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model-development.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
" <a href=\"https://cocl.us/corsera_da0101en_notebook_top\">\n",
" <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/TopAd.png\" width=\"750\" align=\"center\">\n",
" </a>\n",
"</div>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/CCLog.png\" width = 300, align = \"center\"></a>\n",
"\n",
"<h1 align=center><font size=5>Data Analysis with Python</font></h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Module 4: Model Development</h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>In this section, we will develop several models that will predict the price of the car using the variables or features. This is just an estimate but should give us an objective idea of how much the car should cost.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some questions we want to ask in this module\n",
"<ul>\n",
" <li>do I know if the dealer is offering fair value for my trade-in?</li>\n",
" <li>do I know if I put a fair value on my car?</li>\n",
"</ul>\n",
"<p>Data Analytics, we often use <b>Model Development</b> to help us predict future observations from the data we have.</p>\n",
"\n",
"<p>A Model will help us understand the exact relationship between different variables and how these variables are used to predict the result.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Setup</h4>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Import libraries"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"load data and store in dataframe df:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This dataset was hosted on IBM Cloud object click <a href=\"https://cocl.us/DA101EN_object_storage\">HERE</a> for free storage."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>symboling</th>\n",
" <th>normalized-losses</th>\n",
" <th>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 of data \n",
"path = 'https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/automobileEDA.csv'\n",
"df = pd.read_csv(path)\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>1. Linear Regression and Multiple Linear Regression</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Linear Regression</h4>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"<p>One example of a Data Model that we will be using is</p>\n",
"<b>Simple Linear Regression</b>.\n",
"\n",
"<br>\n",
"<p>Simple Linear Regression is a method to help us understand the relationship between two variables:</p>\n",
"<ul>\n",
" <li>The predictor/independent variable (X)</li>\n",
" <li>The response/dependent variable (that we want to predict)(Y)</li>\n",
"</ul>\n",
"\n",
"<p>The result of Linear Regression is a <b>linear function</b> that predicts the response (dependent) variable as a function of the predictor (independent) variable.</p>\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
" Y: Response \\ Variable\\\\\n",
" X: Predictor \\ Variables\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" <b>Linear function:</b>\n",
"$$\n",
"Yhat = a + b X\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<ul>\n",
" <li>a refers to the <b>intercept</b> of the regression line0, in other words: the value of Y when X is 0</li>\n",
" <li>b refers to the <b>slope</b> of the regression line, in other words: the value with which Y changes when X increases by 1 unit</li>\n",
"</ul>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Lets load the modules for linear regression</h4>"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"from sklearn.linear_model import LinearRegression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Create the linear regression object</h4>"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm = LinearRegression()\n",
"lm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>How could Highway-mpg help us predict car price?</h4>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For this example, we want to look at how highway-mpg can help us predict car price.\n",
"Using simple linear regression, we will create a linear function with \"highway-mpg\" as the predictor variable and the \"price\" as the response variable."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>highway-mpg</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>27</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>27</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>26</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>30</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>22</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>196</th>\n",
" <td>28</td>\n",
" </tr>\n",
" <tr>\n",
" <th>197</th>\n",
" <td>25</td>\n",
" </tr>\n",
" <tr>\n",
" <th>198</th>\n",
" <td>23</td>\n",
" </tr>\n",
" <tr>\n",
" <th>199</th>\n",
" <td>27</td>\n",
" </tr>\n",
" <tr>\n",
" <th>200</th>\n",
" <td>25</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>201 rows × 1 columns</p>\n",
"</div>"
],
"text/plain": [
" highway-mpg\n",
"0 27\n",
"1 27\n",
"2 26\n",
"3 30\n",
"4 22\n",
".. ...\n",
"196 28\n",
"197 25\n",
"198 23\n",
"199 27\n",
"200 25\n",
"\n",
"[201 rows x 1 columns]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X = df[['highway-mpg']]\n",
"Y = df['price']\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fit the linear model using highway-mpg."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(X,Y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" We can output a prediction "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
" 20345.17153508])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Yhat=lm.predict(X)\n",
"Yhat[0:5] "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>What is the value of the intercept (a)?</h4>"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"38423.3058581574"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>What is the value of the Slope (b)?</h4>"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([-821.73337832])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>What is the final estimated linear model we get?</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we saw above, we should get a final linear model with the structure:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b X\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plugging in the actual values we get:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b>price</b> = 38423.31 - 821.73 x <b>highway-mpg</b>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 a): </h1>\n",
"\n",
"<b>Create a linear regression object?</b>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1 = LinearRegression()\n",
