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model-development.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center>\n",
" <img src=\"https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/Logos/organization_logo/organization_logo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\" />\n",
"</center>\n",
"\n",
"# Model Development\n",
"\n",
"Estimated time needed: **30** minutes\n",
"\n",
"## Objectives\n",
"\n",
"After completing this lab you will be able to:\n",
"\n",
"- Develop prediction models\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some questions we want to ask in this module\n",
"\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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Setup</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Import libraries\n"
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {},
"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:\n"
]
},
{
"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.\n"
]
},
{
"cell_type": "code",
"execution_count": 116,
"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>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": 116,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# path of data \n",
"path = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Data%20files/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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Linear Regression</h4>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<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"
]
},
{
"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",
"$$\n",
"Yhat = a + b X\n",
"$$\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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Lets load the modules for linear regression</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 117,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.linear_model import LinearRegression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Create the linear regression object</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 118,
"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>\n"
]
},
{
"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.\n"
]
},
{
"cell_type": "code",
"execution_count": 119,
"metadata": {},
"outputs": [],
"source": [
"X = df[['highway-mpg']]\n",
"Y = df['price']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fit the linear model using highway-mpg.\n"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 120,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(X,Y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" We can output a prediction \n"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([16236.50464347, 16236.50464347, 17058.23802179, 13771.3045085 ,\n",
" 20345.17153508])"
]
},
"execution_count": 121,
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38423.3058581574"
]
},
"execution_count": 122,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>What is the value of the Slope (b)?</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([-821.73337832])"
]
},
"execution_count": 123,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>What is the final estimated linear model we get?</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we saw above, we should get a final linear model with the structure:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b X\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plugging in the actual values we get:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<b>price</b> = 38423.31 - 821.73 x <b>highway-mpg</b>\n"
]
},
{
"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",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"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",
"lm_1 = LinearRegression()\n",
"lm_1"
]
},
{
"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",
"-->\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",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 114,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"X_1 = df[['engine-size']]\n",
"Y_1 = df[['price']]\n",
"lm_1.fit(X_1,Y_1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"lm1.fit(df[['engine-size']], df[['price']])\n",
"lm1\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-danger alertdanger\" style=\"margin-top: 20px\">\n",
"<h1>Question #1 c):</h1>\n",
"\n",
"<b>Find the slope and intercept of the model?</b>\n",
"\n",
"</div>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Slope</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"slope = [[166.86001569]]\n"
]
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"\n",
"print('slope = ', lm_1.coef_)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Intercept</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"intercept = [-7963.33890628]\n"
]
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"print('intercept = ', lm_1.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",
"-->\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",
"\n",
"</div>\n"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Yhat= [-7963.33890628] + [[166.86001569]] *X\n"
]
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"# using X and Y \n",
"print('Yhat=',lm_1.intercept_,'+ ', lm_1.coef_, '*X')\n",
"\n",
"#Price=-7963.34 + 166.86*engine-size"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click <b>here</b> for the solution.\n",
"\n",
"<!-- The answer is below:\n",
"\n",
"# using X and Y \n",
"Yhat=-7963.34 + 166.86*X\n",
"\n",
"Price=-7963.34 + 166.86*engine-size\n",
"\n",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Multiple Linear Regression</h4>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Y: Response \\ Variable\\\\\n",
