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model-development.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<center>\n",
" <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DA0101EN-SkillsNetwork/labs/Module%204/images/IDSNlogo.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": 1,
"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": 2,
"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": 2,
"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": 3,
"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": 4,
"metadata": {},
"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>\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": 5,
"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": 6,
"metadata": {},
"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 \n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"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>\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": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1 = LinearRegression()\n",
"lm1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm1 = LinearRegression()\n",
"lm1\n",
"```\n",
"\n",
"</details>\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": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.fit(df[['engine-size']], df[['price']])\n",
"lm1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm1.fit(df[['engine-size']], df[['price']])\n",
"lm1\n",
"```\n",
"\n",
"</details>\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": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[166.86001569]])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h4>Intercept</h4>\n"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-7963.33890628])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm1.intercept_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# Slope \n",
"lm1.coef_\n",
"\n",
"# Intercept\n",
"lm1.intercept_\n",
"```\n",
"\n",
"</details>\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": 26,
"metadata": {
"collapsed": true,
"jupyter": {
"outputs_hidden": true
},
"tags": []
},
"outputs": [
{
"ename": "NameError",
"evalue": "name 'engine' is not defined",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-26-ec440a7f77cb>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mYhat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m7963.34\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m166.86\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mPrice\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m7963.34\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m166.86\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mengine\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0msize\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mNameError\u001b[0m: name 'engine' is not defined"
]
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"Yhat=-7963.34 + 166.86*X\n",
"\n",
"Price=-7963.34 + 166.86*engine-size"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"# using X and Y \n",
"Yhat=-7963.34 + 166.86*X\n",
"\n",
"Price=-7963.34 + 166.86*engine-size\n",
"\n",
"```\n",
"\n",
"</details>\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": 27,
"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": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 28,
"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": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-15806.62462632922"
]
},
"execution_count": 29,
"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": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 30,
"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": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 32,
"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": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm2 = LinearRegression()\n",
"lm2.fit(df[['normalized-losses' , 'highway-mpg']],df['price'])\n",
"\n",
"\n",
"```\n",
"\n",
"</details>\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": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"lm2.coef_"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\n",
"lm2.coef_\n",
"\n",
"```\n",
"\n",
"</details>\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": 36,
"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": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 48269.53068933964)"