"lm1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm1 = LinearRegression()\n",
"lm1 \n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1> Question #1 b): </h1>\n",
"\n",
"<b>Train the model using 'engine-size' as the independent variable and 'price' as the dependent variable?</b>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([13728.4631336 , 13728.4631336 , 17399.38347881, 10224.40280408,\n",
" 14729.62322775])"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"A = df[['engine-size']]\n",
"B = df['price']\n",
"lm1.fit(A,B)\n",
"Yhat2=lm1.predict(A)\n",
"Yhat2[0:5] "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm1.fit(df[['highway-mpg']], df[['price']])\n",
"lm1\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 c):</h1>\n",
"\n",
"<b>Find the slope and intercept of the model?</b>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Slope</h4>"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"-7963.338906281042"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Intercept</h4>"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([166.86001569])"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"# Slope \n",
"lm1.coef_\n",
"# Intercept\n",
"lm1.intercept_\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 d): </h1>\n",
"\n",
"<b>What is the equation of the predicted line. You can use x and yhat or 'engine-size' or 'price'?</b>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# You can type you answer here\n",
"yhat1 = -7963.34 +166.86*A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"# using X and Y \n",
"Yhat=-7963.34 + 166.86*X\n",
"\n",
"Price=-7963.34 + 166.86*engine-size\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Multiple Linear Regression</h4>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>What if we want to predict car price using more than one variable?</p>\n",
"\n",
"<p>If we want to use more variables in our model to predict car price, we can use <b>Multiple Linear Regression</b>.\n",
"Multiple Linear Regression is very similar to Simple Linear Regression, but this method is used to explain the relationship between one continuous response (dependent) variable and <b>two or more</b> predictor (independent) variables.\n",
"Most of the real-world regression models involve multiple predictors. We will illustrate the structure by using four predictor variables, but these results can generalize to any integer:</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Y: Response \\ Variable\\\\\n",
"X_1 :Predictor\\ Variable \\ 1\\\\\n",
"X_2: Predictor\\ Variable \\ 2\\\\\n",
"X_3: Predictor\\ Variable \\ 3\\\\\n",
"X_4: Predictor\\ Variable \\ 4\\\\\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"a: intercept\\\\\n",
"b_1 :coefficients \\ of\\ Variable \\ 1\\\\\n",
"b_2: coefficients \\ of\\ Variable \\ 2\\\\\n",
"b_3: coefficients \\ of\\ Variable \\ 3\\\\\n",
"b_4: coefficients \\ of\\ Variable \\ 4\\\\\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The equation is given by"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>From the previous section we know that other good predictors of price could be:</p>\n",
"<ul>\n",
" <li>Horsepower</li>\n",
" <li>Curb-weight</li>\n",
" <li>Engine-size</li>\n",
" <li>Highway-mpg</li>\n",
"</ul>\n",
"Let's develop a model using these variables as the predictor variables."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fit the linear model using the four above-mentioned variables."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(Z, df['price'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the value of the intercept(a)?"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"-15806.62462632922"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What are the values of the coefficients (b1, b2, b3, b4)?"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" What is the final estimated linear model that we get?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we saw above, we should get a final linear function with the structure:\n",
"\n",
"$$\n",
"Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
"$$\n",
"\n",
"What is the linear function we get in this example?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b>Price</b> = -15678.742628061467 + 52.65851272 x <b>horsepower</b> + 4.69878948 x <b>curb-weight</b> + 81.95906216 x <b>engine-size</b> + 33.58258185 x <b>highway-mpg</b>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1> Question #2 a): </h1>\n",
"Create and train a Multiple Linear Regression model \"lm2\" where the response variable is price, and the predictor variable is 'normalized-losses' and 'highway-mpg'.\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2 = LinearRegression()\n",
"C = df[['normalized-losses','highway-mpg']]\n",
"lm2.fit(C, df['price'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm2 = LinearRegression()\n",
"lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #2 b): </h1>\n",
"<b>Find the coefficient of the model?</b>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm2.coef_\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>2) Model Evaluation using Visualization</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we've developed some models, how do we evaluate our models and how do we choose the best one? One way to do this is by using visualization."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"import the visualization package: seaborn"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [],
"source": [
"# import the visualization package: seaborn\n",
"import seaborn as sns\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Regression Plot</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>When it comes to simple linear regression, an excellent way to visualize the fit of our model is by using <b>regression plots</b>.</p>\n",
"\n",
"<p>This plot will show a combination of a scattered data points (a <b>scatter plot</b>), as well as the fitted <b>linear regression</b> line going through the data. This will give us a reasonable estimate of the relationship between the two variables, the strength of the correlation, as well as the direction (positive or negative correlation).</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's visualize Horsepower as potential predictor variable of price:"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 48287.59114134686)"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"width = 12\n",
"height = 10\n",
"plt.figure(figsize=(width, height))\n",
"sns.regplot(x=\"highway-mpg\", y=\"price\", data=df)\n",
"plt.ylim(0,)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can see from this plot that price is negatively correlated to highway-mpg, since the regression slope is negative.\n",
