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Created March 4, 2020 16:18
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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": 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": 7,
"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": 7,
"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": 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": [
"# 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": 11,
"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": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.fit(df[['highway-mpg']], df[['price']])\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[['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": 12,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[-821.73337832]])"
]
},
"execution_count": 12,
"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": 13,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([38423.30585816])"
]
},
"execution_count": 13,
"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"
]
},
{
"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": 14,
"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": 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": [
"lm.fit(Z, df['price'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the value of the intercept(a)?"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"-15806.62462632922"
]
},
"execution_count": 16,
"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": 17,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 17,
"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": 18,
"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": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2 = LinearRegression()\n",
"lm2.fit(df[['normalized-losses' , 'highway-mpg']],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": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 19,
"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": 20,
"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": 21,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 48264.79876902404)"
]
},
"execution_count": 21,
"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": 22,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 47422.919330307624)"
]
},
"execution_count": 22,
"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": 23,
"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": 23,
"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": 24,
"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": 25,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"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": 28,
"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": 29,
"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": 30,
"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": 31,
"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": 32,
"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": 32,
"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": 37,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 3 2\n",
"-1.557 x + 204.8 x - 8965 x + 1.379e+05\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(p)\n",
"PlotPolly(p1,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": 38,
"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": 39,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 40,
"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": 41,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 41,
"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": 42,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 42,
"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": 43,
"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": 44,
"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": 45,
"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": 45,
"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": 46,
"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": 46,
"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": 47,
"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": 47,
"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": 48,
"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": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \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]"
]
},
{
"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": 49,
"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": 50,
"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": 51,
"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": 52,
"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": 53,
"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": 54,
"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": 55,
"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": 56,
"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": 57,
"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": 58,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 58,
"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": 59,
"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": 60,
"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": 61,
"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": 61,
"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": 62,
"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": 62,
"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": 64,
"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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