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Created February 7, 2020 11:55
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DA0101EN-Review-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/skills_network_DA0101EN_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/da0101en_object_storage_skills_network\">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": 3,
"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": 4,
"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": 4,
"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": 5,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"X = df[['highway-mpg']]\n",
"Y = df['price']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fit the linear model using highway-mpg."
]
},
{
"cell_type": "code",
"execution_count": 6,
"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": 6,
"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": 8,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"38423.3058581574"
]
},
"execution_count": 8,
"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": 9,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([-821.73337832])"
]
},
"execution_count": 9,
"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": 12,
"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": 12,
"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": 23,
"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": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"K = df[['engine-size']]\n",
"L = df[['price']]\n",
"\n",
"lm1.fit(K,L)\n",
"lm1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm1.fit(df[['engine-size']], df[['price']])\n",
"lm1\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 c):</h1>\n",
"\n",
"<b>Find the slope and intercept of the model?</b>\n",
"</div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Slope</h4>"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[166.86001569]])"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Intercept</h4>"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([-7963.33890628])"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.intercept_"
]
},
{
"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",
"Yhat= -7963.33890628 + 166.86001569\\*X <br>\n",
"Price= -7963.33890628 + 166.86001569\\*engine-size"
]
},
{
"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=38423.31-821.733*X\n",
"\n",
"Price=38423.31-821.733*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": 26,
"metadata": {},
"outputs": [],
"source": [
"Z = df[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fit the linear model using the four above-mentioned variables."
]
},
{
"cell_type": "code",
"execution_count": 27,
"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": 27,
"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": 28,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"-15806.62462632922"
]
},
"execution_count": 28,
"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": 29,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 29,
"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": 30,
"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": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2=LinearRegression()\n",
"Z1 = df[['normalized-losses', 'highway-mpg']]\n",
"lm2.fit(Z1, 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": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 31,
"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": 32,
"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": 33,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 48300.16162694483)"
]
},
"execution_count": 33,
"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": 35,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 47422.919330307624)"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"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": 36,
"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": 36,
"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 \"peak-rpm\" has a stronger correlation with \"price\", it is approximate -0.704692 compared to \"highway-mpg\" 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": 37,
"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": [
"width = 12\n",
"height = 10\n",
"plt.figure(figsize=(width, height))\n",
"sns.residplot(df['highway-mpg'], df['price'])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<i>What is this plot telling us?</i>\n",
"\n",
"<p>We can see from this residual plot that the residuals are not randomly spread around the x-axis, which leads us to believe that maybe a non-linear model is more appropriate for this data.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Multiple Linear Regression</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>How do we visualize a model for Multiple Linear Regression? This gets a bit more complicated because you can't visualize it with regression or residual plot.</p>\n",
"\n",
"<p>One way to look at the fit of the model is by looking at the <b>distribution plot</b>: We can look at the distribution of the fitted values that result from the model and compare it to the distribution of the actual values.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First lets make a prediction "
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"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": 40,
"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": 41,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"x = df['highway-mpg']\n",
"y = df['price']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's fit the polynomial using the function <b>polyfit</b>, then use the function <b>poly1d</b> to display the polynomial function."
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"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": 43,
"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": 44,
"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": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.polyfit(x, y, 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function \"hits\" more of the data points.</p>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<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": 45,
"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",
"f1 = np.polyfit(x, y, 11)\n",
"p1 = np.poly1d(f1)\n",
"print(p1)\n",
"PlotPolly(p1,x,y, 'Length')"
]
},
{
"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 3rd order (cubic) \n",
"f1 = np.polyfit(x, y, 11)\n",
"p1 = np.poly1d(f1)\n",
"print(p)\n",
"PlotPolly(p1,x,y, 'Length')\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": 46,
"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": 47,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 48,
"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": 49,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 49,
"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": 50,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 50,
"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": 51,
"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": 52,
"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": 53,
"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": 53,
"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": 54,
"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": 54,
"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": 56,
"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": 56,
"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": 58,
"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([13699.11161184, 13699.11161184, 19051.65470233, 10620.36193015,\n",
" 15521.31420211, 13869.66673213, 15456.16196732, 15974.00907672,\n",
" 17612.35917161, 10722.32509097])"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
"pipe=Pipeline(Input)\n",
"pipe.fit(Z,y)\n",
"ypipe=pipe.predict(Z)\n",
"ypipe[0:10]"
]
},
{
"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": 59,
"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": 60,
"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": 61,
"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": 62,
"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": 63,
"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": 64,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"Y_predict_multifit = lm.predict(Z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" we compare the predicted results with the actual results "
]
},
{
"cell_type": "code",
"execution_count": 65,
"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": 66,
"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": 67,
"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": 68,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 68,
"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": 69,
"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": 70,
"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": 71,
"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": 71,
"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": 72,
"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": 72,
"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": 73,
"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/skills_network_DA0101EN_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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