"One thing to keep in mind when looking at a regression plot is to pay attention to how scattered the data points are around the regression line. This will give you a good indication of the variance of the data, and whether a linear model would be the best fit or not. If the data is too far off from the line, this linear model might not be the best model for this data. Let's compare this plot to the regression plot of \"peak-rpm\".</p>"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 47422.919330307624)"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(width, height))\n",
"sns.regplot(x=\"peak-rpm\", y=\"price\", data=df)\n",
"plt.ylim(0,)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Comparing the regression plot of \"peak-rpm\" and \"highway-mpg\" we see that the points for \"highway-mpg\" are much closer to the generated line and on the average decrease. The points for \"peak-rpm\" have more spread around the predicted line, and it is much harder to determine if the points are decreasing or increasing as the \"highway-mpg\" increases.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #3:</h1>\n",
"<b>Given the regression plots above is \"peak-rpm\" or \"highway-mpg\" more strongly correlated with \"price\". Use the method \".corr()\" to verify your answer.</b>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>peak-rpm</th>\n",
" <th>highway-mpg</th>\n",
" <th>price</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>peak-rpm</th>\n",
" <td>1.000000</td>\n",
" <td>-0.058598</td>\n",
" <td>-0.101616</td>\n",
" </tr>\n",
" <tr>\n",
" <th>highway-mpg</th>\n",
" <td>-0.058598</td>\n",
" <td>1.000000</td>\n",
" <td>-0.704692</td>\n",
" </tr>\n",
" <tr>\n",
" <th>price</th>\n",
" <td>-0.101616</td>\n",
" <td>-0.704692</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" peak-rpm highway-mpg price\n",
"peak-rpm 1.000000 -0.058598 -0.101616\n",
"highway-mpg -0.058598 1.000000 -0.704692\n",
"price -0.101616 -0.704692 1.000000"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"The variable \"highway-mpg\" has a stronger correlation with \"price\", it is approximate -0.704692 compared to \"peak-rpm\" which is approximate -0.101616. You can verify it using the following command:\n",
"df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Residual Plot</h3>\n",
"\n",
"<p>A good way to visualize the variance of the data is to use a residual plot.</p>\n",
"\n",
"<p>What is a <b>residual</b>?</p>\n",
"\n",
"<p>The difference between the observed value (y) and the predicted value (Yhat) is called the residual (e). When we look at a regression plot, the residual is the distance from the data point to the fitted regression line.</p>\n",
"\n",
"<p>So what is a <b>residual plot</b>?</p>\n",
"\n",
"<p>A residual plot is a graph that shows the residuals on the vertical y-axis and the independent variable on the horizontal x-axis.</p>\n",
"\n",
"<p>What do we pay attention to when looking at a residual plot?</p>\n",
"\n",
"<p>We look at the spread of the residuals:</p>\n",
"\n",
"<p>- If the points in a residual plot are <b>randomly spread out around the x-axis</b>, then a <b>linear model is appropriate</b> for the data. Why is that? Randomly spread out residuals means that the variance is constant, and thus the linear model is a good fit for this data.</p>"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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lAAAgNhY2vpCkbGuLCsWyBofHIpNpWEkHAABAosSh8QUhHQAAAIkSh8YXhHQAAAAkShwaXxDSAQAAkChxaHzBxlEAAAAkTtQbXxDSAQC4RkOjeQ0Oj2l8sqCuzqwGersj/Z8+gPig3AUAgGsQhz7LAOKLkA4AwDVY2GfZrHqbSZsGh8d8Tw1AEyCkAwBwDeLQZxlAfBHSAQC4BnHoswwgvgjpAABcgzj0WQYQX4R0AACuQRz6LAOIL1owNgFagAGAH1HvswwgvlhJjzlagAEAADQfVtJjbmELMEnKtraoUCxrcHis7tUdVuIBAACihZX0mAvbAoyVeAAAgOghpMdc2BZgHMYBAAAQPYT0mAvbAozDOAAAAKKHkB5zYVuAcRgHAABA9LBxtAmEaQE20Nut3QdHVCiW1Z5Ja6YUcBgHAACAZ6ykJxyHcQAAAEQPK+ngMA4AAICIYSUdAAAAiBhCOgAAABAxhHQAAAAgYgjpAAAAQMQQ0gEAAICIIaQDAAAAEUNIBwAAACKGPunQ0Gheg8NjGp8sqKszq4HebvqmAwAAeMRKesINjea1++CI8lOz2tieUX5qVrsPjmhoNO97agAAAInFSnrCDQ6PKZM2ZVurPwrZ1hYVimUNDo8lZjWdKwkAACBqCOkJNz5Z0Mb2zKKx9kxaE5MFTzNqrLkrCZm0LbqSsEeKTVDnRQYAAM2HcpeE6+rMaqYULBqbKQXa0pn1NKPGWnglwax6m0mbBofHfE+tLkOjeT144Kh+Mj6p187N6ifjk3rwwFHKlQAATW9oNK9d+w9rx95D2rX/cNP930dIT7iB3m6VAqdCsSznqrelwGmgt9v31BpifLKg9kx60VicriR85onndaZQkqtIaTO5inSmUNJnnnje99QAAFg1SdhTR0hPuL6enPbs3KZcR5vOzpSU62jTnp3bElMuEfcrCcdPF5QyKZUymZlSKVPKquMAADSruF8Jrwc16VBfTy4xofxSA73d2n1wRIViWe2ZtGZKQaKuJAAAEEdJ2FPndSXdzL5iZnkz+9mCsevM7G/N7KXabeeCjz1kZsfM7AUze8+C8Xea2U9rH9tnZlYbX2Nmf10bf8bMbm3k14foi/uVhO4b1qripIpzcnKqOKeKq44DANCs4n4lvB6+y10elfTeS8Y+LukHzrmtkn5Quy8zu0PSfZK21R7zRTObKyb+kqR+SVtrb3N/5gclTTrn3izpc5L2rtpXgtjq68npsf679N/+9F16rP+u2AR0SfrT9/aoM5uRSSoHFZmkzmxGf/reHt9TAwBg1SRhT53XkO6cG5b0+iXD75P01dr7X5X0BwvGv+Gcu+CcOy7pmKQ7zexmSeudc08755ykr13ymLk/64Ckd8+tsgPNoK8npz+/9+369Vs6dfOGdv36LZ3683vfHqsXGgAALFfcr4TXI4o16Tc6516VJOfcq2Y2993eLOnwgs+bqI2Vau9fOj73mPHan1U2s7OSrpd0avWmDzRWkvcUAACSq9n///Nd7rIcS62AuyuMX+kxi/9gs34zO2JmR06ePBliigAAAEB4UVxJf83Mbq6tot8saa7h5YSkrgWft0XSL2vjW5YYX/iYCTNrkbRBbyyvkXNuv6T9krR9+/Y3hHgAAIBmw4nV0RbFlfSDkj5Qe/8Dkv5mwfh9tY4tt6m6QfRHtdKYKTO7q1Zv/v5LHjP3Z90r6VCtbh0AACCxknAYUNz5bsH4mKSnJb3FzCbM7IOSPiPpd83sJUm/W7sv59yIpG9K+kdJ35X0EefcXO+dD0l6RNXNpP8k6Yna+F9Jut7Mjkn6t6p1igEAAEiyJBwGFHdey12cc7su86F3X+bzPy3p00uMH5H0a0uMz0r6wzBzBAAAaDZJOAwo7qJY7gIAAIBVlITDgOKOkI7Qhkbz2rX/sHbsPaRd+w9TzwYAQMQl4TCguCOkIxQ2ngAAED9JOAwo7qLYghExsnDjiSRlW1tUKJY1ODzGLzoAABHW7IcBxR0r6QhlfLKg9kx60RgbTwAAAMIhpCMUNp4AAACsPEI6QmHjCQAAwMojpCMUNp4AAACsPDaOIjQ2ngAAAKwsVtIBAACAiCGkAwAAABFDSAcAAAAihpAOAAAARAwhHQAAAIgYQjoAAAAQMYR0AAAAIGII6QAAAEDEENIBAACAiCGkAwAAABFDSAcAAAAihpAOAAAARAwhHQAAAIgYQjoAAAAQMYR0AAAAIGII6QAAAEDEENIBAACAiGnxPQEAAIA42vfki3rkqeM6Xwy0tjWt+3fcpgfuud33tNAkCOkAAADLtO/JF/XwoWNKmdSSkmZKgR4+dEySCOpYEZS7AAAALNMjTx2vBfSUUpaq3VbHgZVASAcAAFim88VAKVs8lrLqOLASCOkAAADLtLY1rYpbPFZx1XFgJVCTDsTc0Gheg8NjGp8sqKszq4HebvX15HxPCwCa2v07btPDh46pXKkoZdWAXnHVcWAlsJIOxNjQaF67D44oPzWrje0Z5admtfvgiIZG876nBgBN7YF7btcfv+vNas+kVa5I7Zm0/vhdb2bTKFYMK+lAjA0OjymTNmVbq7/K2dYWFYplDQ6PsZoOAKvsgXtuJ5Rj1bCSDsTY+GRB7ZnF9Y/tmbQmJgueZgQAAFYCIR2Isa7OrGZKizsJzJQCbenMepoRAABYCYR0IMYGertVCpwKxbKcq96WAqeB3m7fUwOAyBsazWvX/sPasfeQdu0/zH4eRAohHYixvp6c9uzcplxHm87OlJTraNOenduoRweAq2DjPaKOjaNAzPX15AjlALBMbLxH1BHSAQBA4oxPFpQ2aezktIpBRa3plG5Y18rGe0QG5S4AACBxOta06JUzsypXnNIpU7ni9MqZWa1bw/olooGfRAAAkDjOudo7WnQ7Pw54xko6AABInOlioM0b29SSNgXOqSVt2ryxTeeLwdUfDDQAK+kAACBxujqzyk/NqnvTuvmxQrGsXEebx1kBF7GSDgBAQiW5TzjnTCDqCOkAACRQ0vuEc84Eoo5yFwAAEog+4ZwzgWgjpAMxNzSa1+DwmMYnC+rqzGqgt5v/dABc1fhkQRvbM4vG2jNp+oQDEVF3SDezX5W01Tn3pJm1S2pxzk2t3tQAXM3c5epM2hZdrt4jEdQTghdp4ST5+ze3cXJuJV2SZkqBtnRmPc4KwJy6atLN7H+VdEDSYG1oi6T/