]
},
"execution_count": 38,
"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>\n"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 47414.1)"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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l1zGzpKQ9kq5X+fkPO+eOOueOHjhwoD6/FAAAALADjeyCcsDMhsL3eyT9gKRxSWclvT/8svdL+t3w/bOS7gs7m9yiwmbLJ8MylXkze1dY3/2TFdcpfq97JT0W1okDAAAALamRfcBvlPTZsJNJQtLnnXO/Z2aPS/q8mX1A0ncl/agkOecumNnnJX1TUl7Sh51zxbOOf0rSZyT1SPpC+CZJvybpN83sJRVWvu9r4O8DAAAA7Jp12oLx0aNH3dNPP93saQAAAKDNmdkzzrmjleMcRQ8AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAESIAA4AAABEiAAOAAAARIgADgAAAEQo2ewJIB7OjU/p9PkJTU5nNDrcq5PHxnT8yEizpwUAABA7rIBjS+fGp/SxM8/pa5PTem1uWV+bnNbHzjync+NTzZ4aAABA7BDAsaVPfOEFzWRycoHkmckF0kwmp0984YVmTw0AACB2KEHBli5eyyhhUiJhkiQzyQVOF69lmjwzAACA+GEFHAAAAIgQARxbGtvfp8BJgXNycgqcU+AK4wAAANgeAji29HP3HNFwb0omKe8HMknDvSn93D1Hmj01AACA2CGAY0vHj4zol+69Q2+/aVg37unR228a1i/dewdtCAEAAHaATZioyfEjIwRuAACAOmAFHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIhQstkTQDycG5/S6fMTmpzOaHS4VyePjen4kZFmTwsAACB2WAHHls6NT+mBsxc0Nb+soZ6UpuaX9cDZCzo3PtXsqQEAAMQOARxbOn1+QinP1JtOyqxwmfJMp89PNHtqAAAAsUMAx5YmpzPqSXllYz0pT5emM02aEQAAQHwRwLGl0eFeLeX8srGlnK/Dw71NmhEAAEB8EcCxpZPHxpTznTLZvJwrXOZ8p5PHxpo9NQAAgNghgGNLx4+M6NSJ2zQy0K3ZpZxGBrp16sRtdEEBAADYAdoQoibHj4wQuAEAAOqAFXAAAAAgQgRwAAAAIEIEcAAAACBC1IC3AY6JBwAAiA9WwGOOY+IBAADipeYAbmZvMLMfCN/vMbOBxk0LteKYeAAAgHipKYCb2d+RdEbS6XDosKTfadCcsA0cEw8AABAvta6Af1jS90makyTn3IuSKDJuARwTDwAAEC+1BvAV51y2+IGZJSW5xkwJ28Ex8QAAAPFSawD/YzP7R5J6zOyvSPpPkv5r46aFWnFMPAAAQLyYc1svZJtZQtIHJP1VSSbpDyQ94mq5cos5evSoe/rpp5s9DQAAALQ5M3vGOXe0crzWPuA9kn7dOfer4TfzwjF2+gEAGoIzDgC0q1pLUL6sQuAu6pH0h/WfDgAAnHEAoL3VGsC7nXMLxQ/C92mzAQBoCM44ANDOag3gi2Z2Z/EDM3uHpKXGTAkA0Ok44wBAO6u1BvzvS/pPZvZK+PGNkn68ITMCAHS80eFeTc0vqze99jDFGQcA2kVNK+DOuackHZH0U5L+nqS3OOeeaeTEAACdizMOALSzTVfAzez7nXOPmdn/WPGpW81Mzrn/0sC5AQA61PEjIzqlQi34pemMDtMFBUAb2aoE5S9JekzSX6vyOSeJAA4AaIjjR0YI3ADa0qYB3Dn3f4aH8HzBOff5iOYEAAAAtK0ta8Cdc4Gkn45gLgAAAEDbq7UN4ZfM7GNmNmpme4tvDZ0ZAAAA0IZqbUP4v6hQ8/33KsbZjg4AAABsQ60B/K0qhO+7VQjifyLp3zVqUgAAAEC7qjWAf1bSnKRPhR/fH479WCMmBQAAALSrWgP4m51zd5R8/Edm9lwjJgQAaH3nxqd0+vyEJqczGqVHNwBsS62bML9mZu8qfmBmf0HSnzZmSgCAVnZufEoPnL2gqfllDfWkNDW/rAfOXtC58almTw0AYqHWFfC/IOknzey74cc3SXrBzL4hyTnnbm/I7ADUBauVqKfT5yeU8ky96cJDSG86qUw2r9PnJ/h3BQA1qDWA39PQWQBomOJqZcqzstXKUxJhCTsyOZ3RUE+qbKwn5enSdKZJMwKAeKkpgDvnvtPoiQBoDFYrUW+jw72aml9e/TclSUs5X4eHe5s4KwCIj1prwAHE1OR0Rj0pr2yM1UrsxsljY8r5TplsXs4VLnO+08ljHA0BALUggANtbnS4V0s5v2yM1UrsxvEjIzp14jaNDHRrdimnkYFunTpxG6+oAECNaq0BBxBTJ4+N6YGzF5TJ5tWT8rSU81mtxK4dPzLS8MDN5mEA7YoVcKDNsVqJOKLVIYB2xgo40AGiWK0E6onNwwDaGSvgAICWw+ZhAO2MAA4AaDlsHgbQzgjgAICWQ6tDAO2MAA4AaDnHj4zo3jsP6er8il64Mq+r8yu6985D1H8DaAsEcABAyzk3PqUzz17WgYEuveXggA4MdOnMs5fpggKgLRDAAQAtp7QLilnhMuWZTp+faPbUAGDXCOAAgJZDFxQA7YwADgBoOXRBAdDOCOBt4Nz4lO5/+And/eBjuv/hJ6iRBBB7dEEB0M4I4DF3bnxKP3vmOX3tu9O6Mrukr313Wj975jlCOIBYO35kRKdO3KaRgW7NLuU0MtCtUyduowsKgLbAUfQx9+AXxzWdyclLmJJeQs5J05mcHvziOA9UAGLt+JER/o4BaEsE8JibeH1RCZMSZpIkM8mZ08Tri02eGQAAAKqhBAUAAACIEAE85m7Z16vASUHg5JxTEDgFrjAOAACA1kMAj7mP/9BbNNSbkiUk3zlZQhrqTenjP/SWZk8NAAAAVRDAY+74kRH98r136O2jwzo42K23jw7rl++9g41LAAAALYpNmG2ATgEAAADxwQo4AAAAECECOAAAABAhAjgAAAAQoYYFcDMbNbM/MrMXzOyCmX00HN9rZl8ysxfDy+GS6/y8mb1kZt8ysx8sGX+HmX0j/NynzAqnzphZl5l9Lhz/qpnd3KjfBwAAAKiHRq6A5yX9b865t0h6l6QPm9lbJX1c0pedc7dK+nL4scLP3SfpNkn3SPoVM/PC7/VpSR+SdGv4dk84/gFJ0865N0r6pKQHG/j7AAAAALvWsADunHvVOfds+P68pBckHZL0XkmfDb/ss5LeF77/XkmPOudWnHMXJb0k6S4zu1HSoHPuceeck/QbFdcpfq8zkt5TXB0HAAAAWlEkNeBhacjbJX1V0g3OuVelQkiXVOyfd0jSZMnVLoVjh8L3K8fLruOcy0ualbSvIb8EAAAAUAcN7wNuZv2S/rOkv++cm9tkgbraJ9wm45tdp3IOH1KhhEU33XTTVlMGgIY5Nz6l0+cnNDmd0ehwr04eG6OPPwB0mIaugJtZSoXw/R+cc/8lHH4tLCtReDkVjl+SNFpy9cOSXgnHD1cZL7uOmSUl7ZF0vXIezrmHnXNHnXNHDxw4UI9fDQC27dz4lB44e0FT88sa6klpan5ZD5y9oHPjU1tfGQDQNhrZBcUk/ZqkF5xz/7LkU2clvT98//2Sfrdk/L6ws8ktKmy2fDIsU5k3s3eF3/MnK65T/F73SnosrBMHgJZz+vyEUp6pN52UWeEy5ZlOn59o9tQAABFqZAnK90n6CUnfMLOvh2P/SNInJH3ezD4g6buSflSSnHMXzOzzkr6pQgeVDzvn/PB6PyXpM5J6JH0hfJMKAf83zewlFVa+72vg7wMAuzI5ndFQT6psrCfl6dJ0pkkzAgA0Q8MCuHPuK6peoy1J79ngOv9M0j+rMv60pO+tMr6sMMADQKsbHe7V1PyyetNrf3qXcr4OD/c2cVYAgKhxEiYAROTksTHlfKdMNi/nCpc53+nksbFmTw0AECECOABE5PiREZ06cZtGBro1u5TTyEC3Tp24jS4oANBhGt6GEACw5viRkYYHblodAkBrYwUcANoIrQ4BoPWxAg4AJeK+elza6lCSetNJZbJ5nT4/EavfQ4r/bQEAG2EFHABC7bB6PDmdUU/KKxuLY6