels', 'price']].groupby(['drive-wheels'])\n",
"grouped_test2.head(2)"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>drive-wheels</th>\n",
" <th>body-style</th>\n",
" <th>price</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>rwd</td>\n",
" <td>convertible</td>\n",
" <td>13495.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>rwd</td>\n",
" <td>convertible</td>\n",
" <td>16500.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>rwd</td>\n",
" <td>hatchback</td>\n",
" <td>16500.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>13950.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>4wd</td>\n",
" <td>sedan</td>\n",
" <td>17450.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>15250.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>17710.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>fwd</td>\n",
" <td>wagon</td>\n",
" <td>18920.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>23875.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>16430.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>16925.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>20970.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>21105.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>24565.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>30760.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>41315.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>36880.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>5151.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>6295.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>6575.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>5572.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>6377.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>7957.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>23</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>6229.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>24</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>6692.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>7609.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>26</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>8558.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>27</th>\n",
" <td>fwd</td>\n",
" <td>wagon</td>\n",
" <td>8921.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>28</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>12964.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>29</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>6479.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>171</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>9988.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>172</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>10898.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>173</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>11248.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>174</th>\n",
" <td>rwd</td>\n",
" <td>hatchback</td>\n",
" <td>16558.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>175</th>\n",
" <td>rwd</td>\n",
" <td>hatchback</td>\n",
" <td>15998.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>176</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>15690.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>177</th>\n",
" <td>rwd</td>\n",
" <td>wagon</td>\n",
" <td>15750.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>178</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>7775.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>179</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>7975.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>180</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>7995.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>181</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>8195.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>182</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>8495.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>183</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>9495.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>184</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>9995.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>185</th>\n",
" <td>fwd</td>\n",
" <td>convertible</td>\n",
" <td>11595.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>186</th>\n",
" <td>fwd</td>\n",
" <td>hatchback</td>\n",
" <td>9980.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>187</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>13295.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>188</th>\n",
" <td>fwd</td>\n",
" <td>sedan</td>\n",
" <td>13845.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>189</th>\n",
" <td>fwd</td>\n",
" <td>wagon</td>\n",
" <td>12290.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>190</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>12940.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>191</th>\n",
" <td>rwd</td>\n",
" <td>wagon</td>\n",
" <td>13415.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>192</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>15985.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>193</th>\n",
" <td>rwd</td>\n",
" <td>wagon</td>\n",
" <td>16515.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>194</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>18420.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>195</th>\n",
" <td>rwd</td>\n",
" <td>wagon</td>\n",
" <td>18950.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>196</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>16845.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>197</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>19045.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>198</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>21485.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>199</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>22470.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>200</th>\n",
" <td>rwd</td>\n",
" <td>sedan</td>\n",
" <td>22625.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>201 rows × 3 columns</p>\n",
"</div>"
],
"text/plain": [
" drive-wheels body-style price\n",
"0 rwd convertible 13495.0\n",
"1 rwd convertible 16500.0\n",
"2 rwd hatchback 16500.0\n",
"3 fwd sedan 13950.0\n",