e7UmBaA+Cy9Xm1VvM2nT4PCY76mhAZJeUxxW0r9/bJwEoq3ejaMfkfTbks5JknPuJUnJWGoAImx8sqD2THrRGJerk4MXaeEk/fvHxkkg2uotd7ngnCuamSTJzFp08YwuAJ5wuTrZqCkOh+8fGyeBKKt3Jf3/NbM/k9RuZr8r6VuSvrN60wJQDy5XJ1tXZ1YzpcWnI/IirX58/wBEWb0h/eOSTkr6qaQBSY9L+t9Xa1IA6sPl6mTjRVo4fP8ARJk5d/WqFTNbK2nWORfU7qclrXHONd01we3bt7sjR474ngYA1GWuO8nEZEFbEtadZCXw/QPgk5k965zbvuTH6gzphyXd45ybrt1fJ+n7zrn/fkVnGgGEdGB5ktzCDgCAMK4U0ustd2mbC+iSVHufoj0g4ZLewg4AgNVSb0g/b2a/MXfHzN4paWZ1pgQgLpLewg4AgNVSbwvGP5H0LTP7Ze3+zZL+p9WZEoC4oIUdAACro66Q7pz7ezPrkfQWSSZp1DlXWtWZAYg8+rQDALA6rljuYmbvqt3+D5L+paTbJW2V9C9rYwASjBZ2AACsjqutpP+OpEOqBvRLOUn/dcVnBCA2+npy2iPRwg4AgBV2xZDunPs/zCwl6Qnn3DcbNCcAMXT1Zq4AAKBeV+3u4pyrSPqjBswFQMzQghEAgNVRb3eXvzWzByX9taTzc4POuddXZVYAYmFhC0ZJyra2qFAsa3B4rO6SFw5DAgDgjeoN6f+LqlezP3zJOLvDgAQL24JxbiU+k7ZFK/F7JIJ6nXiRAwDNqd6QfoeqAX2HqmH9v0n68mpNCkA8hG3BODg8plIQ6PR0WcWgotZ0SuvbW5a1Ep9kvMhBWLzIA6Kr3hNHvyrprZL2SfrL2vtfXa1JAYiHsC0YX8pP6dRUUeWKUzplKlecTk0V9VJ+apVn3hw48RVhsKcEiLZ6V9Lf4px7+4L7f2dmR1djQgDiI2wLxmK5IpmUMpMkmUkVc9VxXBUnviKMldhTAmD11BvSf2JmdznnDkuSmf2WpP9v9aYFIC76enLX/B96Jm2aKUmVipOZ5Gp9HFvTtoIzbF6c+IoweJEHRFu95S6/JemHZvaymb0s6WlJv2NmPzWz51ZtdgCa2u03rtf1a1vVkjYFzqklbbp+bau23rje99RigRNfEUZXZ1YzpWDRGC/ygOiodyX9vas6CwCJNNDbrd0HR3TThha1Z9KaKQWEzGXgxFeEMff7VyiW+f0DIsic45zAhbZv3+6OHDniexpAYsx1lyBkAo3H7x/gl5k965zbvuTHCOmLEdIBAADQCFcK6fXWpDdcrf79p2b2D2Z2pDZ2nZn9rZm9VLvtXPD5D5nZMTN7wczes2D8nbU/55iZ7TMzdqQBAAAg0iIb0mv+mXPuHQteYXxc0g+cc1sl/aB2X2Z2h6T7JG1TtX7+i2aWrj3mS5L6JW2tvVFfDwAAgEiLeki/1Pt08RClr0r6gwXj33DOXXDOHZd0TNKdZnazpPXOuaddta7nawseAwAAAERSlEO6k/R9M3vWzPprYzc6516VpNrt3O6WzZLGFzx2oja2ufb+peMAAABAZNXbgtGH33bO/dLMcpL+1sxGr/C5S9WZuyuML35w9UVAvyTdcsst1zJXAAAAYMVEdiXdOffL2m1e0rcl3SnptVoJi2q3+dqnT0jqWvDwLZJ+WRvfssT4pc+13zm33Tm3fdOmTSv9pQAAAADLEsmQbmZrzaxj7n1JvyfpZ5IOSvpA7dM+IOlvau8flHSfma0xs9tU3SD6o1pJzJSZ3VXr6vL+BY8BmsLQaF679h/Wjr2HtGv/YQ2N5q/+IAAAEGlRLXe5UdK3a90SWyT9F+fcd83s7yV908w+KOkXkv5QkpxzI2b2TUn/KKks6SPOubmzjj8k6VFJ7ZKeqL0BTWFoNK/dB0eUSZs2tmeUn5rV7oMj2iNxIAkAADHGYUaX4DAjxMmu/YeVn5pVtvXi6+1CsaxcR5se67/L48wAAMDVxPIwIwBXNz5ZUHsmvWisPZPWxGTB04wAAMBKIKQDMdbVmdVMKVg0NlMKtKUz62lGAABgJRDSgRgb6O1WKXAqFMtyrnpbCpwGert9Tw0AAIRASAdirK8npz07tynX0aazMyXlOtq0Z+c2No0CABBzUe3uAqBOfT05QjkAAE2GlXQAAAAgYgjpAAAAQMQQ0gEAAICIIaQDAAAAEUNIBwAAACKGkA4AAABEDC0YASTa0Gheg8NjGp8sqKszq4HeblpaAgC8YyUdQGINjea1++CI8lOz2tieUX5qVrsPjmhoNO97agCAhCOkA0isweExZdKmbGuLzKq3mbRpcHjM99QAAAlHSAeQWOOTBbVn0ovG2jNpTUwWPM0IAIAqQjqAxOrqzGqmFCwamykF2tKZ9TQjAACqCOkAEmugt1ulwKlQLMu56m0pcBro7fY9NQBAwhHSASRWX09Oe3ZuU66jTWdnSsp1tGnPzm10dwEAeEcLRgCJ1teTI5QD14gWpsDqYSUdAAAsGy1MgdVFSAcAAMtGC1NgdRHSAQDAstHCFFhd1KQDAIBl6+rM6uXT0zo3U1YxqKg1ndL69hbdev0631MDmgIr6QAAYNnu7r5O+amiikFFKZOKQUX5qaLu7r7O99SApkBIBwAAy/b02OvatK5VremUKk5qTae0aV2rnh573ffUgKZAuQsAAFi28cmCbli3Rps62ubHnHPUpAMrhJV0AACwbF2dWc2UgkVjM6VAWzqznmYENBdCOgAAWLaB3m6VAqdCsSznqrelwGmgt9v31ICmQEgHAADL1teT056d25TraNPZmZJyHW3as3MbJ44CK4SadAAAcE36enKEcmCVsJIOAAAARAwhHQAAAIgYQjoAAAAQMYR0AAAAIGII6QAAAEDEENIBAACAiF5qz9MAACAASURBVCGkAwAAABFDn3QAsTY0mtfg8JjGJwvq6sxqoLebvs0AgNhjJR1AbA2N5rX74IjyU7Pa2J5RfmpWuw+OaGg073tqAACEQkgHEFuDw2PKpE3Z1haZVW8zadPg8JjvqQEAEAohHUBsjU8W1J5JLxprz6Q1MVnwNCMAAFYGIR1AbHV1ZjVTChaNzZQCbenMepoRAAArg5AOIJSh0bx27T+sHXsPadf+ww2tBx/o7VYpcCoUy3KuelsKnAZ6uxs2BwAAVgPdXYCQktxdZG7jZiZtizZu7pEa8j3o68lpj6q16ROTBW1J2PcfANC8COnwLs4h13dI9W3hxk1Jyra2qFAsa3B4rGFff19PLhHf68uJ8+8PAODyKHeBV3FvoZf07iJR2Ljps9zGt7j//gAALo+QDq/iHnKjEFJ98r1xM+khNe6/PwCAyyOkw6u4h1zfIdU33xs3kx5S4/77AwC4PEI6vIp7yPUdUn3r68lpz85tynW06exMSbmONu3Zua1hNdFJD6lx//0BAFweG0fh1UBvt3YfHFGhWFZ7Jq2ZUhCrkEt3Eb8bN7s6s8pPzc5vXJWSFVLj/vsDALg8Qjq8aoaQG/fuInHuDpL0kNoMvz8AgKWZc873HCJl+/bt7siRI76nATTEwhaSC0NuI0tWwpp7kUFIBZYvzi/SgWZgZs8657Yv9TFW0oEEi0Kf87AhIe5XMgBfkn7OAxB1bBwFEsz3xsukt1AEfEp6dyQg6gjpQIL57g5CSAD88f0iHcCVEdKBBPPdQpKQAPjj+0U6gCsjpAMxNzSa1679h7Vj7yHt2n94WaUivvucExIAf3y/SAdwZXR3uQTdXRAnce/OMjSa18cOHNXUbFnlSkUtqZQ62lr05/e+PRbzB+KO7kiAX3R3AZrU4PCYSkGg09NlFYOKWtMprW9vWVZ3Ft8t2JwkmWRmktXuA2gIuiMB0UVIB2LspfyUzhZKSqVM6ZSpXHE6NVVUKZiq6/G+W7ANDo9pQ3tGN29onx9rdAtIAACiiJp0IMaK5YpkUspMJlOqthpdLFfqerzv7ipsHAUAYGmEdCDGMmmTJFUqTs45VSrVYpHW2vjV+A7JbBwFAGBphHQgxm6/cb2uX9uqlrQpcE4tadP1a1u19cb1dT3ed0imuwQQzr4nX9TbPvk9venPHtfbPvk97XvyRd9TArBCCOlAjA30dqu1Ja2bNrTpLTd26KYNbWptSdcdcn2HZN8tIIE42/fki3r40DHNlAK1pKovsB8+dIygDjQJWjBeghaMiJuwLdRowQbE09s++b1aQL+43lauVNSeSeu5T77H48wA1IsWjEATC9tCjRZsQDydLwZKyelCOZBzkpmUtuo4gPgjpAPwynefdiCu1qRTKpQCzW0Td04qOSmboZIVaAaEdCDm4hxyffdpB+LsurUZFc4EbzgA7Lq1GS/zAbCyeLkNxNhcyM1PzS4KuUOjed9Tq4vvPu1ArJlp07qMUrWl9JRJm9Zlqqf3Aog9VtKBGFsYciUp29oSqxM7xycL2ti+eNWPw4zQSPuefFGPPHVc54uB1ramdf+O2/TAPbf7nlZdujqzyk/N6qYNF1umFopl5TraPM4KwEphJR2IMd+HEYXlu087ki3uLQx9t1AFsLoI6UCMRSHkDo3mtWv/Ye3Ye0i79h9eVqkNIQM+PfLUcaVMakmllLJU7bY6HgecMwA0N8pdgBgb6O3W7oMjKhTLas+kNVMKGhpyw2787OvJaY9En3ZcszAbp88XqyvoC6Vi1sKQFqpA8yKkAyH57K7iO+SuRE2875AR5+44SRf2ReLa1rTOXyjL6WKfcZO0dg3/NQLwj3+JgBCi0ELQZ8hdiY2fPkNyFP7+cO3Cvkh8d88mffsfXp2/P3cA97t7Nq3KfAFgORJRk25m7zWzF8zsmJl93Pd80DyS3kIwbE287xaSSf/7i7uwG6dPnCuqM9uyqIVhZ7ZFJ84VV3qqALBsTR/SzSwt6T9J+n1Jd0jaZWZ3+J0VmkXcu6uEFXbjp++QnPS/v7jr6szq9PkLGjs5rdET5zR2clqnz1+o+0Xi+GRBmzdmte1XNui/27xB235lgzZvzPL3DyASmj6kS7pT0jHn3JhzrijpG5Le53lOaBJR6K7iU9juEr5DctL//uLu7u7rlJ8qqhhUlDKpGFSUnyrq7u7r6no8f/8AoiwJIX2zpPEF9ydqY0v6+c9/ru985zuSpHK5rP7+fj3++OOSpNnZWfX39+v73/++JGl6elr9/f06dOiQJOnMmTPq7+/X8PCwJOnUqVPq7+/XD3/4Q0nSiRMn1N/fr2eeeaY6kYkJ9ff369lnn5Ukvfzyy+rv79fRo0clSceOHVN/f79GRkYkSS+88IL6+/v1wgsvSJJGRkbU39+vY8eOSZKOHj2q/v5+vfzyy5KkZ599Vv39/ZqYmJAkPfPMM+rv79eJEyckST/84Q/V39+vU6dOSZKGh4fV39+vM2fOSJIOHTqk/v5+TU9PS5K+//3vq7+/X7Ozs5Kkxx9/XP39/SqXy5Kk73znO+rv75//Xn7729/Whz/84fn73/rWt/TAAw/M33/sscf00Y9+dP7+17/+dX3sYx+bv//oo4/qoYcemr//yCOP6BOf+MT8/S9/+cv61Kc+NX//C1/4gj796U/P3//85z+vvXv3zt//7Gc/q89+9rPz9/fu3avPf/7z8/c//elP6wtf+ML8/U996lP68pe/PH//E5/4hB555JH5+w899JC2njkyv5L8+t99RZNHn5xfSf7oRz+qxx57bP7zH3jgAX3rW9+av//hD39Y3/72t+fv9/f3x/Jnr68np4//Vrve+k/f0L//vZvU15Or+2fv5jVlzZQCzY7/TKe/+5eqzE5rphRo45kXG/KzN3clYPLok3r9774yfyVg65kjkf/Ze/TRR+fvf+xjH9PXv/71+ftJ+dl7eux13XDhVa37+69I06fUmk7phpkJfevh3XX9uzfQ262Z8RHln9inYGZKhWJZMz9/TsHwIP/u1fCzx/+5c/jZW72fvctJQkhf6nxkt+gTzPrN7IiZHSmVSg2aFppBd27d/EpyKaho3ZqWhvcpHhrNq/9rR/ST8TP68++90LB67pXwb+66RaXA6UI5kJNUqLWQ/L07bmzI889dCVi3pkWloDJ/JaA7t64hz49wxicLyqQX/xOfSZsulCt1Pb6vJ6f/+c5b1JpO6dxs9aTOXb/ZpY3ZzNUfDACrzJxzV/+sGDOzuyV90jn3ntr9hyTJOffvl/r87du3uyNHjjRwhsC1W9idZGGf9DgdaDLX3YU+6Viu3//8sF7KTyudMplVu7MEFaetuXV64k96fU8PAK7KzJ51zm1f6mNJaMH495K2mtltkl6RdJ+kf+13SsDKWIk+5b757pOO+JpfZJpba3KXjANAjDV9SHfOlc3sjyR9T1Ja0leccyOepwWsiJXoU+4bhwnhWk0XA23e2KZT09XNo63plG5at2ZZJ4by8wcgqpo+pEuSc+5xSY/7ngew0ro6s8pPzc6vpEvx6k7BYUIIY+7nv3vTxT0EhWK1trweQ6N5PXjgqKYvlBVUnE5NX9CDB47qP977dn7+AHiXhI2jQNMK26fcN9990hFvA73dOjtT0kv5KY2eOKeX8lM6O1Oq++f/M088r1PTRc2WKioFTrOlik5NF/WZJ55f5ZkDwNUlYiUdiLIwl9v7enLaI4XaeOnzcn8zlOvAL5MkV6tDd7ZkO6/LGX1telnjANBIhHTAo5Uo9wiz8dJ3uUncy3WiIMk11YPDY1rfntFNG9rnx+K2cRoALodyF8CjlSj3GBrNa9f+w9qx95B27T+8rD7pvstN4l6uI4X7/q/Ec+8+OKL81OyiF1lx6pUfxvhkQeWgorGT0xo9cU5jJ6dVDipciQHQFAjpgEfjkwW1Z9KLxpZT7hE2pIV9/rDmDhPKdbTp7Exp/jChuKyC+g7Jvl9k+daxpkUTkzMqlAKVA6dCKdDE5IzWreEiMYD4418ywKOw5R6Dw2MqlgOdni7Pt6DraGup+3J/FMpN4twn3Xef+qTX9E/NFBUsbInupKA2Xo+ONSlNXXjj6aQda1i/AuAf/xIBHoUt93jxtXM6fb6ocuCUNlM5cDp9vqiXXjvXkOdPupW4EhGmXKarM6uZ0uKe4Emq6T95vvSGjaJWG6/HxuyaZY0DQCMR0gGPwpZ7lGrLiKmUycyUSlUjSzGo78TFuJeb+BY2JA+N5vWxA0f1k19M6sTZGf3kF5P62IGjdQf1lXiR5bOmPqygUtGlP+muNl6PE2dnlzUOAI1EuQvgWZhyj9aWlGaKgSrOyUxyTpKrjjfi+ZNuoLdbuw+OqFAsqz2T1kwpWFZI3vvdUU0WSkqnTC3plJyTJgsl7f3uaF1/J2FbcPru7jM3h2vtTpNOpVReIpCnU/X9/Jfd0i9mLzcOAI3ESjoQY1tzHbqho1UtKVNQcWpJmW7oaNXWXIfvqSVC2CsRY6fOK2VSykwmU8pMKauOL9e1xErfG0/DbrytVJb+qi83/gaX+7RlfDPjfCUCQLSxkg7E2NxK7k0bWq5pJRfh+bwSEXYl3PfG07Abb1Mpk1XcokxttfG6mJYO5HU+PApXIgA0L1bSgRijpjzebrs+q4qrrvw651SpOFVcdbweYVfCfW88Dbvxdl1rasma9HWt9f3XdrmqlnqrXXxfiQDQ3FhJB2KOmvL4+vjvv1X/22M/1vlioIqTUiatbU3r47//1roeH3YlfKC3Ww8eOKpXzswoqDilU6Z1a1r0iX9xx7K/lmsRtgXodHHpDaKXG19pvq9EAGhurKQDgEdtmbRa0ym1pKTWdEptl6wsX8lKrISbJDnJOSe5uis9VkTY7jQXykuH8cuNX+pyVTH1Vsv4vhIBoLkR0gHAk8HhMa1vz2jrjR16680btPXGDq1vz9RdLhE25IZ9/rDClmuZXbyde1s4fjW359Yt2Wf99ty6uh7POQMAVhPlLki8MC3ggDDClkuEbcEYhXKNMOVam9ev0cTZC2+oId+8vr7DiD7++2/VgweOavpCeVG5T73lRmG//wBwJYR0JBrdGeBT2JpsKVzIXYnn9+l//M1b9BdPvrTkeD36enL6j/e+PVTIZk8IgNVCSEeihW0BB4Qx0Nutjx04qlcmZ1SuVNSSSqmjrXEbNwd6u/XAYz/W9IKNq+ta0w17/rCeHntdN61fo6nZsopBRa3p6vfv6bHX9UCdfwYhG0BUEdKRaFG43I9kc5JkkplJdm2HEl2r5ybOzAd0Sao4aboY6LmJM7EIruOTBd2wbo02dbTNjznn+P0F0BTYOIpEozsDfBocHtOG9oy25jrUc9N6bc11aEMDN24+8tRxpVOm9kx6/i2dMj3y1PGGPH9Y/P4CaGaEdCQa3RngU9jDfMI6Xwze0G4wZdXxOOD3F0AzI6Qj0TixEz75Xgle25qeL3WZU3HV8Tjg9xdAM6MmHYnHxjH4MtDbrd0HR1QoltWeSWumFDR0Jfj+Hbfp4UPHVK5UlLJqQK+46nhc8PsLoFmxkg4AnvT15HTvb2zWyakLev7ElE5OXdC9v7G5YaHzgXtu1x+/681qz6RVrlRLbf74XW/WA/fc3pDnBwBcHivpSDwOM4IvQ6N5HfjxK9rUsUa31FbSD/z4Fb1ty8aGBnVCOQBEDyEdiRaFw4yS/iIhyV9/FPr0J/n7DwBRRrkLEm1hSDKr3mbS1rAWeEOjeT144Kh+Mj6p187N6ifjk3rwwFENjeYb8vy+zb1Iyk/NLnqRlJSv33d3l6R//wEgygjpSDTfIekzTzyvM4WSXEVKm8lVpDOFkj7zxPMNeX7ffL9I8q2rM6tT0xc0dnJaoyfOaezktE5NX2hYd5fB4TGVgkAnzs7qhdemdOLsrEpBkJjvPwBEGSEdiea7Bd7x0wVVKk4XgopmyxVdCCqqVJyOn07GiYm+XyT5dnf3dXrt3AWdL1a7upwvBnrt3AXd3X1dQ57/pfyUTk0VVa44pVOmcsXp1FRRL+WnGvL8AIDLI6Qj0XwfhlIqV1S5ZKxSG08C3y+SpGrJx679h7Vj7yHt2n+4oaUe33p2Qpe0KZerjdcrzPyL5YoqzqkUVHShVFEpqN4vJuTnDwCijJCORPN+GIotc7zJ+H6R5Lsme2JyRpJkdvFt4fjVhJ1/xVUU1HqjO1VvAyc5R0gHAN/o7oLE4zAUf/p6ctqjam30xGRBWxrcXcR3d5VLV9GvNn6psPMPLpPFWUgHAP8I6YBH69a06PyFspwk52qrqZLWrknOr6bPF0njkwVtbM8sGmtkTXx7JqWZUkXOvXG8HmHnX64s/XLgcuMAgMah3AXw6P4dt0lmSqdMrS3VW5nF6lj2sPY9+aLe9snv6U1/9rje9snvad+TLzbsuX3XxH/od94k08Xqprn3P/Q7b6rr8aG7w4RdygcArBpCOuBR0o9l3/fki3r40DHNlAK1pKoB+eFDxxoW1H3XxD9wz+366D1b1dHWonTK1NHWoo/es7Xuv/+7u6/TyemiikFFKZOKQUUnp4t1d4fJpJf+L+By41Hkc+MvAKym5FxTByIqyceyP/LUcaVMaklVQ2HKpHKlokeeOt6Q70lfT073TpzRI08d1/lioLWtad2/47Zlld+EPbEzzN//02OvK9fRqnMzZRWDilrTKa1vb9HTY6/rgToen0otvWSevsx41EThxGAAWC2EdCDm4nys+/lidQV9oZRVxxthaDSvAz9+RZs61uiWTFozpUAHfvyK3rZlY13fQ98hcXyyoOvXrtEN69rmx5xzddekpyyllFVqj7vYXcYsHivpvjf+AsBqise/xEATC3O53ncLwbDWtqZ16R7FiquON0LYE099n5gatqa+tSWltJky6ZTWZFLKpKv3Wy995RRRST8MC0Bzi8e/xECTChuyfYdEKdyLjPt33KaKq5a4VFyldquGbZwNG/LGJwsqB5VFGzfLQaVhITFsTf3WXIdu6GhVS8oUVJxaUqYbOlq1NdexyjNfGb43/gLAaiKkAx6FDdm+VxLDvsjwvXE2bMhb15rWK2dmVQ6c0mYqB06vnJlt2JWAsIdxDfR2K5NO66YNbXrLjR26aUObMul0wzbOhuV74y8ArCZq0pF4Pmu6w/a57urMKj81O1+TKzV2JXElaoJ9bpwd6O3W7oMjKhTLaq/VpC8n5Nl8Ebcu9lF0C8YbIEyfed+HSYUV9/kDwJUQ0pFovjf+dXVmdfzUtKZmL3bn6Ghr0W03rKvr8WFDZli+DwMKK2zIm7pQ1uaNbTpVa4PYmk7ppvVrNH2hvLoTX0FxP3E37vMHgMshpCPRfHeHuLv7Oj1z/PT85slSEGimFOhf33lLXY/3vZLoeyVfCn8lJEzIm/v6uzddfFFVKJaV62i7wqMAALg6QjoSzfdK8BM/OzFfKeF0sWriiZ+dqLsExOdKou+VfN9XQgZ6u/WxA0f1yuSMypWKWlLVKyGf+Bd3rPpzAwCaGxtHkWi+u0OMnTovs2p/apPm3x87db4hzx9W2I2LYUWhu42TJKvVoVvtPgAAIbGSjkTzvRJccU7lSm3PoVUPlCk7ySw+Uc/nSr7vKyGDw2Pa0J7RzRva58fidpjOvidffMOJq0k9ARcAooSQjkTzXdPdkjKVAlddfXWLx5MiTE2575p43y8Swtr35It6+NAxpUxqSVW/dw8fOiZJBHUA8IyQjsTzuRKcbU3rQrki5xbUpFvjTtz0LWxNue+a8JV4keCzBegjTx2vBfRq5WPKqgdLPfLUcUI6AHhGTTrg0e03rleuY42yrelabXVauY412nrjet9Ta4iVqCn3WRMe9jCdodG8HjxwVD8Zn9Rr52b1k/FJPXjg6LJObQ3jfDGQnNOFcqDZUqAL5er988Xg6g8GAKwqQjrg0UBvt1pbFp/42NoSnxMfwwp7YupcTfjWXId6blqvrbkObWjPNGzjaNiNs5954nmdKZTkKlLaTK4inSmU9Jknnq97DkOjee3af1g79h7Srv2HlxXw17SkVKpU90LM7YkoVarjAAC/KHcBPPJdE+9b2HKRKNSEhymXOn66oJRJqdoeBDPJVZyOn65v/mHLha5rb1GhGLxhT8R17fzXAAC+8S8x4FmST0wMW1Pe1ZnVy6endW7m4omt69tbdOv19Z3YGneDw2MqlgOdnl58Ym3d3WVSKW1al9Hp8yVVXLUm/fq1GVmKlXQA8I2QDsCrMDXld3dfpx+9/Hp1NdqkYlBRfqqoXb953SrNdmV137BWoyemVAwu1oCbpJ6b6nuR8eJr53RutqyUTGkzlQOn0+eLKgfn6nr83JWMmzZcvHLBiakAEA0slwDwJmxN+dNjr2vTula1plOqOKk1ndKmda16euz1VZ75RWFqwntuWveGFyVO9Yf0UlB9dCplMrP5spliUN9LnbAbXwEAq4eVdADehK0pH58s6IZ1a7Rpwcqvc65hNelha8J/MHpScy3xnavWpM+N16O1JaWZYqCKc9V6difJVcfrEYU9ET5bUAJAlBHSAXgTduPoSvQpD3Pi5sIWkpKUbW1Z1omj54uBMmlTyi6G6oqr1N0CcWuu4401+Wszy6rJ97knIuyLHABoZpS7AJ6FKZeIu7DlFmEfP3fi5kwpWHTi5r4nX6zr8WFbSK5tTatySWVKxdV/mNVAb7cy6cUtPDPp+LTwXIk++QDQrAjpQEhhQvbcSmJ+anbRSmJSgnrYPuNhH7/wxM2UpWq31fF6dHVmNVNavOq9nJX8+3fcpoqrnvJZcZXabXW8HmG/ft/CvsgBgGZGuQsQQtjL9WHLJZpB2HKLMI8/X6yuoC+UMtVdbjLQ263dB0dUKJbVnklrphQsayX/gXtu1/FT0zr43AmVAqd0yrTzbTfVXW4jhf/++awJX4lyJQBoVqykAyGEvVy/EiuJSS6XCStsuUnYleyh0bye/cVZ3Xp9Vr/2K+t16/VZPfuLsw37O/R9JYfuMgBweaykAyGE7U4SdiWRjXfh3L/jNj186JjKlYpSVg3oyyk3kcKtZPu+kuL7+aPQXQYAooqQDoQQNmSHLZfwHbLibiXKTcII+yIv7s8vJfvEXQC4EspdgBDCXq7v68np3t/YrJNTF/T8iSmdnLqge39jc92hhY134fguN+nqzOrU9AWNnZzW6IlzGjs5rVPTFxpWkx124ysAYPUQ0oEQVqIm+cCPX9GmjjV6600d2tSxRgd+/ErdIZGQFY7vFoB3d1+nk9NFFYNquU0xqOjkdFF3d1/XkOenJhwAootyFyAknzXJYctlks53ucfTY68r19G6+DCi9hY9Pfa6HmjA81MTDgDRRUgHPAobEvt6crp34swbTswkZNXHdwvA8cmCrl+7Rjesa5sfc85REw4AoNwF8ClsuUrYcpmk813uQbkSAOByCOmAR2FDou+a6rjr68npnbds0MunC/rZL8/p5dMFvfOWDQ1bWfb9IgEAEF2EdMCjsBtP6e4Szr4nX9TB504oZdKaFlPKpIPPndC+J19syPOH/fsHADQvatIBz8LUBPuuqY6CMMfaP/LUcaVMaklV1ytSJpUrFT3y1PGG9UqnJhwAsBRW0oEYS3q5RNhj7c8XA6Vs8VjKquONMjSa1679h7Vj7yHt2n+Y/QQAAEmEdCDWkl4uEbYmf21rWhW3eKziquONEPZFBgCgeVHuAsRcksslwrawvH/HbXr40DGVK9XDhCqu+nb/jttWY7pvELZPPgCgebGSDiC2wrYwfOCe23Xnr25UKXC6UHYqBU53/urGhtWjs/EXAHA5kQvpZvZJM3vFzP6h9vbPF3zsITM7ZmYvmNl7Foy/08x+WvvYPjOz2vgaM/vr2vgzZnZr478iAKslbE3+vidf1I9+fkaZtGlNiymTNv3o52ca1t2FPukAgMuJXEiv+Zxz7h21t8clyczukHSfpG2S3ivpi2Y2twT1JUn9krbW3t5bG/+gpEnn3JslfU7S3gZ+DQBWWdia/IXdXVKWqt1Wxxsh6Rt/AQCXF9WQvpT3SfqGc+6Cc+64pGOS7jSzmyWtd8497Zxzkr4m6Q8WPOartfcPSHr33Co7gObirv4pb+C7u0vSN/4CAC4vqhtH/8jM3i/piKR/55yblLRZ0uEFnzNRGyvV3r90XLXbcUlyzpXN7Kyk6yWdWt3pA2iEue4ombQt6o6yR6or6K5tTWumtDioN7K7i5Tsjb8AgMvzspJuZk+a2c+WeHufqqUrb5L0DkmvSvrs3MOW+KPcFcav9JhL59NvZkfM7MjJkyeX/fUA8CNsC8b7d9ymiqseYFRxldpt47q7SPRJBwAszctKunPunno+z8z+s6T/p3Z3QlLXgg9vkfTL2viWJcYXPmbCzFokbZD0+hLz2S9pvyRt3779Wq6aA/AgbAvGB+65XcdPTevgcydUCpzSKdPOt93UsO4uYa8EAACaV+Rq0ms15nP+laSf1d4/KOm+WseW21TdIPoj59yrkqbM7K5avfn7Jf3Ngsd8oPb+vZIO1erWATSBrs6sTp+/oLGT0xo9cU5jJ6d1+vyFurujDI3m9ewvzurW67P6tV9Zr1uvz+rZX5xt2Gp22CsBAIDmFcWa9P9gZu9QtSzlZUkDkuScGzGzb0r6R0llSR9xzs3t7vqQpEcltf//7d17cFxXfcDx70+rVSTHSuwQO4HYaTDN4GLKBBBpKambFsqrTHiUR9IBQsvDLTDQoQwtpeMEd9IpTMurpYwDhATKoxRIMTBQwgRXpISHnYSHiYGMEmoHiEiixHZkWdLq1z/2OkhGsle+kvZa+n5m1rt77p69Rz+fsX979NtzgS8WN4APAh+JiNtorqBfvEA/g6QF8MR1p/GtO+6lI5pf+BxtTDC4f5RLnnBaS/239g8wOt7gngPjjDYm6Kp10NvdOauLCW3fPcjW/gH2D/mXlQAAEh9JREFUDA2zduUyNm1c13Lfsr8JkCQtXpVL0jPzJUc5dgVwxTTtO4BHT9M+ArxgTgcozbEySd5Sd+PAvaxa3sX+kalJ9o0D9/K6Fvr/6K597BsZp4OgFsF4I7nngVHGG/taOn/ZcpW1K5cxuH/kwSuOgvukS5KaKlfuIi0lh5O8wf0jU5I8vzzYmj1Dw5y+/CTWrVrO+jNPYd2q5Zy+/KSWV6LHGs3qt46OICLoKLZ5GW20VhVXtlzFfdIlSTMxSZfayJrkcspesbOrswMSJjJJkolMyKK9BXuGhumpT92ucTblKu6TLkmaSeXKXaSlxJrkcjZtXMfmbbsYHh2np97c83w2K9Hnru7ljnsOsO/gL8tlTjm5zjkPWd5S/7koV3GfdEnSdFxJl9qo7ErwUld2JXrTxnXUazXOPLWbR57Ry5mndlOv1VpO8i1XkSTNF1fSpTYquxKscivRF65fzRaaZUd7h4ZZM8sv7pbtL0nSTMJtw6fq6+vLHTt2tHsYWkLe85Uf8YEbbueB0QYnd9V4xQUPX7CL6UiSpPaJiJ2Z2TfdMVfSpTbavnuQT910J6t6T+LsYiX9UzfdyWPWrHA1doH4IUmSVEUm6VJJZfY5n7y7C8Cyrk6GR8dndTEdHb/3fOVHvPv62+gI6Oxofh/g3dffBtByou4+95Kk+eAXR7Xkbd89yCVXfoML3nY9l1z5jVntUV52n/M9Q8OMNyamXNZ+vDHh7i4L5AM33F4k6B10REdx32xvhfvcS5Lmi0m6lrSySVbZfc6Xd9W4874Rxhv54BUv77xvhJO7asfurNIeGG1QXL/oQR3RbG+F+9xLkuaLSbqWtLJJVtmL2UQEmcnoxASHxicYnZggM4mIY3dWaSd31RhvJIfGG4yMNTg03mC8kS1/SCr79y9J0kxM0rWklU2yyu5z/osDh5oPmhe6LP6Y1K559eT1q2gkTBTxn0hoZLO9Fe5zL0maLybpWtLKJlllL2YzOj5BR0fQXa/RU6/RXa/R0RGMjk/M+mfR7P183ygrl3U+WPLSEbByWSc/3zfaUn8vZiRJmi8m6VrSyiZZZa94Wa8FE5mMjDU4ONYsuZjIpKtmuctC2DM0zFkrlrHhYafym2edyoaHncpZK5a1/JuUsn//kiTNxC0YtaTNxRUjy1zxctXykxh6YGxKW07A6ctPOq730+ysXbmMwf0jD26BCbMvVynz9y9J0kxM0rXktTPJigg6OoJaRxABmdCY8IujC2XTxnVs3raL4dFxeoqLSVmuIkmqAstdpDbaf2ics1Z009kRNCaSzo7grBXdHDg03u6hLQmWq0iSqsqVdKmNDpdbrFu1/MG24dFxVvd2t3FUS4vlKpKkKnIlXWojdweRJEnTcSVdaqO5+OLqUrd99yBb+wfYMzTMWuMnSVokTNKlNrPc4vht3z3I5m27qNeCFT11BvePsHnbLraAMZUkndAsd5F0wtraP0C9Fizr6iSieV+vBVv7B9o9NEmSSnElXWozyzWO356hYVb01Ke09dRrLV+MSJKkqjJJ15LXziTZco1y5uJiRJIkVZHlLlrSDifJg/tHpiTJ23cPLsj5Ldcox91xJEmLlUm6lrR2J8l7hobpqdemtFmu0TovRiRJWqwsd9GS1u6aZss1ynN3HEnSYuRKupa0tSuXcXCsMaVtIZNkyzUkSdJ0TNK1pLU7SbZcQ5IkTcdyFy1pVbjip+UakiTpSCbpWvJMkiVJUtVY7iJJkiRVjEm6JEmSVDEm6ZIkSVLFmKRLkiRJFWOSLkmSJFWMSbokSZJUMW7BKJW0ffcgW/sH2DM0zNo27LMuSZIWH5N0qYTtuwfZvG0X9VqwoqfO4P4RNm/bxRYwUV8i/JAmSZoPJulSCVv7Bxgdb3DPgXFGGxN01Tro7e5ka/+AidoCaWeS7Ic0SdJ8sSZdKuFHd+3jngdGGW8ktQjGG8k9D4zy47v2tXtoS8LhJHlw/8iUJHn77sEFOf/W/gHqtWBZVycRzft6LdjaP7Ag55ckLV4m6VIJY40EoKMjiAg6OgKA0aJd86vdSfKeoWF66rUpbT31GnuHhhfk/JKkxcskXSqhq7MDEiYySZKJTMiiXfOu3Uny2pXLODjWmNJ2cKzBmpXLFuT8kqTFy0xCKuHc1b2c3ttFZ0fQmEg6O4LTe7s4d3Vvu4e2JLQ7Sd60cR1jjWR4dJzM5v1YI9m0cd2CnF+StHiZpEslbNq4jnqtxpmndvPIM3o589Ru6rWaSdoCaXeSfOH61Wy5aAOre7u5/+AYq3u72XLRBr80KkkqLTKtnZ2sr68vd+zY0e5h6ARyeHeRvUPDrHELvgVn/CVJJ6qI2JmZfdMeM0mfyiRdkiRJC+FoSbrlLpIkSVLFmKRLkiRJFWOSLkmSJFWMSbokSZJUMSbpkiRJUsV0tnsA0onu8BaAe4aGWesWgJIkaQ6YpEslbN89yOZtu6jXghU9dQb3j7B52y62wIIl6n5IkCRp8bHcRSpha/8A9VqwrKuTiOZ9vRZs7R9YkPMf/pAwuH9kyoeE7bsHF+T8kiRpfpikSyXsGRqmp16b0tZTr7F3aHhBzt/uDwmSJGl+mKRLJaxduYyDY40pbQfHGqxZuWxBzt/uDwmSJGl+mKRLJWzauI6xRjI8Ok5m836skWzauG5Bzt/uDwmSJGl+mKRLJVy4fjVbLtrA6t5u7j84xurebrZctGHBvrjZ7g8JkiRpfri7i1TShetXt203lQvXr2YLzdr0vUPDrHF3F0mSFgWTdOkE184PCZIkaX5Y7iJJkiRVjEm6JEmSVDEm6ZIkSVLFmKRLkiRJFWOSLkmSJFWMSbokSZJUMSbpkiRJUsWYpEuSJEkVY5IuSZIkVYxJuiRJklQxJumSJElSxZikS5IkSRVjki5JkiRVjEm6JEmSVDFtSdIj4gURsSsiJiKi74hjb46I2yLihxHxtEntj4+I7xXH3hMRUbSfFBH/UbR/MyLOmdTn0oj4cXG7dKF+PkmSJKmMdq2kfx94HtA/uTEiHgVcDGwAng78W0TUisPvA14FnFvcnl60vxwYysxfB94JvK14r9OAy4DfAs4HLouIlfP4M0mSJElzoi1Jembempk/nObQs4FPZOahzLwduA04PyIeCpySmTdmZgIfBp4zqc81xeNPAU8uVtmfBlyXmfdm5hBwHb9M7CVJkqTKqlpN+lnAnknP9xZtZxWPj2yf0iczx4H7gYcc5b0kSZKkSuucrzeOiK8AZ05z6C2Z+dmZuk3TlkdpP94+U08a8SqapTScffbZMwxNkiRJWhjzlqRn5lOOo9teYO2k52uAnxbta6Zpn9xnb0R0AqcC9xbtFx7RZ/sMY70SuBKgr69v2kRekiRJWijzlqQfp23AxyLiHcDDaH5B9FuZ2YiI/RHx28A3gZcC/zKpz6XAjcDzgeszMyPiv4F/mPRl0acCbz7WAHbu3Hl3RPzkOMd/OnD3cfaV8SvL+JVj/MoxfuUYv3KMXznGr5wy8fu1mQ60JUmPiOfSTLJXAV+IiFsy82mZuSsiPgn8ABgHXpOZjaLbXwBXAz3AF4sbwAeBj0TEbTRX0C8GyMx7I+LvgW8Xr9uSmfcea2yZuarEz7UjM/uO/UpNx/iVY/zKMX7lGL9yjF85xq8c41fOfMWvLUl6Zl4LXDvDsSuAK6Zp3wE8epr2EeAFM7zXVcBVpQYrSZIkLbCq7e4iSZIkLXkm6XPrynYP4ARn/MoxfuUYv3KMXznGrxzjV47xK2de4hfNawNJkiRJqgpX0iVJkqSKMUk/ThFxVUQMRsT3J7VdHhF3RsQtxe2Z7RxjlUXE2oj4akTcGhG7IuL1RftpEXFdRPy4uF95rPdaio4SP+dgCyKiOyK+FRHfKeL31qLd+deCo8TP+deiiKhFxM0R8fniuXNvFqaJn3NvFiLijoj4XhGrHUWbc7BFM8Rvzueg5S7HKSI2AgeAD2fmo4u2y4EDmflP7RzbiSAiHgo8NDNvioheYCfwHOBlwL2Z+Y8R8TfAysz86zYOtZKOEr8X4hw8pogI4OTMPBARdeAG4PXA83D+HdNR4vd0nH8tiYg3AH3AKZn5rIh4O869lk0Tv8tx7rUsIu4A+jLz7kltzsEWzRC/y5njOehK+nHKzH6a+7LrOGTmzzLzpuLxfuBW4Czg2cA1xcuuoZl46ghHiZ9akE0Hiqf14pY4/1pylPipBRGxBvgj4AOTmp17LZohfirPOVgxJulz77UR8d2iHMZfFbUgIs4BHkvzarJnZObPoJmIAqvbN7ITwxHxA+dgS4pfl98CDALXZabzbxZmiB84/1rxLuBNwMSkNude66aLHzj3ZiOBL0fEzoh4VdHmHGzddPGDOZ6DJulz633AI4DzgJ8B/9ze4VRfRCwHPg38ZWbua/d4TjTTxM852KLMbGTmecAa4PyI+JWLpWlmM8TP+XcMEfEsYDAzd7Z7LCeio8TPuTc7T8rMxwHPAF5TlPCqddPFb87noEn6HMrMu4r/uCaA9wPnt3tMVVbUsn4a+GhmfqZovquotz5cdz3YrvFV3XTxcw7OXmbeB2ynWU/t/JulyfFz/rXkScBFRU3rJ4A/iIh/x7nXqmnj59ybncz8aXE/SPMK8OfjHGzZdPGbjzlokj6HDk/uwnOB78/02qWu+OLZB4FbM/Mdkw5tAy4tHl8KfHahx3YimCl+zsHWRMSqiFhRPO4BngLsxvnXkpni5/w7tsx8c2auycxzgIuB6zPzxTj3WjJT/Jx7rYuIk4sNB4iIk4Gn0oyXc7AFM8VvPuZgZ9k3WKoi4uPAhcDpEbEXuAy4MCLOo1mrdAewqW0DrL4nAS8BvlfUtQL8LfCPwCcj4uXA/wEvaNP4qm6m+F3iHGzJQ4FrIqJGc7Hik5n5+Yi4EedfK2aK30ecf8fNf/vKebtzr2VnANc213roBD6WmV+KiG/jHGzFTPGb83//3IJRkiRJqhjLXSRJkqSKMUmXJEmSKsYkXZIkSaoYk3RJkiSpYkzSJUmSpIoxSZekE1xEnBMRv7Inb0RsiYinHKPv5RHxxvkbnSTpeLhPuiQtUpm5ud1jkCQdH1fSJWlxqEXE+yNiV0R8OSJ6IuLqiHg+QEQ8MyJ2R8QNEfGeiPj8pL6PiojtETEQEa8rXv+mSY/fGRHXF4+fXFzGnoh4X0TsKM751knHrz38xhHxhxHxmSMHGxEvi4j/iojPRcTtEfHaiHhDRNwcEd+IiNOK122PiHdFxNcj4vsRcX7RvioirouImyJia0T8JCJOn5fISlIbmKRL0uJwLvDezNwA3Af88eEDEdENbAWekZkXAKuO6LseeBpwPnBZRNSBfuB3i+N9wPKi/QLga0X7WzKzD3gM8HsR8RjgeuA3IuLwOf4U+NAMY3408CfFea8AhjPzscCNwEsnve7kzPwd4NXAVUXbZTQvCf844Frg7GPER5JOKCbpkrQ43J6ZtxSPdwLnTDq2HhjIzNuL5x8/ou8XMvNQZt4NDNK87PVO4PER0Qscopk499FM3A8n6S+MiJuAm4ENwKOyeRnrjwAvjogVwBOBL84w5q9m5v7M/AVwP/C5ov17R4z/4wCZ2Q+cUrzvBcAnivYvAUNHiY0knXCsSZekxeHQpMcNoGfS85hl387MHIuIO2iuhH8d+C7w+8AjgFsj4uHAG4EnZOZQRFwNdBfv8SGaCfcI8J+ZOR4Rz6W5+g3wimnOOzHp+QRT/3/KI8abLfxMknRCcyVdkha/3cC6iDineP6iFvv100zE+2munv85cEuxWn4K8ABwf0ScATzjcKfM/CnwU+DvgKuLtmsz87zitmOW438RQERcANyfmfcDNwAvLNqfCqyc5XtKUqW5ki5Ji1xmHoyIVwNfioi7gW+12PVrwFuAGzPzgYgYKdrIzO9ExM3ALmAA+N8j+n4UWJWZP5iDH2EoIr5O84PBnxVtbwU+HhEvAv4H+Bmwfw7OJUmVEM0FEUnSYhYRyzPzQEQE8F7gx5n5znk8378CN2fmB0u+z3bgjUeuvkfESUCjKKV5IvC+zDyvzLkkqUpcSZekpeGVEXEp0EXzi55b5+tEEbGTZinMX83XOWju5vLJiOgARoFXzuO5JGnBuZIuSZIkVYxfHJUkSZIqxiRdkiRJqhiTdEmSJKliTNIlSZKkijFJlyRJkirGJF2SJEmqmP8HAvsGg6Jo3hMAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"width = 12\n",