"X_1 :Predictor\\ Variable \\ 1\\\\\n",
"X_2: Predictor\\ Variable \\ 2\\\\\n",
"X_3: Predictor\\ Variable \\ 3\\\\\n",
"X_4: Predictor\\ Variable \\ 4\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"a: intercept\\\\\n",
"b_1 :coefficients \\ of\\ Variable \\ 1\\\\\n",
"b_2: coefficients \\ of\\ Variable \\ 2\\\\\n",
"b_3: coefficients \\ of\\ Variable \\ 3\\\\\n",
"b_4: coefficients \\ of\\ Variable \\ 4\\\\\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The equation is given by\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b_1 X_1 + b_2 X_2 + b_3 X_3 + b_4 X_4\n",
"$$\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.\n"
]
},
{
"cell_type": "code",
"execution_count": 124,
"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.\n"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 125,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(Z, df['price'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is the value of the intercept(a)?\n"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-15806.62462632922"
]
},
"execution_count": 126,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What are the values of the coefficients (b1, b2, b3, b4)?\n"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 127,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" What is the final estimated linear model that we get?\n"
]
},
{
"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?\n"
]
},
{
"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>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 128,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2 = LinearRegression()\n",
"X_1 = df[['normalized-losses','highway-mpg']]\n",
"Y_1 = df['price']\n",
"lm2.fit(X_1,Y_1)"
]
},
{
"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",
"-->\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>\n"
]
},
{
"cell_type": "code",
"execution_count": 129,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 129,
"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",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>2) Model Evaluation using Visualization</h3>\n"
]
},
{
"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.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"import the visualization package: seaborn\n"
]
},
{
"cell_type": "code",
"execution_count": 130,
"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>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's visualize **highway-mpg** as potential predictor variable of price:\n"
]
},
{
"cell_type": "code",
"execution_count": 131,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 48308.591520931215)"
]
},
"execution_count": 131,
"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": [
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 47414.1)"
]
},
"execution_count": 33,
"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>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 132,
"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": 132,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"df[['peak-rpm','highway-mpg','price']].corr()\n"
]
},
{
"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",
"-->\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>\n"
]
},
{
"cell_type": "code",
"execution_count": 133,
"metadata": {},
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Multiple Linear Regression</h3>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First lets make a prediction \n"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 134,
"metadata": {},
"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(Y_hat, 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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 3: Polynomial Regression and Pipelines</h2>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center><b>Quadratic - 2nd order</b></center>\n",
"$$\n",
"Yhat = a + b_1 X +b_2 X^2 \n",
"$$\n",
"\n",
"<center><b>Cubic - 3rd order</b></center>\n",
"$$\n",
"Yhat = a + b_1 X +b_2 X^2 +b_3 X^3\\\\\\\\\n",
"$$\n",
"\n",
"<center><b>Higher order</b>:</center>\n",
"$$\n",
"Y = a + b_1 X +b_2 X^2 +b_3 X^3 ....\\\\\\\\\n",
"$$\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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We will use the following function to plot the data:</p>\n"
]
},
{
"cell_type": "code",
"execution_count": 135,
"metadata": {},
"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\n"
]
},
{
"cell_type": "code",
"execution_count": 136,
"metadata": {},
"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.\n"
]
},
{
"cell_type": "code",
"execution_count": 137,
"metadata": {},
"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 \n"
]
},
{
"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": [
"PlotPolly(p, x, y, 'highway-mpg')"
]
},
{
"cell_type": "code",
"execution_count": 138,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.55663829e+00, 2.04754306e+02, -8.96543312e+03, 1.37923594e+05])"
]
},
"execution_count": 138,
"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>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 139,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 11 10 9 8 7\n",
"-1.243e-08 x + 4.722e-06 x - 0.0008028 x + 0.08056 x - 5.297 x\n",
" 6 5 4 3 2\n",
" + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"#np.polyfit(x,y,11)\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(p1)\n",
"PlotPolly(p1,x,y, 'Highway MPG')\n",
"\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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"Yhat = a + b_1 X_1 +b_2 X_2 +b_3 X_1 X_2+b_4 X_1^2+b_5 X_2^2\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can perform a polynomial transform on multiple features. First, we import the module:\n"