vDdrgtAGAjBHAACLXDQTmjw71ayvllY3FsddgOtwUAbIQADgChdlg9bpdWh5PTGeX9QBNXFzR+ZU4TVxeU94NY3RYAsBECOACE2mH1uF1aHfanPV2eWVbed/LMlPedLs8sqy/tbX1lAGhxbMIEgNDJY2N64OwFZbJ59aQ8LeX8WK4eR9HqsNHMwoOUTWtnKruScQCIMQJ4C2LnP9Acx4+M6N5LM3rkKxe1mPXVl/b0wbtvqev9j/t3beZX8jo01K3XF7LK+oHSXkIHB7u0sJJv9tQAYNcI4C2muPM/5VnZzv9TEg/S6HiNDq/nxqd05tnLOjDQpZvCFfAzz17W7YeH6vJzuH/XbnS4V1Pzyxo70L86lsnmNTLQ3cRZAUB9UAPeYtj5D1QXRVu6Rt//uH/Xrl02kwJANQTwFtMOXRiARogivDb6/sf9u3bHj4zo3jsP6er8il64Mq+r8yu6985DdX+l4Nz4lO5/+And/eBjuv/hJ+gzDiASBPAW0w5dGIBGiCK8Nvr+x/27dqXlQG85OKADA1068+zlugZkDvsB0CwE8AhsZ4WFl12B6qIIr42+/3H/rl0Ur3hQEgSgWTougAdOyvtBZD9vuyss7dLDF6i3KMJro+9/3L9rF8UrHpQEAWiWjuuCkvcDffd6RgkzpZMJpbyE0smEusL3vUR9e8yWrrBIUm86qUw2r9PnJzZ80G2HHr5AvR0/MqJTKtynLk1ndLhBLfwaff/j/l2bYheU4t9Oqf6veETxMwCgmo4L4EWBc1rO+VqueEk7mSgE8kI4L4T0tJfY8eEPk9MZDfWkysZYYUHU2qX3NOG1c5w8NqafPfOcLk8vKR8ESiYSGuhO6hd++K11/RntcPASgPjp2AC+kXwQKJ8NlMmujZmZkglTV7I0nBfetsIKC5qN3tOIKydJFp5+aeHHdRTVqyoAUIkAXgPnnHK+U84PpJW18WplLGkvoURJGQsrLGi2nZRBAc12+vyE9vSkdOOentWxRvy75VUVAM1AAN+FWspY3nHzsH7hh9+iX/vKRV2eWWKFBZGjDApxNDmdkWfSxNWF1aPo9/en+XcLoC0QwBugsozlz4306//+n24v1JSHq+WZbF5pL6FkDWUswG5QBoU4GuhK6sWpBXkJk5cw5QOnyzPLunWkf+srA0CLI4BHxDmnbN4pm69exrL65q0vYwF2gzIoxJFzYcV3sfDbVYwDQIwRwJusljKW1Y4su+jGgs7FRrPW0i4daRptIevr0FC3Xl/IrpagHOzv0mLW3/rKANDiCOAReHLiuh59alKvzi3pxsEe3ffOUd01tnfT62zUjaW0NWLxkjIWbIWNZq2BjjS1K5ZOjR1YKznJZPMaGehu4qwAoD5Ibg325MR1PfTYi7q2uKLB7qSuLa7oocde1JMT17f9vQplLIEWlvO6vpjVldllffd6Rt+5tqhXZpZ0dX5Fs5lceEJgdKd9AqgNR5/XLoqTTwGgWVgBb7BHn5pU3vc1k/GV8wOlvIT6uzw9+tTklqvgtfIDJz9YX8ayumIe9ixPelZomUiNOdAUdKSpHaVTtaOsCYgfAniDfef6ouaXcrKEKRHu5J9ezCkfLDb8Z5dt/KzgJWz1MKG0l1AqaUomCrXm1JkDjdFOHWmiCH2UTm2NsiYgngjgDZbNB5IVup1IkpnkW/VQHKXNVs2Tq+HclArrzFNeQh6r5miyuK/0tUtHGkJf6+CgLSCeCOANlvJMK3kpCJzMpGIHrbTXmmG27NTPCglbC+TdqYS6kp7SSbYRIBrnxqf0sTPPaWElLz9wen1hRR8785x++d47YhM02qWsgtDXOihrAuKJAN5gN+/r16XpRS1m12rA+9JJHR7ua/bUti1wTis5Xys5X/PLhTEvYepOeepOeupKJdSVpFUiGuMTX3hBM5mcPDN5ZnKBNJPJ6RNfeCGWoS/O3aw5pbJ1tFNZE9BJWL5ssPveOapU0tP+/i7dsr9P+/u7lEp6uu+do82eWl34gdPiSl7XFlf0ysySXr6W0eWwI8vcck4reZ+DM1AXF69lFAROK36g5XygFT9QEDhdvBaf0Fcs3ZiaXy4r3Tg3PtXsqW3LQFdSl2eWlQ9c2SmV/V2s6UTt5LExzS3l9OJr83rh1Vm9+Nq85pZysStrAjoNfy0b7K6xvfqobtWjT03qytySDtbYBzyuXJVVcgtP+0yFG1GTpZdhzbmXYPMnNpfzA1UWRgXheFy0S+kGp1S2FidJVvhbK4v3qytApyCAR+Cusb1tG7hrsRrKt/g6rxjIvUKJQSJhSpWcCMom0M4WbJAqNhpvRe1Sr8spla3j9PkJ7elJ6cY9PatjcXxSB3QaAjhahh84+XLKbfAY7iXKTwFlEyjipl3qdTmlsnW0y5M6oNOQXhAbfuC0lPU1u5TT1fkVXZrO6LvXMpqaW9bsUqHeHO1ro1dA4vTKSLuc7tguv0c7GB3u1VLFqkUcn9QBnYYAjljLB4EWVvK6trCiy9NL+s61Rb02t6yZTFaZbKFdHdrDidsPbmu8FR0/MqJ77zykq/MreuHKvK7Or+jeOw/FrlTg+JERnTpxm0YGujW7lNPIQLdOnbgtdr9HO+DJEBBPlKCgrRS7siyWFJwnE8WSlcJlKixhQbx88r47JT2rs89fkR923zhx+8FwPB7OjU/pzLOXdWCgSzeFB/Gcefaybj88FNvwylPc5mqX3vJAp7FO27V++9vudL/zpfPNngaarHjiZ1cYyFPJwsmfaY8+5mic+x9+Yl0NeLF2+rc+9K4mzmx7Sk/CLD3Rk1VwAChnZs84545WjrMCjo600YmfxZaJXSUr5l1Jr0mzRLtplwNs2qWdIgA0CwEcKFHax7yotI950iuslKe8hJLhx0Ct+tOeXpxaUOAKpRt539el6SXdOtK/5XVbCZ030Ajnxqd0+vyEJqczGqWUBm2OAA5sYbM+5mZWKF0J2yMW68tTBPOGiPsD9GLWl+8kU+FNknyn2PXPbpd2imgdpWVNpafEnpJidR8HakUAB3bBOads3imbr17KkvYS6kqFl0nqy3ejHR6gp+ZXlEwUDg9yTjKTPCuMb6bVnnicPDamB85eUCabL6sBp/MGdoqyJnQalumABiiums8v5/T6/IpemVnSy9cyujSd0dR8oW/5cs5XQJvEmpU+QJsVLlOe6fT5iWZPbVsSZupKeupOeepKekps8aSs+MRjan657InHufGpiGa8Hm0IUW+T0xn1pMr321DWhHbGCjgQkdLV8gXlV8dTJaUra6Usxmp5hXaoO75lX69eurooC5zMCqvggZPeuH/j0o1WXRk8fmSEwI26oawJnYYADjRZzg+U8wNlsuXjKS+hZLjhM5VIKJW01bDeidrhAfrjP/QWfezMc1pYya/2Mh/qSunjP/SWDa/TDk88dqrVSm/QOJQ1odN05iM5EAM5P9BS1tfcUk7XFld0ZXZZk9czevn1Rb0ys6TXF1Y0v5zTSt5XJ/Tzb4cT/44fGdEv33uH3j46rIOD3Xr76LB++d47Ng2VnXrUeCuW3qBxKGtCp+EgHqANFA8WKnZgKbZKTHkJeYn2KWUproh20ol/58an9LNnntP8cl75IFAykdBAd1K/tEVwj7t2ObQIQGfjIB6gjW10sJAkeYm1MF4azONYZ96pdcdOkqzwREvWGce/d3LpDYD213EB/OK1Rf2Dz31de3pS2tOT0mB4We2tO0XbOMSfHzj5ga/lijKG4qp50jMlE4VAvnrQUCKhRAuunHdiTfDp8xPa05PSjXt6VsdaYRNmo7VDzT8AbKTjAng2H+i5S7M1fW3Ks3WhvBjYB7uLY8myz3elOLYc8bC2ai5J6w+CSZjJCwO6lyiE9EJYb85m0HboA74TnboSzKY8AO2s4wL4yECXfuJdN2l2Ka/ZpZxml3KaW8ppJrzMl/RlzvlOry9k9fpCdpPvWK47mdhwVX1tPFk21qldLdDaAucUrAb09RK2VnOeThYOGkp7jVs5b9V2fI3WqSvBx4+M6JTUcTX/ADpDxwXw4d60/vb33VL1c4XOCv5qMJ9dymluOa/ZTLZwWTJeDO6zSzmVnqWynA+0PL+y5cl2pfrSXtXQPhgG9crPDXan2mpjHeIpcE7LufWlLanw1M9iX/OupFeXf6+sBHfeSnCn1vwDaH8dF8A3Y2bq60qqryup7xnq2foKKoSQxZXKcB5+XCW4zy3lNL+cL9tEtZj1tZj19erscs1zHehOVpTCrK2sD1ZZdR/oTm554h5QD8W+5ip5DppMlKySh5fJbb7yw0owK8EA0C4I4LuUMNNAd