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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": [],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lmr = LinearRegression()\n"
]
},
{
"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",
"P= df[['engine-size']]\n",
"Q = df['price']\n",
"lmr.fit(P,Q)"
]
},
{
"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([166.86001569])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lmr.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": [
"-7963.338906281042"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lmr.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, 48276.04718058161)"
]
},
"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": 24,
"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>highway-mpg</th>\n",
" <th>price</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>highway-mpg</th>\n",
" <td>1.000000</td>\n",
" <td>-0.704692</td>\n",
" </tr>\n",
" <tr>\n",
" <th>price</th>\n",
" <td>-0.704692</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" highway-mpg price\n",
"highway-mpg 1.000000 -0.704692\n",
"price -0.704692 1.000000"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"df[[\"peak-rpm\", \"price\"]].corr()\n",
"df[[\"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": 25,
"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": 26,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"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": 33,
"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": 33,
"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": 34,
"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": 35,
"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": 36,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 37,
"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": 38,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 38,
"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": 39,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 39,
"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": 41,
"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": 42,
"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": null,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"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": null,
"metadata": {},
"outputs": [],
"source": [
"# Write your code below and press Shift+Enter to execute \n"
]
},
{
"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": 47,
"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": 48,
"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": 49,
"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": 50,
"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": 51,
"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": 52,
"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": 53,
"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": 54,
"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": 55,
"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": 56,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 56,
"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": 57,
"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": 58,
"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": 59,
"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": 59,
"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": 60,
"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": 60,
"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": 61,
"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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