]
},
{
"cell_type": "code",
"execution_count": 140,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.preprocessing import PolynomialFeatures"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We create a <b>PolynomialFeatures</b> object of degree 2: \n"
]
},
{
"cell_type": "code",
"execution_count": 141,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 141,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 142,
"metadata": {},
"outputs": [],
"source": [
"Z_pr=pr.fit_transform(Z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The original data is of 201 samples and 4 features \n"
]
},
{
"cell_type": "code",
"execution_count": 143,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 143,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"after the transformation, there 201 samples and 15 features\n"
]
},
{
"cell_type": "code",
"execution_count": 144,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 144,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z_pr.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Pipeline</h2>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 145,
"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.\n"
]
},
{
"cell_type": "code",
"execution_count": 146,
"metadata": {},
"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 \n"
]
},
{
"cell_type": "code",
"execution_count": 147,
"metadata": {},
"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": 147,
"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. \n"
]
},
{
"cell_type": "code",
"execution_count": 148,
"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"
]
},
{
"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": 148,
"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\n"
]
},
{
"cell_type": "code",
"execution_count": 149,
"metadata": {},
"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": 149,
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 150,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.partial_fit(X, y)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.fit(X, y, **fit_params).transform(X)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" Xt = transform.transform(Xt)\n"
]
},
{
"data": {
"text/plain": [
"array([13102.74784201, 13102.74784201, 18225.54572197, 10390.29636555,\n",
" 16136.29619164, 13880.09787302, 15041.58694037, 15457.93465485,\n",
" 17974.49032347, 10510.56542385, 10510.56542385, 15845.70697835,\n",
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" 5976.20889391, 5832.72306295, 10109.23396371, 6061.05969767,\n",
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" 18336.04622938, 7336.72885437, 6420.49643279, 5174.21296336,\n",
" 6619.35236359, 6652.09244229, 6765.45204951, 6795.56233742,\n",
" 8796.64497511, 8948.23637645, 8991.91184621, 9194.18038695,\n",
" 10928.27635866, 10052.96792101, 9660.68466801, 12124.39546671,\n",
" 36318.61803898, 36318.61803898, 41642.8179005 , 5912.27956733,\n",
" 5928.15567673, 5941.11734652, 6046.17348651, 6059.47585172,\n",
" 10195.17246527, 10195.17246527, 10183.58560528, 15943.91103394,\n",
" 10255.79037208, 10380.12258884, 10255.79037208, 10380.12258884,\n",
" 10840.99181324, 10455.17617947, 14409.33460485, 13374.99392567,\n",
" 23845.18430719, 25660.83650127, 23694.52193108, 25819.22130713,\n",
" 33467.88380606, 32977.3323232 , 43675.1876574 , 40887.93971531,\n",
" 21725.64934084, 6133.16487359, 6085.05002803, 6253.80059193,\n",
" 10090.74982707, 11854.93594171, 10016.61577698, 18326.329704 ,\n",
" 18294.79233972, 18293.35249597, 10170.11422978, 10338.39037401,\n",
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" 6237.02226217, 6303.17324643, 6594.52421107, 6346.49618251,\n",
" 6608.34797507, 6413.64654004, 6639.54002489, 6539.47142737,\n",
" 9873.86832774, 9834.0864611 , 21542.40070894, 21943.92002198,\n",
" 19962.95857269, 20356.0183024 , 26222.11317103, 20341.71353538,\n",
" 14818.06559816, 17551.99876768, 15859.21897961, 22522.92300522,\n",
" 15235.77892428, 17955.44126309, 16372.90437956, 23030.2532818 ,\n",
" 15084.294341 , 17955.44126309, 16250.91973598, 6055.84397892,\n",
" 10109.23396371, 6061.05969767, 6118.14411398, 7233.51510587,\n",
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" 29495.55178338, 29142.08639481, 12016.62613202, 11697.23318166,\n",
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" 18242.95384024, 17949.00448273, 6700.20551188, 7997.30024417,\n",
" 8636.26729049, 7944.41290334, 8390.53558175, 9428.00408123,\n",
" 10474.44703897, 11297.44802676, 8851.7365991 , 9797.87067058,\n",
" 9844.28010745, 13096.77282426, 6056.63496474, 6245.63877429,\n",
" 6145.27113649, 7292.72653992, 7665.13318655, 12736.87506656,\n",
" 6871.06981567, 6968.66287912, 9283.38827884, 9464.77139239,\n",
" 7169.3719601 , 7136.3122441 , 7210.40024787, 7330.79618254,\n",
" 7477.79752708, 11470.87491749, 11381.87464018, 13425.15063307,\n",
" 13416.04571804, 13450.31407106, 13756.595326 , 13844.6633676 ,\n",
" 14559.88992624, 9806.11748135, 9879.53213034, 10407.28472047,\n",
" 10407.28472047, 10562.89821641, 20451.82473939, 20392.24997134,\n",
" 19935.66449178, 19170.99696916, 8417.3909446 , 8516.96887281,\n",
" 8433.178976 , 8524.96214343, 8695.96885206, 7520.25782581,\n",
" 9838.62475227, 9575.08567915, 9484.96194069, 14720.52537862,\n",
" 8713.09236566, 10070.069151 , 14626.38856972, 15008.62680132,\n",
" 14696.7259568 , 15034.47898838, 19307.91162797, 18667.09940953,\n",
" 14749.22928895, 18027.49072084, 19827.65641803, 17324.32982519,\n",
" 16292.72734879])"
]
},
"execution_count": 150,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"Input_1 = [('scale',StandardScaler()),('Linear Regression',LinearRegression())]\n",