"height = 10\n",
"plt.figure(figsize=(width, height))\n",
"sns.residplot(df['highway-mpg'], df['price'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<i>What is this plot telling us?</i>\n",
"\n",
"<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, which leads us to believe that maybe a non-linear model is more appropriate for this data.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Multiple Linear Regression</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
"\n",
"<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>: We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First lets make a prediction "
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(width, height))\n",
"\n",
"\n",
"ax1 = sns.distplot(df['price'], hist=False, color=\"r\", label=\"Actual Value\")\n",
"sns.distplot(Yhat, hist=False, color=\"b\", label=\"Fitted Values\" , ax=ax1)\n",
"\n",
"\n",
"plt.title('Actual vs Fitted Values for Price')\n",
"plt.xlabel('Price (in dollars)')\n",
"plt.ylabel('Proportion of Cars')\n",
"\n",
"plt.show()\n",
"plt.close()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can see that the fitted values are reasonably close to the actual values, since the two distributions overlap a bit. However, there is definitely some room for improvement.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 3: Polynomial Regression and Pipelines</h2>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p><b>Polynomial regression</b> is a particular case of the general linear regression model or multiple linear regression models.</p> \n",
"<p>We get non-linear relationships by squaring or setting higher-order terms of the predictor variables.</p>\n",
"\n",
"<p>There are different orders of polynomial regression:</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center><b>Quadratic - 2nd order</b></center>\n",
"$$\n",
"Yhat = a + b_1 X^2 +b_2 X^2 \n",
"$$\n",
"\n",
"\n",
"<center><b>Cubic - 3rd order</b></center>\n",
"$$\n",
"Yhat = a + b_1 X^2 +b_2 X^2 +b_3 X^3\\\\\n",
"$$\n",
"\n",
"\n",
"<center><b>Higher order</b>:</center>\n",
"$$\n",
"Y = a + b_1 X^2 +b_2 X^2 +b_3 X^3 ....\\\\\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We saw earlier that a linear model did not provide the best fit while using highway-mpg as the predictor variable. Let's see if we can try fitting a polynomial model to the data instead.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We will use the following function to plot the data:</p>"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"def PlotPolly(model, independent_variable, dependent_variabble, Name):\n",
" x_new = np.linspace(15, 55, 100)\n",
" y_new = model(x_new)\n",
"\n",
" plt.plot(independent_variable, dependent_variabble, '.', x_new, y_new, '-')\n",
" plt.title('Polynomial Fit with Matplotlib for Price ~ Length')\n",
" ax = plt.gca()\n",
" ax.set_facecolor((0.898, 0.898, 0.898))\n",
" fig = plt.gcf()\n",
" plt.xlabel(Name)\n",
" plt.ylabel('Price of Cars')\n",
"\n",
" plt.show()\n",
" plt.close()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"lets get the variables"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"x = df['highway-mpg']\n",
"y = df['price']\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's fit the polynomial using the function <b>polyfit</b>, then use the function <b>poly1d</b> to display the polynomial function."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 3 2\n",
"-1.557 x + 204.8 x - 8965 x + 1.379e+05\n"
]
}
],
"source": [
"# Here we use a polynomial of the 3rd order (cubic) \n",
"f = np.polyfit(x, y, 3)\n",
"p = np.poly1d(f)\n",
"print(p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's plot the function "
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"PlotPolly(p, x, y, 'highway-mpg')"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.55663829e+00, 2.04754306e+02, -8.96543312e+03, 1.37923594e+05])"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.polyfit(x, y, 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function \"hits\" more of the data points.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #4:</h1>\n",
"<b>Create 11 order polynomial model with the variables x and y from above?</b>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 11 10 9 8 7\n",
"-1.243e-08 x + 4.722e-06 x - 0.0008028 x + 0.08056 x - 5.297 x\n",
" 6 5 4 3 2\n",
" + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
]
},
{
"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",
"g = np.polyfit(x, y, 11)\n",
"q = np.poly1d(g)\n",
"print(q)\n",
"PlotPolly(q, x, y, 'highway-mpg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"# calculate polynomial\n",
"# Here we use a polynomial of the 11rd order (cubic) \n",
"f1 = np.polyfit(x, y, 11)\n",
"p1 = np.poly1d(f1)\n",
"print(p)\n",
"PlotPolly(p1,x,y, 'Highway MPG')\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>The analytical expression for Multivariate Polynomial function gets complicated. For example, the expression for a second-order (degree=2)polynomial with two variables is given by:</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b_1 X_1 +b_2 X_2 +b_3 X_1 X_2+b_4 X_1^2+b_5 X_2^2\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can perform a polynomial transform on multiple features. First, we import the module:"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.preprocessing import PolynomialFeatures"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We create a <b>PolynomialFeatures</b> object of degree 2: "
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [],
"source": [
"Z_pr=pr.fit_transform(Z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The original data is of 201 samples and 4 features "
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 72,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"after the transformation, there 201 samples and 15 features"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 73,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z_pr.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Pipeline</h2>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Data Pipelines simplify the steps of processing the data. We use the module <b>Pipeline</b> to create a pipeline. We also use <b>StandardScaler</b> as a step in our pipeline.</p>"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.pipeline import Pipeline\n",
"from sklearn.preprocessing import StandardScaler"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We create the pipeline, by creating a list of tuples including the name of the model or estimator and its corresponding constructor."