0oD3SkdHq7tOn7gtFBlRX1t1X392OJK+Srj/HJe88t5SUs1zlMaKKlb32zzafFzfWmPTaioi3wQKJ8tP2zIC9smdiW9wgbQRCLs2FK9O8vJY2P62JnndHlmafUQm/6upH7hh98a4W/SHKwEA0DrcM6FJxk7BU5yKny8NubkJCU3efWXAN4EXsK0pzelPb2prb84lPMDzRVLYqoF90whuM+V1LaXHt4ROK2Ob2ueq2UvyXUBnc4x2A0/cFrK+lrKri8y9xLlGz9TiUSh1MU5ucAVDh5ypjj+S+vETi4AEDUXhuOgJCy7MCwHbu3zG4Xpddcrvh9+71r0dW0cswngMZHyEtrX36V9/V01XyebD8pq1auutpeUzMwsZZXz1/5R+YHT9cWsri/Wvgl1s84xVVfbu5N0jsE6hdaJTlmt9TX/d388oZ50Unv7ulaf5C3n8vrXj72kO0aHlFgN7WuXrfZksFM7uQBAURCshVintYAraV1AdpJcsEFoVklodutDc6sjgLexdDKhAwNdOjBQW2h3zmk5DO3FFfWNQnvpSvuuO8ekEhW17HSOwXqvzi1psLvwJ6u4+pBOJnR5JqPpzPp/b8U+5ylvbRU9lSyEcy9ssRh1QO/UTi4A4skP3GpJRRCslVeUhmE/cIWAXBGUi6vGq+UZqn3luBMQwLHKzNST8tST8nRwsLum61TtHFNtQ+pSsUSmSueYXKDl3O46xwxWCel0jmkvNw726NriinpKXjFZzgU6OFh9w/Rmp4MWeQlb7XdefD+ZMHle6Up6om7/djq1kwuA6ipXdEsDq0o+Xnt/LcQWv77Y1aHselr7nmXfp+zz68stKleg0TgEcOxKPTrHzGTWaturlcsUa99L1btzTLXQ3k/nmJZy3ztH9dBjL2op56s7ldByLlA+cLrvnaM7/p5+4ORr417nRWamhBU2XScShfc9K6yge+HHiWKYN5NZebgv6tROLkA7Wl3llaqvEofv+84pCMJLVyjBKK4so3MRwBG5nXaOmV8uBvL86sFJlZ1jZkpKZ+rROaYY1gfpHNN0d43t1Ud1qx59alJX5pZ0cLBH971zVHeN7W34z3bOyXeSL1ft0NAtFcP4vXce0r/4w28r7wfqSXlazgfK+04/+e43aCnrK5EoBPti0O90bFhtL6WBdXXlt2TVtvA15Su+kkpWccsDa+lHZZ8K3y/dMFfZqaJyVbl0fpXfs7SEoto8gJ2wTvuHdPvb7nS/86Xzkf7MJyeu69GnJvXq3JJujDA0tLut/r/m/EDzFV1jSgP6XJXx5dzG5Qq1KO0cU9rucaMadzrHdJ7iv9tankQUg3tx1T1hYecXk0yFlXZTYYXeVFyhDy/Dlfji5Waqfbrav0lb/Vz1z9dT6YbV0gOITp24LdYhvDTkVS0nKFH8X7z2/33j20RaC5zVygnWxkpKDlSyWW1d2C1+XB6aa40M1P4ChS4oB/f0POOcO1r5OQJ4gz05cV0PPfaikgkre9n8o99/KyF8Fxr1/3WjzjGlK+6bdY7Zie12jtnTk1I6ySZUNFexvCYRbmotXb3fjuKXV64wnvzNZ3R1obzmfynna39fl/7dT7yj7Hs4rQ+R1QJgtYe7jUJv8f1i6LW1b786x2rfY7PVVQCdZbMATglKgz361KSSCVt9ECmu5Dz61CQBfBca9f91N51j1oX2davta6vxfh06x1RuMqVzDKIUOKfA31lJTi0mpzMa7E4qKLmvpD3T5ZmM5pdrP88A8cGrxegkBPAGK22dVtSdSujKXG11yKiuVf6/NqJzzExJm8fVVffl6p1jXpvbeeeYrdo9DtA5Bk203a43iLfSVzUHu5O6triihx57UR8VrxajPRHAG4wHkcaI8//XnXaOmV/Ol288Xcppdjmv2Ux23Qmp9egcYyp0jqkW2gd7UtpT5XON7hzTDitkv/nfX9bnn7mkpZyvnpSnH3vHYf3EX7y52dNqOY3oeoPWxavF6DQE8AbjQaQxOu3/a8LW6sRr/Q2LnWNmKkpg1q+2r4X2xZJj4Z2kueW85pbzujRde+eYge611fR6do5phxWy3/zvL+uzT3yn0MYwIa3kfX32ie9IUuxCeKOfDDWz6w2i1yqvagJRIYA3GA8ijcH/1615CdNQb1pDvemar5PzA82VBPNqK+szFaeklnaOCZxWx7czz2qdYyrffv1PL0rOqSvpSS6eK2Sff+ZSGL7DenyTFAT6/DOXYhXAo34yxPbF9hfnVzWBnSCAR4gHkfq6a2xvbIJXXKS8hPb1d2lff22bUCVpJeevBvWZDcphKlfbSzvH+IHT9cWsri/Wugl1RSatduB4bW5Z//T3vhmLzjFLOV+Ve2HNCuNxEkW5QDu84oHaddqrmgABvMF4EEG760p5OpDyttc5JheUh/Tl8g4y5avt+XWdY5ykfKG5sSTpj751dcufW9k5Zqt2j4PdSSXr3DmmJ+VpJe+XNW924Wp+nERRLkBNcGfhVU10GgJ4g/EgApQzM/WkPfWkPR3cU3vnmD/59uv6t+dekpkpmSi8PJ0LnN5x07D6upLlwX0pp/kW7BzzY+84XKj5DgKZKTwQpTAeJ1GUC1AT3Hl4VROdhADeYDyIALtnZjr25gP6zrXFmjuIBM5poaQcprDKXr1rTPFtvsGdY/YPdusvv+mA/vTPrmklH6gnlYhlF5T73jmqB/9gXK/NLcsPnLxEobPPh4+/sW4/g5rg2rVDdyCg0xDAG4wHEaA+npy4ri9+8zXt7Uuv1oh+8Zuv6c0HB6uGjYSZBsPgu93OMWuhvBjUs6u92SvLZHbTOSaTC/QbX/2ufue5V6uUxCQ3LJXprbFzTMNZeHJkA6ZCTXBtKHME4okA3mA8iAD18ehTk8rlfc1kfeX8QCkvob60V9dyrt10jpmt0jVmNlO9vr2yc8xMWDZTq2RJ55itQnvxsjuZqFtof/SpSfV3JXWgZLNuvUvrqAmuDWWOQDwRwBuMBxGgPl6+tqCFlbxMpoSZ8r7TzFJOfrDQ1HnttnPMurcNQntp55h84HRtMatrNXeOkdLJhPZss0f7Rp1joiqtoyZ4a5Q5AvFEAI8ADyLA7uV8pyCQnJycClUPJinrx6/B5246x1QL5+XBfS3Yl3aOyeYDXV1Y0dWF2jeh9qS8qj3aTabXF7LqTnryEoVXDnK+0w0DtW2qRf1Q5gjEEwEcQGwEJe87dU5v/Z12jlnM+huuqFcL7ZWdY5ZyvpZyvq7MbbQJtbxs5pXZZf21f/OVinaOu+scg81R5gjEEwEcQGyYykM3sW1jZqb+rqT6u5I6pNpWQ/3AaWElv1rTXnqQUuWm1Km5FU1ncvJd+dOgxRVfiyu+XpmpT+eYYk/20vH+7qQSrbAJtQVQ5gjEEwEcQCw4F6xb8XaS5IIqX42d8Eo2d26nc8zqCnsmp9nlDUJ7yUp8ZhedYyQpYVpdWY9d55gGoMwRiB8COIBYMEvIVAhuxRrwwieaf8R8J/MSpuHetIZ709K+2q6TzQcV7R4LQX2uokTm1dklTc2vlG1AlerfOaYyrDeicwwAlCKAo6nMrKyMoPhYVxwtfewz0+qDoRU/likR7sYrvl/5gFnrw2fpQ7wLX1Z3qx+Xzq18/uvHSn4HK86z0Je6OOfNHtNLX9F3JbMqjq/Nqfxo9tJ5VM4rcIXv5MJNjIVT3J3cLoqonZzC/+Rc+Vwrb79aboPArc3NhXNzTvKdk3NO6WRCKzlflrDVUyRd4Dbs1NFO2u2glXRy684xxf7WBwe71Z1KKJP1lfOdfvzoqEb39lQP7cvlpTOt1DkGAEoRwNtMMdBWBr2Nwmvxc8Xx4jvF61qV71kaKjf9eSWBeC0Yrg/IwFacc3rzDQN6+dqC5pbyyvqB0l5CA30pjQ73abAnpSBYe2LhBy485t0p2M2zjBbQqQetVPa37ksntZTz9Scvvq5/+eN3bHn90s4xpaehzlRsSp0rq21vXOeYjcL7YHdSSY/QDnSajg3gZmE4LAZNW79CadJqGC1aXeVbtxpZ/vnSx/xqq7ql33v1Z6skyCY2DriVc1ydN8EWbcrM9Hf/0p/TA2cv6Mah1OphIznf6af/8hu1f4se3IVwvhbQy94Pg3shtDv5xc+VXMc1McR36kEru+1vvavOMes2n5YH99LQvv3OMev1dXlVgvnGq+393Uk6xwAx13EBPJ1MaOxAf7OnAWCbjh8Z0b2XZvTIVy5qMeurL+3pg3ffouNHRra8biJhSuyiZ4oLV9UrA/xqaA9cWCpTGPPrGN479aCVZvS3LuscM1Tbzwmc00LFoUrF8D6zlNNcyep6McDPL+fLvsdOO8dUK4Op1upxT09KfV10jgFaSccFcADxdG58SmeevawDA126KVwFPvPsZd1+eKimEL4bZqakt7Pw4gdO+SBQEKjs0neFg4X81VV4V1b+UHTjYI8uzyxqYcVXzg+U8hLq7/J0aKhvt79WS4tLf+uE2Wrw3U7nmMpDlebWrbbnV8fnlnJa3KBzzOQ2OsdsVAqzUWjvSUXbOabd9joAmyGAA4iF0+cnlPJMvenCn63edFKZbF6nz080PIDvhpcweYniKq636ddK5SvofuD0fW/cq0//8YwSVghROT/QtcVAP/Ln9zR24k3Wzv2tvYRpb19ae/vSNV8n5wcVQT1fZbW9PNAv59dadAZOms7kNJ2pvXNMyrPywL7a+nHjdo/dqa3/jVfTqXsd0LkI4EAHODc+pdPnJzQ5ndHocK9OHhtr6dBazeR0RkM9qbKxnpSnS9OZJs2oMQqBfW3V8dnvzmpkoEvzy4XNp13JhAa6k3rhyrxG9/Yq7zvlgkC+75QvCe7+JqvqcUF/6zUpL6H9/V1b7ncotZzzNVcWzvPr69sr+raXdo7J+U7XFrK6tlB755iuZGKDlfaS0F7Rwz2dTHTsXgd0LgI40ObOjU/pY2ee08JKXn7g9PrCij525jn98r13xCqEjw73amp+eXUFXCpseDs83NvEWTXe5HRG+/u7dGBgbSOhc06XZ5aU8hJKeVLPFivrOT9YDeq5fKCc7wpjYQ17q6IkYXe6U566U55GBmvfhFrsHDOzlC2rX99stb30Od5KPtDU/Iqm5rfXOWYl7yvlJQpPQM3CJ6LS7FJOf/ztq3SOQdshgANt7hNfeEEzmVzhQc1MLpBmMjl94gsvxCqAnzw2pgfOXlAmmy/rgnLy2Fizp9ZQ9XjisVlQrwzn+cCtjjWzhSMlCdHbceeYFX+tfr0iuM+VrLIXa9vnlnJl5y4s5Qr17Sv56qfa/pP/+s11Y3SOQdwRwIE2d/FaplA/nFhrg+kCp4vX4lW6cfzIiE6pUAt+aTqjwzEtpdmuRj/x2CycB0GhrKXY5aVQ5rK2gbS4qbR4WFI9UZIQD2am/u6k+ruTOjRcW+cYP3BaWFkrh5nJ5PTc5Iz+2wuvrR5zm/MD+YHTYHdKK/lACyv16xyz0cmndI5BlAjgAGLj+JGRtg/clZr5xCORMKVrXDUMiiE9XEEvXBYCez6sT99OSO/U9oudwEvYasgtuvvW/XrnzXtLNt32l5Uc5f2grDNMZSnM3HL5qvtMJre6si6Vd45RG3WOQXwRwFtQO2yYQ+sY29+n8SvzyvprD0Ym6chB+uHHRRyeeBR7rac8bdgJI++H9efFUO4Hym5Q7tKMPuBors023Sa9xLY7x2TzQdVWj5VtHkvr3Ffq2DmmvCSm/p1jEG8E8BZzbnxKD5y9oJRnGupJaWp+WQ+cvaBTUss/AKM1DfUkVbnu6MJxIEpJL6HkBuUuxZXzXBjS/9ZffIP++R98S8t5X13J1u0DjtaVTu68c8xaKM+vq2WfrXiLpHNMRa17Oskm1LjjEbjFxLXXMVrXk9+Z2dZ4K+PVofZV7JdeXA18352HNdSbLtze1xf1PUO9ev+736B3ju0trKLng6ZuEkV72knnmKWcv65jTLXuMaVvu+0c05v2SlbZk1XLZCqDO5tQWwsBvMV0Sq9jRKfYB7q0LLF4ZHqc8OpQ59mq9GZ1xTzvtOL7BPOYi2PbSbPCgllvOrmtzjELK/n1bR6L5TKZ0tX2tRX40n/VmayvTNbXq7O1bUKVpP6u5OrK+kaBvTS093fROaaRCOAtZnS4Vy9fW9DcUuHQjbSX0GBPUjfvo14XO+MlrGrYjtsfVl4dQqVCB5eElJaktYWLVm2tiI11UttJM9NAd0oD3antd47J5Mrq2quvthdCe2XnmIWVvBZW8ro8U9s8E1Ya2quvqle+9XWxCbVWBPAW8+6xvXry5eurx05n/UBT81nd/872+gPUzlqtTOLE7Qf1219/VZW548TtB5szoR3i1SHUarPWisVa86xffihRzq/egxrRoO3k5qp1jtnKus4x62rY85rNZDUb9mafXcopk13brB+4tc4xkzV2jvHCJ1DbCe3dqURHhnYCeIt5fOK6DvSnV4+dTnuFY6cfn7iujzR7ci2m1YJucU6tVibxyfvulPSszj5/RX7g5CVMJ24/GI7HR6eehIn6qqw1L3LOKesHyuYLbyvhJSvm0aDtZP3tunPMutX2kpKZ8HMzSzllSzrH+IHbVeeYPT0p7ekuhvb27hxDAG8xGx07zSpfuVYMulLrlkm8922HdWUuu/pk5b1vO9y0uexUp56EiWiYmbqSnrqS5Q/sOX8tjBfbJub8+h881OloO9kadto5prwMpkqLx+W12vbZTE75gM4xBPAWwypfbVo16LZimUSrPlnZrk49CRPNtVpnXpFHijXl2dXWiYXNoPmAUpaduO+do3rosRe1lPPVnaLtZJwUO8fcsM3OMWX165lcWSlM5efmlnffOaYn5ZUF9a06xwx2J5X0GhfaCeAthlW+2rRi0JVa8wlUqz5Z2Yk4HEiDzrBRnXkQhJs/w44suaBwKuhOTgPtJHeN7dVHdWvJSZjx6IKC7SvtHHPjntpe4Qic0+JKft0qe/E01GrBfX45X9Y5Zinnaynn68pca3SOIYC3GFb5atOKQVdqzSdQrfpkBdhKK+7z2EoiYepKeOpKat2quVTYGJcPXEkoLwT0XODk+529gr7ZSZjobImSzjGHh2u7jh84LSxv0p+9SjeZxRW/7HvspHPMQPfaKvvevo1LeQjgLYhVvq21YtCVWvMJ1Ohwry6+vrBuY+8t+2ltidbVLqVTlYqngW7EOadcWNqykvPDy803g8axfzbQaF7CtKc3pT29u+gcsy60l67CV+8cU/z8VgjgiKVWDLqlc2uFeRRVa215dSGrv3EXD9DNEMdV3WZop9Kp7TAzpZOmdDKh/q61h+jSzaC5sFtLPnD66p9d65j+2UCj7bpzTEVwX1zx9csb/az6THk9M/t1ST8iaco5973h2F5Jn5N0s6SXJf2Yc246/NzPS/qAJF/SR5xzfxCOv0PSZyT1SPp9SR91zjkz65L0G5LeIemapB93zr3cqN8HrafVgm6renziukYG0usOd6K1ZfTadVW3ESidKrfRZtCP/+fn1Z1KqDvlyTmpN51QJpunfzYQkc06x/R1JTcM4I3syfIZSfdUjH1c0pedc7dK+nL4sczsrZLuk3RbeJ1fMbPii3SflvQhSbeGb8Xv+QFJ0865N0r6pKQHG/abROzc+JTuf/gJ3f3gY7r/4Sd0bnyq2VNCjE1OZ5Su2Mmd9hIdG2SaqXRVt7gRKeWZTp+faPbUWs7ocK8uTWd04ZVZfePyrC68Mrv6ahfWXJ5ZUl86qWSiENDTYXu21xeWdcNgt4Z70+rvShbCO4CW0bAVcOfceTO7uWL4vZKOh+9/VtI5ST8Xjj/qnFuRdNHMXpJ0l5m9LGnQOfe4JJnZb0h6n6QvhNf5x+H3OiPp35iZuZhvMWeFDPXWn/b00tVFeWbyzJT3nS7PLOuNB/qaPbVYqUfpyOR0Rp5JE1cXVl+N2N+f5slQFQcH03p8Yu0o7cBJM0t5HRys/aXhTrDRhvTRvX3q60qqdA9YELjVmvIV3189dAhA9KJ+SnyDc+5VSQovi49ehyRNlnzdpXDsUPh+5XjZdZxzeUmzkvY1bOYRYYUM9bZ6xK+VvJWOY0vFJ8ZT88tlT4y3++rUQFdSl2eWlQ9PJM0HhSdDpbW+KPiDb1b/f7vReKc6eWxMOd8pk83LucLlRhvSEwlTd8rTnt6URga6dXi4V7fs79P3DPVob19afV2FlXQAjdcq97RqScBtMr7ZddZ/c7MPmdnTZvb01atXdzjFaExOZ8pOApM6u+4Ruze/ktehoW4lEyY/cEomTIeGurWwkt/6ypBUvyfGqy/QuZK30nGsKnYWMFt7Kx1HwfEjIzp14jaNDHRrdimnkYFunTpxW82vzpgVQvlQb1o3DHbrpn29Gt3bq5HBbu3pSakn7dXc1xhA7aJednnNzG50zr1qZjdKKi5lXJJUetzVYUmvhOOHq4yXXueSmSUl7ZF0vdoPdc49LOlhSTp69GhLP9K1an9rxNfocK9evrZQNpb1A928jzaEtarXhsCFrK9DQ916fSG7WoJysL9Li4TKdcykas9LeOFmvXpvSC9u+Cx9ZSbvB8qG3Vey+UJHlpxP+QqwU1GvgJ+V9P7w/fdL+t2S8fvMrMvMblFhs+WTYZnKvJm9ywqvl/9kxXWK3+teSY/Fvf5b2t7LiUAt3j22V1PzhcBXbEM4NZ/Vu+mQULPR4V4t5cpD8k6eGI8O9ypbEVqyfsAT7CoODRaKl51beysdR7SSXkK96aSGetMaGezW6N5C+cqh4R4dGOjSnp6UetOUsKC1PDlxXT/zued0/68+oZ/53HN6cqLqOm1TNOyeYma/JelxSW82s0tm9gFJn5D0V8zsRUl/JfxYzrkLkj4v6ZuSvijpw8654qPdT0l6RNJLkv5MhQ2YkvRrkvaFGzZ/RmFHlbjb7cuJnYRuMbV5fOK6DvSnlfYSClyhA8qB/rQeb6E/RK2uXk+MeTJUu1/867droMtTsfohYdJAl6df/Ou3N3diWGVm6kp6GuhOaV9/lw7uKZSw3LyvUFd+YKBLQ2EXlnQywb4TROrJiet66LEXdW1xpaxHfquEcGuDReNtOXr0qHv66aebPQ3sUmm3mNKTMHmyst7dDz6moZ5U2YOfc06zSzn9yc99fxNnFi/FLii7Ofjp/oef2PBU0t/60LsaNPP4qsf/c7QO51xZGUvxfT/orByCaPzM557TtcWVsn11Szlf+/q69C9//I5I5tDXldTBPT3POOeOVn6OrfeIpU49JW8n2FdQX7uJCpPTGe3v79KBge617+ccm6w38PylGV14ZVaLWV+zSzk9f2mG+3eMFVfMu5LljQaoL0cjvDq3JM+kyekV5fxAKS+h4d6UrswtNXtqkgjgiClOyavdyWNj+ujnvqa5pcXV1kKDPUn9wg+/tdlTi4169efnyVDtPvWH39ZDj72khEnJROH/00OPvSRJ+sgPvKnJs0M9Jb1EWGO+NrbaszwM4zlWy7FNfemkvnNtUYmEKRG2fX1tbkVv2NcaZ2CwWwKxVK9NcZ3g+Uszmlsqbzk4t5TX85dmmjOhGKpXG0I2Wdfuka9cDMN3QglLhJeFcbS/1Z7lPSnt7+/SjXt69IZ9fXpDWF++n42f2MoGbV+rtldqAlbAEUsnj43pgbMXlMnmy2rACTLrPfKVi0p6VvYglQ8CPfKVi6wk1qher7gcPzKiUxJ1zTVYzPpKVuSqhImWjVXU45TWuPASJi/hqbvivIziinnWD5TLFy+d8gGlLJ1qMefrhsEuTWdyJSUoaWVyrfE3hADegjrpj+lOEWRqR5DZvUaUjrTGGkzr6ksXnliXngETuMI41tSrPCruEglTdw3BPOc75fxA+cBxAFabu3GwR9cWVzRa8nd6KedrpK81WpkSwFsMf0xrV+/DJ9pVX9rTYjYv53w5t3aqYF86fnf/T/3ht/XIVy5qMeurL+3pg3ffEskqfr1eceH+XbsP3n2LHnrsJeWDQsvGwBXePnj3Lc2eWks5fX5C2byvawvlnXXYkF6wUTCXCps/84FTPnDyfadcECgfBnQ2gcbffe8c1UOPvailnK/uVELLucLtfd87R7e+cgTi9wjc5ujugXp7z5ED+u2vv7r6sQtr4d5z5EDzJrUDzdyUV69XXLh/1654mzbjCVecfPu1Oc0t55WQyTNT3ne6tphV3p9r9tRaXmHzZ/XPOedWV8tzJV1acj4r53Fx19hefVS36tGnJnVlbkkHB3t03ztHdVeLnLtAAG8xdPdAvb3w6rxM5SUPFo7HSemmPKlQRhNlLXs9XnHh/r09H/mBNxG4t5DzC/fsRFirY1YsuyAk7oaZKZ00pSvq9+hlHi93je1tmcBdiQDeYmhThnq7eC2jlGfySjZh+kGgi9fiFfraoZad+zfqLZ1MaCnrK3BOZmuvcFUGR9THRr3Ms/lAy3lfK7lAyzmfEhZsiQDeYujugUbwA6d8UFIDLinpxetY6L60p8WVvJzKf4++rvj8Gdvp/btTN2Z36u+9HbeODOjlawuaW1qrAR/sS+nmff3NnlpHSScThSc94RlbfuC0EgbyXNjPnI2fKMVT5BZz/MiITp24TSMD3ZpdymlkoJvj1bErIwNd8sMNbE6FS98VxuPkPUcOVP094lTLvpP7d3Hj5tT8ctnGzXPjUxHOPHqd+ntv18ljY0p5ng7u6dabbxjQwT3dSnkeizZN5iUKez2G+9IaGezW6N5e3byvV4eGe3RgoEtDvenwPAFiWKeKz9JRB6G7B+rJbdAHd6PxVnVlLqvh3qRml/IKXKH8ZE9PUlfmss2e2rZs9/7dqRs3O/X33i5assbHRuUrxVaJuZKNnnRiaX8EcKDNXZmvHlBf22C8VU1OZ3RoqFeHh9dKZ5xzsdvAuN2yik7duNmpv/dOsGgTb1v1MC8N5tl8wOFCbYIADrS5jXbn52O2a390uFcXX1/Q/HJ5v+Nb9sen1nUnfcBHh3vX1/j2JNu+xpcNq+h02zlciGAePxQfAYiFd4/t1dWFrLJ+4WCWrB/o6kJW727RFlPVlJZVmFlYA2o6fX5iw+u8e2yvpubLf++p+Xj93jtx8tiYcr5TJpuXc4VLNqQDYTBPeRrsTmlff5cO7unWTft6dfO+Pn3PUI/2D3RpT09KPWlvtW0rWg8r4ECbq+wBXjoeJ49PXNfIQHrdSvDjE9f1kWZPrkaT0xl5Jk1cXVj9Hfb3pzctq3h84roGuz3NLuWVK6l9j9PvvRPUNgPbs9GKuR+4isOEAuXyjhXzJiOAI7ZoUVabREKq9nc2bgsjk9MZ7evr0v7+7tWxuNWAD3Ql9eLUgryEyUuY8oHT5Zll3TqycTnJi1PzWlj2lfISq32eF5Z9vTgVr4OUduL5SzO68MqsFrO+Zpdyev7SDPfxKvhbiM0U/t5sHMxX8mt15tl8oIBWiZEggCOWdlJL26nyGyxybDTeqtqhJti5Qh/gbN7JqfAqRMK0aW/gbD6QTEpYyUmHVqj5bGef+sNv66HHXgpPPy3c1g899pIkcTpmCf4WYqc2Cub51fpypxW/cFZBjmBedzFbA0OcnBuf0v0PP6G7H3xM9z/8RF37954+P6Fs3teV2WV967V5XZldVjbvb1pLi3hrh5rg1xezhZMKi/U/4Yr264sbd6RJhQcmBeEhHkG4eTYds4OUtuuRr1wMw3dCCUuEl4VxrNnJvgJgM0kvod50Unt6UxoZ6NahoR7dvL9Po3t7dXBPt/b1dam/O6mulLe6MIDtYwUcDdHoVZlvvzanueW8EjJ5Zsr7TtcWs8r7c7ufPFpSO9QEZ/OBPM/KNkblg2DT1ew33TBYpftLKlbdX3ZiMesrocJpgsWTTz0rjGMN7RoRlZSXKBwclJaktX9zxZ7lrJhvDwEcDXH6/IRyvq9rC+Ub5up1iEbOL9yxE4mSl+UDp6zPHb6dxb3fccozLeUK/1aL9dzS5qvZxePrD+5Jbuv4+rjr8hLK5NbCtgtPQe1N8cJtqXYozUK8bSeYZ/PBpiV3nYQAjoZ4cWpes5mcEiWbzV6fzyrn12fjWDqZ0FLWV+BKgowrjKNcwgrBpdo4ovWmGwb1wquzmlteO81zsDupW28Y3PA67bDyvxNeovqD9Ebjnar4BC2TzXfUEzS0vq2CeTZf2pnFdVwwJ4CjIRq9cezWkYH1h5P0pdr+cJKd6E55ylR52b5y400cxL3bw7vH9urJl6/LS5hS4ROj+RV/y57ecV/534mFbPW/FRuNd6pOfYKG+CoG8950+XiupE1iMZy3czAngKMhdvJS+3Z06svyO7G3J1k1gO/tidfdvx26PTw+cV09qYQWVtZuj/4ur+17eu9E8W9G6R4v59bGsaZdnqB96g+/rUe+clGLWV99aU8fvPsWOt50kNUV8wqlobzYz7wdgnm8HoERG43eOMaqzzYkEhrsSmhuZW3lcLArIYtZI/DSbg+S1JtOKpPN121fQRQuvDKrhRW/7BCkhRVfF16ZbdqcWlVvyivUgLv142g/tJ3ERtLJhNLJhPq61sacc8r5hU3aK/lAy+EiXJxCOQEcDRHFCnW7rPo0Wn/a0ysz5S/bL2QDfc9QvIJMO3R7WO3gUZrAHZ09qvm7f2lM/+rLL5btX0hYYRztp9Be0skPpHzY9cbCtpMEcFQyM6WTpnQyoYFwLAicVvKBVvK+lnOFS7/aBqgWQQBHQxw/MqJ7L82sezmRwBy91xez6zZhBlv0nm5F7dDtodjDu3KRJmjhB4lmKYYuShI6w8JKYWOySav98QNXGAdqkUiYetKeetJri0vZikDeSgeYEcDREOfGp3Tm2cs6MNClm8IV8DPPXtbth4cI4RG7tlA9aG803qpOHhvTx848p8szS/IDJy9h6u9K6hd++K3NnlrNBrqTq4Gi2Ntakvq7+FNczUd+4E0E7g5hxc1CJYdUyYXjwA4Vy1cGugsfl66SF8J5oa68GeJVBIrY4HS21rHR2moc11xNklx4dLsrr+SIgw/efYukwsqe01p7yOI40Kl6UoV7c3GjbfFVot5U3O7laGXFVfKh3rRGBrs1urdXN+/r0/cM9Whff5cGulORnfDJsgsaoh3qddFaTp+fUNIr9JX3XeEyGT6pi8urKrcfHlJf2tNi1l/tA96X9nT74aFmTw1oqtHhPr1wZf05EYeH+5owG3SSRMLUnfDWteatbItY79VyAjgaoh3qddtF+Epu1fE4eXFqXtOLWQWS5KR84K/ufI+L0+cnNDLYXXa/iFsnlyj9g0ef1dnnr6yWHJ24/aA+ed+dzZ4WGsA5p2TC5Jmttq71Xby6WqC9VGuLWM+NngRwNASns7WORMKq/oFIxOwozMyKL7+07MRJfjgeF5PTGXkmTVxdWG3Pub8/HctXhhp9KNI/ePRZ/fbXX1392A9c+PGzhPA2tJD1dWioW68vZFfvGwf7u+gQhJZSbaNnzi+sjq/kfC3nC6vltTxxpAYcDXH8yIhOnbhNIwPdml3KaWSgW6dO3MYqXxP0bFBDGbfayqxfeCB2JW+l43Ew0JXU5Zll5cMV3XzgdHlmOXabMIuHIk3NL5cdinRufKpuP+Ps81ckrbWjK5ZkFsfRXkaHe7VS0aFiJR/wqilaXspLqL8rqX39XTo01KOb9/Wu1pSXBvVK8fqrj1ihT3drODzUq/HXFtaNHxqK1wObl0jIuaAQvot9gsPxuFhdFSk+e3AV4zERxaFIG72s28p9fbFz7x7bqydfvq6EFfZGZP1AVxey+ht37W321IBtMTN1p9bXlFeKzyMXgB3Z6CXcuL20O7a/T2amlJdQV6pQm2dmGtsfn01axZfZk57Jd05Jz3RoqDt2t8XkdEY9FQ8u9d5k7SWqd8XwYlY6hdo8PnFdIwNppb2EAielvYRGBtJ6fOJ6s6cGNAQr4ECbuzK7vK3xVvVz9xzRz555TvPLeeX9QMlEQsO9Kf3cPUeaPbWaFTcnjx3oXx3LZPMaKTapjYnR4V69fG1Bc0v51XrdwZ6kbt7Xv/WVa3TXG4b0+MXpquNoP5PTGe3r69L+/rX7gnMulvsjgFqwAg60uXy4dFhZS5uPWdnD8SMj+qV779DbbxrWjXt69PabhvVL994RqzKnk8fGlPOdMtm8nCtcxnFz8rvH9mpqvrBZrlguMDWf1bvH6lcuMHm9evDaaBzxNjrcq6Vc+StBdM5COyOAA23OCwP3upfyY/xKfryeOqxpl83Jj09c14H+8nKBA/31LRe4PLuyrXHEW7s8OQVqRQkK0OZuHRnQt67My1nJ5kVXGI+TYueNlGdlnTdOSbEKsO2wOXlyOqP9/V06MNC4coF2OsEVWzt+ZESnVNjge2k6o8MNaG0JtBICONDmymqng0Lt9EB3Mla101I0nTdQmygO2mqXA6RQu3Z4cgrUihIUoM21Q+20FE3nDdQminKBQ0PVN6ZuNA4AccIKONAB2mFlKYpVV9QminKBX3zfn9dHfutZLWR9Ba7QG7o/7ekX3/fn6/YzAKBZCOAAYuHksTE9cPaCMtm8elKelnI+m7SaqNFP6o4fGdGn7r+TmmAAbYkSFACx0C4dRFC75y/N6MIrs3pldlkXXpnV85dmmj0lAKgLVsABxEY7lNKcG5/S6fMTmpzOaJRV3Q196g+/rYcee0kJk5KJQrnRQ4+9JEn6yA+8qcmzA4DdYQUc6ADnxqd0/8NP6O4HH9P9Dz+hc+NTzZ5SRyq2UpyaXy5rpcjtsd4jX7koFzjlfKeVfOHSBU6PfOVis6cGALtGAAfaHKGvdZS2UjQrXKY80+nzE82eWsuZX84rqBgLwnEAiDtKUIA21079s+NevjE5ndFQT6psjFaK1XEQD4B2RgAH2lxUoa/R4TiqkzAb+XvQShEAIFGCArS90eFeLeX8srF6h74oylyiKN9o9O8RxQE27WKwO7nu1EsLxwEg7gjgQJuLIvRFEY6jOAmz0b8HrRRr98G7b1EiYUp5pq5k4TKRMH3w7luaPTUA2DWWEoA2F8WphVGUuURRvhHF79EOrRSjUGw1+MhXLmox66sv7emDd99CC0IAbYEADnSARoe+KMJxFCdhUqPdWj7yA28icANoS5SgANi1KMpcoijfoEYbABAFc66zmjodPXrUPf30082eBtB2it1DGlXmEpV2+T0AAM1nZs84546uGyeAAwAAAPW3UQCnBAUAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiFDsA7iZ3WNm3zKzl8zs482eDwAAALCZWAdwM/Mk/VtJPyTprZLuN7O3NndWAAAAwMZiHcAl3SXpJefchHMuK+lRSe9t8pwAAACADcU9gB+SNFny8aVwDAAAAGhJyWZPYJesyphb90VmH5L0ofDDBTP7VkNnhajtl/R6syeBSHGbdxZu787C7d1Z2v32fkO1wbgH8EuSRks+Pizplcovcs49LOnhqCaFaJnZ0865o82eB6LDbd5ZuL07C7d3Z+nU2zvuJShPSbrVzG4xs7Sk+ySdbfKcAAAAgA3FegXcOZc3s5+W9AeSPEm/7py70ORpAQAAABuKdQCXJOfc70v6/WbPA01FeVHn4TbvLNzenYXbu7N05O1tzq3bswgAAACgQeJeAw4AAADECgEcLcvMPDP7mpn9XvjxPzazy2b29fDtfyj52p83s5fM7Ftm9oMl4+8ws2+En/uUmVVrXYkWYGYvh7fV183s6XBsr5l9ycxeDC+HS76e2zzGNri9uY+3KTMbMrMzZjZuZi+Y2bu5f7evDW5v7t8lCOBoZR+V9ELF2Cedc28L335fkszsrSp0wLlN0j2SfsXMvPDrP61CD/hbw7d7Ipk5duovh7dtsSXVxyV92Tl3q6Qvhx9zm7ePyttb4j7erh6S9EXn3BFJd6jwt537d/uqdntL3L9XEcDRkszssKQflvRIDV/+XkmPOudWnHMXJb0k6S4zu1HSoHPucVfY7PAbkt7XqDmjId4r6bPh+5/V2u3Hbd5ZuL1jzMwGJR2T9GuS5JzLOudmxP27LW1ye2+kI29vAjha1b+S9A8lBRXjP21mz5vZr5e8XHlI0mTJ11wKxw6F71eOozU5Sf/NzJ6xwum1knSDc+5VSQovR8JxbvP4q3Z7S9zH29GYpKuS/p+wrPARM+sT9+92tdHtLXH/XkUAR8sxsx+RNOWce6biU5+W9OckvU3Sq5L+RfEqVb6N22Qcren7nHN3SvohSR82s2ObfC23efxVu725j7enpKQ7JX3aOfd2SYsKy002wO0dbxvd3ty/SxDA0Yq+T9IJM3tZ0qOSvt/M/r1z7jXnnO+cCyT9qqS7wq+/JGm05PqHJb0Sjh+uMo4W5Jx7JbyckvTbKty+r4UvQyq8nAq/nNs85qrd3tzH29YlSZecc18NPz6jQkDj/t2eqt7e3L/LEcDRcpxzP++cO+ycu1mFjRmPOef+ZvEPdeivS/r/wvfPSrrPzLrM7BYVNmo8Gb6kOW9m7wp3Tv+kpN+N7jdBrcysz8wGiu9L+qsq3L5nJb0//LL3a+324zaPsY1ub+7j7ck5d0XSpJm9ORx6j6Rvivt3W9ro9ub+XS72J2Gio/xzM3ubCi9BvSzppCQ55y6Y2edV+IOel/Rh55wfXuenJH1GUo+kL4RvaD03SPrtsMNUUtJ/dM590cyekvR5M/uApO9K+lGJ27wNbHR7/yb38bb1v0r6D2aWljQh6W+rsAjI/bs9Vbu9P8X9ew0nYQIAAAARogQFAAAAiBABHAAAAIgQARwAAACIEAEcAAAAiBABHAAAAIgQARwAUMbMPmNm9zZ7HgDQrgjgAIBdMTOv2XMAgDghgANAmzCzm81s3Mw+a2bPm9kZM+s1s3eY2R+b2TNm9gclx3//HTN7ysyeM7P/bGa9Vb7nPw1XxBMV48fN7I/M7D9K+sZGPzv82pfN7P8ys8fN7GkzuzOcx5+Z2d+N5H8OALQQAjgAtJc3S3rYOXe7pDlJH5b0ryXd65x7h6Rfl/TPwq/9L865dzrn7pD0gqQPlH4jM/vnkkYk/W3nXFDlZ90l6X93zr11g5/990q+dtI5925Jf6LCyXb3SnqXpFO7/H0BIHYI4ADQXiadc38avv/vJf2gpO+V9CUz+7qk/0PS4fDz32tmf2Jm35D0P0u6reT7/IKkIefcSbfxkclPOucubvKz7y753Nnw8huSvuqcm3fOXZW0bGZD2/4tASDGks2eAACgrirD8rykC+Hqc6XPSHqfc+45M/tbko6XfO4pSe8ws73Ouetm9hcknQ4/94AKK9yLW/zs0o9Xwsug5P3ixzwWAegorIADQHu5ycyKYft+SU9IOlAcM7OUmRVXugckvWpmKRVWwEt9UdInJP2/ZjbgnPuqc+5t4dtZVVf5s79Sr18KANoJARwA2ssLkt5vZs9L2quw/lvSg2b2nKSvS/qL4df+gqSvSvqSpPHKb+Sc+0+SflXSWTPr2cHP/vTufhUAaE+2cWkfACBOzOxmSb/nnPveTvrZABA3rIADAAAAEWIFHAAAAIgQK+AAAABAhAjgAAAAQIQI4AAAAECECOAAAABAhAjgAAAAQIQI4AAAAECE/n92tJeurqqyegAAAABJRU5ErkJggg==\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": 42,
