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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": 19,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1 = LinearRegression()"
]
},
{
"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": 20,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([13728.4631336 , 13728.4631336 , 17399.38347881, 10224.40280408,\n",
" 14729.62322775])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"X = df[['engine-size']]\n",
"Y = df['price']\n",
"lm1.fit(X,Y)\n",
"Yhat2=lm1.predict(X)\n",
"Yhat2[0:5] \n"
]
},
{
"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": 21,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([166.86001569])"
]
},
"execution_count": 21,
"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": 22,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"-7963.338906281042"
]
},
"execution_count": 22,
"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": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"y = -7963.338906281042 +166.86001569 * engine-size"
]
},
{
"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": 31,
"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": 16,
"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": 16,
"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": 17,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"-15806.62462632922"
]
},
"execution_count": 17,
"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": 18,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 18,
"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": 23,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"38201.31327245728"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2 = LinearRegression()\n",
"Z = df[['normalized-losses', 'highway-mpg']]\n",
"lm2.fit(Z, df['price'])\n",
"lm2.intercept_"
]
},
{
"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": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 24,
"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": 25,
"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": 26,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 48267.763750542916)"
]
},
"execution_count": 26,
"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": 27,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 47422.919330307624)"
]
},
"execution_count": 27,
"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": 28,
"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": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \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()"
]
},
{
"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": 29,
"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": 32,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"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": 34,
"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": 35,
"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": 41,
"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": 42,
"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": 38,
"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": 38,
"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": 43,
"metadata": {},
"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": [
"# Write your code below and press Shift+Enter to execute \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(p1)\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": 44,
"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": 45,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 46,
"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": 47,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 47,
"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": 48,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 48,
"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": 49,
"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": 50,
"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": 51,
"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": 51,
"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": 53,
"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": 53,
"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": 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/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": 54,
"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": 55,
"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": 55,
"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": 56,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The R-square is: 0.7609686443622008\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": 57,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The output of the first four predicted value is: [13728.4631336 13728.4631336 17399.38347881 10224.40280408]\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": 58,
"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": 59,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mean square error of price and predicted value is: 15021126.025174143\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": 60,
"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": 61,
"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": 62,
"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": 63,
"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": 64,
"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": 65,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 65,
"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": 66,
"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": 67,
"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": 68,
"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": 68,
"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": 69,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([-7796.47889059, -7629.6188749 , -7462.75885921, -7295.89884352,\n",
" -7129.03882782])"
]
},
"execution_count": 69,
"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": 70,
"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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