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we input the list as an argument to the pipeline constructor "
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"Pipeline(memory=None,\n",
" steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False))])"
]
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pipe=Pipeline(Input)\n",
"pipe"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can normalize the data, perform a transform and fit the model simultaneously. "
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.partial_fit(X, y)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.fit(X, y, **fit_params).transform(X)\n"
]
},
{
"data": {
"text/plain": [
"Pipeline(memory=None,\n",
" steps=[('scale', StandardScaler(copy=True, with_mean=True, with_std=True)), ('polynomial', PolynomialFeatures(degree=2, include_bias=False, interaction_only=False)), ('model', LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False))])"
]
},
"execution_count": 80,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pipe.fit(Z,y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Similarly, we can normalize the data, perform a transform and produce a prediction simultaneously"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" Xt = transform.transform(Xt)\n"
]
},
{
"data": {
"text/plain": [
"array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555])"
]
},
"execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ypipe=pipe.predict(Z)\n",
"ypipe[0:4]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #5:</h1>\n",
"<b>Create a pipeline that Standardizes the data, then perform prediction using a linear regression model using the features Z and targets y</b>\n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.partial_fit(X, y)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.fit(X, y, **fit_params).transform(X)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" Xt = transform.transform(Xt)\n"
]
},
{
"data": {
"text/plain": [
"array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555,\n",
" 16136.29619164, 13880.09787302, 15041.58694037])"
]
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"Input=[('scale',StandardScaler()), ('polynomial', PolynomialFeatures(include_bias=False)), ('model',LinearRegression())]\n",
"pipe=Pipeline(Input)\n",
"pipe.fit(Z,y)\n",
"ypipe=pipe.predict(Z)\n",
"ypipe[0:7]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"</div>\n",
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
"\n",
"pipe=Pipeline(Input)\n",
"\n",
"pipe.fit(Z,y)\n",
"\n",
"ypipe=pipe.predict(Z)\n",
"ypipe[0:10]\n",
"\n",
"-->"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 4: Measures for In-Sample Evaluation</h2>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>When evaluating our models, not only do we want to visualize the results, but we also want a quantitative measure to determine how accurate the model is.</p>\n",
"\n",
"<p>Two very important measures that are often used in Statistics to determine the accuracy of a model are:</p>\n",
"<ul>\n",
" <li><b>R^2 / R-squared</b></li>\n",
" <li><b>Mean Squared Error (MSE)</b></li>\n",
"</ul>\n",
" \n",
"<b>R-squared</b>\n",
"\n",
"<p>R squared, also known as the coefficient of determination, is a measure to indicate how close the data is to the fitted regression line.</p>\n",
" \n",
"<p>The value of the R-squared is the percentage of variation of the response variable (y) that is explained by a linear model.</p>\n",
"\n",
"\n",
"\n",
"<b>Mean Squared Error (MSE)</b>\n",
"\n",
"<p>The Mean Squared Error measures the average of the squares of errors, that is, the difference between actual value (y) and the estimated value (ŷ).</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 1: Simple Linear Regression</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The R-square is: 0.4965911884339176\n"
]
}
],
"source": [
"#highway_mpg_fit\n",
"lm.fit(X, Y)\n",
"# Find the R^2\n",
"print('The R-square is: ', lm.score(X, Y))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can say that ~ 49.659% of the variation of the price is explained by this simple linear model \"horsepower_fit\"."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the MSE"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The output of the first four predicted value is: [16236.50464347 16236.50464347 17058.23802179 13771.3045085 ]\n"
]
}
],
"source": [
"Yhat=lm.predict(X)\n",
"print('The output of the first four predicted value is: ', Yhat[0:4])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"lets import the function <b>mean_squared_error</b> from the module <b>metrics</b>"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.metrics import mean_squared_error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we compare the predicted results with the actual results "
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mean square error of price and predicted value is: 31635042.944639888\n"
]
}
],
"source": [
"mse = mean_squared_error(df['price'], Yhat)\n",
"print('The mean square error of price and predicted value is: ', mse)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 2: Multiple Linear Regression</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The R-square is: 0.8093562806577457\n"
]
}
],
"source": [
"# fit the model \n",
"lm.fit(Z, df['price'])\n",
"# Find the R^2\n",
"print('The R-square is: ', lm.score(Z, df['price']))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can say that ~ 80.896 % of the variation of price is explained by this multiple linear regression \"multi_fit\"."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the MSE"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" we produce a prediction "
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([13699.11161184, 13699.11161184, 19051.65470233, 10620.36193015])"
]
},
"execution_count": 93,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Y_predict_multifit = lm.predict(Z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" we compare the predicted results with the actual results "
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mean square error of price and predicted value using multifit is: 11980366.87072649\n"
]
}
],
"source": [
"print('The mean square error of price and predicted value using multifit is: ', \\\n",
" mean_squared_error(df['price'], Y_predict_multifit))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 3: Polynomial Fit</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"let’s import the function <b>r2_score</b> from the module <b>metrics</b> as we are using a different function"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.metrics import r2_score"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We apply the function to get the value of r^2"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The R-square value is: 0.674194666390652\n"
]
}
],
"source": [
"r_squared = r2_score(y, p(x))\n",
"print('The R-square value is: ', r_squared)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can say that ~ 67.419 % of the variation of price is explained by this polynomial fit"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>MSE</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also calculate the MSE: "
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 97,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_squared_error(df['price'], p(x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 5: Prediction and Decision Making</h2>\n",
"<h3>Prediction</h3>\n",
"\n",
"<p>In the previous section, we trained the model using the method <b>fit</b>. Now we will use the method <b>predict</b> to produce a prediction. Lets import <b>pyplot</b> for plotting; we will also be using some functions from numpy.</p>"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create a new input "
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"new_input=np.arange(1, 100, 1).reshape(-1, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Fit the model "
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(X, Y)\n",
"lm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Produce a prediction"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([37601.57247984, 36779.83910151, 35958.10572319, 35136.37234487,\n",
" 34314.63896655])"
]
},
"execution_count": 101,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"yhat=lm.predict(new_input)\n",
"yhat[0:5]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we can plot the data "
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(new_input, yhat)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Decision Making: Determining a Good Model Fit</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Now that we have visualized the different models, and generated the R-squared and MSE values for the fits, how do we determine a good model fit?\n",
"<ul>\n",
" <li><i>What is a good R-squared value?</i></li>\n",
"</ul>\n",
"</p>\n",
"\n",
"<p>When comparing models, <b>the model with the higher R-squared value is a better fit</b> for the data.\n",
"<ul>\n",
" <li><i>What is a good MSE?</i></li>\n",
"</ul>\n",
"</p>\n",
"\n",
"<p>When comparing models, <b>the model with the smallest MSE value is a better fit</b> for the data.</p>\n",
"\n",
"\n",
"<h4>Let's take a look at the values for the different models.</h4>\n",
"<p>Simple Linear Regression: Using Highway-mpg as a Predictor Variable of Price.\n",
"<ul>\n",
" <li>R-squared: 0.49659118843391759</li>\n",
" <li>MSE: 3.16 x10^7</li>\n",
"</ul>\n",
"</p>\n",
" \n",
"<p>Multiple Linear Regression: Using Horsepower, Curb-weight, Engine-size, and Highway-mpg as Predictor Variables of Price.\n",
"<ul>\n",
" <li>R-squared: 0.80896354913783497</li>\n",
" <li>MSE: 1.2 x10^7</li>\n",
"</ul>\n",
"</p>\n",
" \n",
"<p>Polynomial Fit: Using Highway-mpg as a Predictor Variable of Price.\n",
"<ul>\n",
" <li>R-squared: 0.6741946663906514</li>\n",
" <li>MSE: 2.05 x 10^7</li>\n",
"</ul>\n",
"</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Simple Linear Regression model (SLR) vs Multiple Linear Regression model (MLR)</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Usually, the more variables you have, the better your model is at predicting, but this is not always true. Sometimes you may not have enough data, you may run into numerical problems, or many of the variables may not be useful and or even act as noise. As a result, you should always check the MSE and R^2.</p>\n",
"\n",
"<p>So to be able to compare the results of the MLR vs SLR models, we look at a combination of both the R-squared and MSE to make the best conclusion about the fit of the model.\n",
"<ul>\n",
" <li><b>MSE</b>The MSE of SLR is 3.16x10^7 while MLR has an MSE of 1.2 x10^7. The MSE of MLR is much smaller.</li>\n",
" <li><b>R-squared</b>: In this case, we can also see that there is a big difference between the R-squared of the SLR and the R-squared of the MLR. The R-squared for the SLR (~0.497) is very small compared to the R-squared for the MLR (~0.809).</li>\n",
"</ul>\n",
"</p>\n",
"\n",
"This R-squared in combination with the MSE show that MLR seems like the better model fit in this case, compared to SLR."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Simple Linear Model (SLR) vs Polynomial Fit</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<ul>\n",
" <li><b>MSE</b>: We can see that Polynomial Fit brought down the MSE, since this MSE is smaller than the one from the SLR.</li> \n",
" <li><b>R-squared</b>: The R-squared for the Polyfit is larger than the R-squared for the SLR, so the Polynomial Fit also brought up the R-squared quite a bit.</li>\n",
"</ul>\n",
"<p>Since the Polynomial Fit resulted in a lower MSE and a higher R-squared, we can conclude that this was a better fit model than the simple linear regression for predicting Price with Highway-mpg as a predictor variable.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Multiple Linear Regression (MLR) vs Polynomial Fit</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<ul>\n",
" <li><b>MSE</b>: The MSE for the MLR is smaller than the MSE for the Polynomial Fit.</li>\n",
" <li><b>R-squared</b>: The R-squared for the MLR is also much larger than for the Polynomial Fit.</li>\n",
"</ul>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Conclusion:</h2>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>Comparing these three models, we conclude that <b>the MLR model is the best model</b> to be able to predict price from our dataset. This result makes sense, since we have 27 variables in total, and we know that more than one of those variables are potential predictors of the final car price.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Thank you for completing this notebook</h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
"\n",
" <p><a href=\"https://cocl.us/corsera_da0101en_notebook_bottom\"><img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/Images/BottomAd.png\" width=\"750\" align=\"center\"></a></p>\n",
"</div>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>About the Authors:</h3>\n",
"\n",
"This notebook was written by <a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>, <a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>, Bahare Talayian, Eric Xiao, Steven Dong, Parizad, Hima Vsudevan and <a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a> and <a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
"\n",
"<p><a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a> is a Data Scientist at IBM, and holds a PhD in Electrical Engineering. His research focused on using Machine Learning, Signal Processing, and Computer Vision to determine how videos impact human cognition. Joseph has been working for IBM since he completed his PhD.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<hr>\n",
"<p>Copyright &copy; 2018 IBM Developer Skills Network. This notebook and its source code are released under the terms of the <a href=\"https://cognitiveclass.ai/mit-license/\">MIT License</a>.</p>"
]
}
],
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