"4 4wd sedan 17450.0\n",
"5 fwd sedan 15250.0\n",
"6 fwd sedan 17710.0\n",
"7 fwd wagon 18920.0\n",
"8 fwd sedan 23875.0\n",
"9 rwd sedan 16430.0\n",
"10 rwd sedan 16925.0\n",
"11 rwd sedan 20970.0\n",
"12 rwd sedan 21105.0\n",
"13 rwd sedan 24565.0\n",
"14 rwd sedan 30760.0\n",
"15 rwd sedan 41315.0\n",
"16 rwd sedan 36880.0\n",
"17 fwd hatchback 5151.0\n",
"18 fwd hatchback 6295.0\n",
"19 fwd sedan 6575.0\n",
"20 fwd hatchback 5572.0\n",
"21 fwd hatchback 6377.0\n",
"22 fwd hatchback 7957.0\n",
"23 fwd hatchback 6229.0\n",
"24 fwd sedan 6692.0\n",
"25 fwd sedan 7609.0\n",
"26 fwd sedan 8558.0\n",
"27 fwd wagon 8921.0\n",
"28 fwd hatchback 12964.0\n",
"29 fwd hatchback 6479.0\n",
".. ... ... ...\n",
"171 fwd hatchback 9988.0\n",
"172 fwd sedan 10898.0\n",
"173 fwd hatchback 11248.0\n",
"174 rwd hatchback 16558.0\n",
"175 rwd hatchback 15998.0\n",
"176 rwd sedan 15690.0\n",
"177 rwd wagon 15750.0\n",
"178 fwd sedan 7775.0\n",
"179 fwd sedan 7975.0\n",
"180 fwd sedan 7995.0\n",
"181 fwd sedan 8195.0\n",
"182 fwd sedan 8495.0\n",
"183 fwd sedan 9495.0\n",
"184 fwd sedan 9995.0\n",
"185 fwd convertible 11595.0\n",
"186 fwd hatchback 9980.0\n",
"187 fwd sedan 13295.0\n",
"188 fwd sedan 13845.0\n",
"189 fwd wagon 12290.0\n",
"190 rwd sedan 12940.0\n",
"191 rwd wagon 13415.0\n",
"192 rwd sedan 15985.0\n",
"193 rwd wagon 16515.0\n",
"194 rwd sedan 18420.0\n",
"195 rwd wagon 18950.0\n",
"196 rwd sedan 16845.0\n",
"197 rwd sedan 19045.0\n",
"198 rwd sedan 21485.0\n",
"199 rwd sedan 22470.0\n",
"200 rwd sedan 22625.0\n",
"\n",
"[201 rows x 3 columns]"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_gptest"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" We can obtain the values of the method group using the method \"get_group\". "
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"4 17450.0\n",
"136 7603.0\n",
"140 9233.0\n",
"141 11259.0\n",
"144 8013.0\n",
"145 11694.0\n",
"150 7898.0\n",
"151 8778.0\n",
"Name: price, dtype: float64"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"grouped_test2.get_group('4wd')['price']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we can use the function 'f_oneway' in the module 'stats' to obtain the <b>F-test score</b> and <b>P-value</b>."
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ANOVA results: F= 67.95406500780399 , P = 3.3945443577151245e-23\n"
]
}
],
"source": [
"# ANOVA\n",
"f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price'], grouped_test2.get_group('4wd')['price']) \n",
" \n",
"print( \"ANOVA results: F=\", f_val, \", P =\", p_val) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a great result, with a large F test score showing a strong correlation and a P value of almost 0 implying almost certain statistical significance. But does this mean all three tested groups are all this highly correlated? "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Separately: fwd and rwd"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ANOVA results: F= 130.5533160959111 , P = 2.2355306355677845e-23\n"
]
}
],
"source": [
"f_val, p_val = stats.f_oneway(grouped_test2.get_group('fwd')['price'], grouped_test2.get_group('rwd')['price']) \n",
" \n",
"print( \"ANOVA results: F=\", f_val, \", P =\", p_val )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's examine the other groups "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 4wd and rwd"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ANOVA results: F= 8.580681368924756 , P = 0.004411492211225333\n"
]
}
],
"source": [
"f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('rwd')['price']) \n",
" \n",
"print( \"ANOVA results: F=\", f_val, \", P =\", p_val) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>4wd and fwd</h4>"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ANOVA results: F= 0.665465750252303 , P = 0.41620116697845666\n"
]
}
],
"source": [
"f_val, p_val = stats.f_oneway(grouped_test2.get_group('4wd')['price'], grouped_test2.get_group('fwd')['price']) \n",
" \n",
"print(\"ANOVA results: F=\", f_val, \", P =\", p_val) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Conclusion: Important Variables</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We now have a better idea of what our data looks like and which variables are important to take into account when predicting the car price. We have narrowed it down to the following variables:</p>\n",
"\n",
"Continuous numerical variables:\n",
"<ul>\n",
" <li>Length</li>\n",
" <li>Width</li>\n",
" <li>Curb-weight</li>\n",
" <li>Engine-size</li>\n",
" <li>Horsepower</li>\n",
" <li>City-mpg</li>\n",
" <li>Highway-mpg</li>\n",
" <li>Wheel-base</li>\n",
" <li>Bore</li>\n",
"</ul>\n",
" \n",
"Categorical variables:\n",
"<ul>\n",
" <li>Drive-wheels</li>\n",
"</ul>\n",
"\n",
"<p>As we now move into building machine learning models to automate our analysis, feeding the model with variables that meaningfully affect our target variable will improve our model's prediction performance.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Thank you for completing this notebook</h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
"\n",
" <p><a href=\"https://cocl.us/corsera_da0101en_notebook_bottom\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/BottomAd.png\" width=\"750\" align=\"center\"></a></p>\n",
"</div>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>About the Authors:</h3>\n",
"\n",
"This notebook was written by <a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>, <a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>, Bahare Talayian, Eric Xiao, Steven Dong, Parizad, Hima Vsudevan and <a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a> and <a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
"\n",
"<p><a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a> is a Data Scientist at IBM, and holds a PhD in Electrical Engineering. His research focused on using Machine Learning, Signal Processing, and Computer Vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<hr>\n",
"<p>Copyright &copy; 2018 IBM Developer Skills Network. This notebook and its source code are released under the terms of the <a href=\"https://cognitiveclass.ai/mit-license/\">MIT License</a>.</p>"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.8"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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