"pipe_1 = Pipeline(Input_1)\n",
"pipe.fit(Z,y)\n",
"ypipe_1 = pipe.predict(Z)\n",
"ypipe_1"
]
},
{
"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",
"-->\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Part 4: Measures for In-Sample Evaluation</h2>\n"
]
},
{
"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",
"<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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Model 1: Simple Linear Regression</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2\n"
]
},
{
"cell_type": "code",
"execution_count": 151,
"metadata": {
"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\".\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the MSE\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can predict the output i.e., \"yhat\" using the predict method, where X is the input variable:\n"
]
},
{
"cell_type": "code",
"execution_count": 152,
"metadata": {},
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 153,
"metadata": {},
"outputs": [],
"source": [
"from sklearn.metrics import mean_squared_error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we compare the predicted results with the actual results \n"
]
},
{
"cell_type": "code",
"execution_count": 154,
"metadata": {},
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2\n"
]
},
{
"cell_type": "code",
"execution_count": 155,
"metadata": {},
"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\".\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the MSE\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" we produce a prediction \n"
]
},
{
"cell_type": "code",
"execution_count": 156,
"metadata": {},
"outputs": [],
"source": [
"Y_predict_multifit = lm.predict(Z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" we compare the predicted results with the actual results \n"
]
},
{
"cell_type": "code",
"execution_count": 157,
"metadata": {},
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's calculate the R^2\n"
]
},
{
"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\n"
]
},
{
"cell_type": "code",
"execution_count": 158,
"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\n"
]
},
{
"cell_type": "code",
"execution_count": 159,
"metadata": {},
"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\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>MSE</h3>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also calculate the MSE: \n"
]
},
{
"cell_type": "code",
"execution_count": 160,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 160,
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 161,
"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 \n"
]
},
{
"cell_type": "code",
"execution_count": 162,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(99, 1)"
]
},
"execution_count": 162,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_input=np.arange(1, 100, 1).reshape(-1, 1)\n",
"np.shape(new_input)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Fit the model \n"
]
},
{
"cell_type": "code",
"execution_count": 163,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.4965911884339176"
]
},
"execution_count": 163,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(X, Y)\n",
"lm.score(X,Y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Produce a prediction\n"
]
},
{
"cell_type": "code",
"execution_count": 164,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([37601.57247984, 36779.83910151, 35958.10572319, 35136.37234487,\n",
" 34314.63896655])"
]
},
"execution_count": 164,
"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 \n"
]
},
{
"cell_type": "code",
"execution_count": 165,
"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": [
"plt.plot(new_input, yhat)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Decision Making: Determining a Good Model Fit</h3>\n"
]
},
{
"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",
"<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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Simple Linear Regression model (SLR) vs Multiple Linear Regression model (MLR)</h3>\n"
]
},
{
"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.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Simple Linear Model (SLR) vs Polynomial Fit</h3>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Multiple Linear Regression (MLR) vs Polynomial Fit</h3>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Conclusion:</h2>\n"
]
},
{
"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>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Thank you for completing this lab!\n",
"\n",
"## Author\n",
"\n",
"<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
"\n",
"### Other Contributors\n",
"\n",
"<a href=\"https://www.linkedin.com/in/mahdi-noorian-58219234/\" target=\"_blank\">Mahdi Noorian PhD</a>\n",
"\n",
"Bahare Talayian\n",
"\n",
"Eric Xiao\n",
"\n",
"Steven Dong\n",
"\n",
"Parizad\n",
"\n",
"Hima Vasudevan\n",
"\n",
"<a href=\"https://www.linkedin.com/in/fiorellawever/\" target=\"_blank\">Fiorella Wenver</a>\n",
"\n",
"<a href=\" https://www.linkedin.com/in/yi-leng-yao-84451275/ \" target=\"_blank\" >Yi Yao</a>.\n",
"\n",
"## Change Log\n",
"\n",
"| Date (YYYY-MM-DD) | Version | Changed By | Change Description |\n",
"| ----------------- | ------- | ---------- | --------------------------------------------- |\n",
"| 2020-10-30 | 2.2 | Lakshmi | Changed url of csv |\n",
"| 2020-09-09 | 2.1 | Lakshmi | Fixes made in Polynomial Regression Equations |\n",
"| 2020-08-27 | 2.0 | Lavanya | Moved lab to course repo in GitLab |\n",
"\n",
"<hr>\n",
"\n",
"## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n"
]
}
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