"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": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\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",
"\n",
"df[[\"peak-rpm\",\"highway-mpg\",\"price\"]].corr()\n",
"\n",
"```\n",
"\n",
"</details>\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": 43,
"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": 46,
"metadata": {},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 47,
"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": 49,
"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": 52,
"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": 53,
"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": 54,
"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": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.55663829e+00, 2.04754306e+02, -8.96543312e+03, 1.37923594e+05])"
]
},
"execution_count": 55,
"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": 56,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 11 10 9 8 7\n",
"-1.243e-08 x + 4.722e-06 x - 0.0008028 x + 0.08056 x - 5.297 x\n",
" 6 5 4 3 2\n",
" + 239.5 x - 7588 x + 1.684e+05 x - 2.565e+06 x + 2.551e+07 x - 1.491e+08 x + 3.879e+08\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"f1 = np.polyfit(x, y, 11)\n",
"p1 = np.poly1d(f1)\n",
"print(p1)\n",
"PlotPolly(p1,x,y, 'Highway MPG')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\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",
"\n",
"</details>\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": 57,
"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": 58,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 59,
"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": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 60,
"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": 62,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 62,
"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": 63,
"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": 64,
"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": 65,
"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": 65,
"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": 66,
"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": 66,
"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": 67,
"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": 67,
"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": 68,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.partial_fit(X, y)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.fit(X, y, **fit_params).transform(X)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/pipeline.py:331: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" Xt = transform.transform(Xt)\n"
]
},
{
"data": {
"text/plain": [
"array([13699.11161184, 13699.11161184, 19051.65470233, 10620.36193015,\n",
" 15521.31420211, 13869.66673213, 15456.16196732, 15974.00907672,\n",
" 17612.35917161, 10722.32509097])"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"Input=[('scale',StandardScaler()),('model',LinearRegression())]\n",
"\n",
"pipe=Pipeline(Input)\n",
"\n",
"pipe.fit(Z,y)\n",
"\n",
"ypipe=pipe.predict(Z)\n",
"ypipe[0:10]\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python\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",
"\n",
"</details>\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": 69,
"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": 70,
"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": 71,
"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": 72,
"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": 73,
"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": 74,
"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": 75,
"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": 76,
"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": 77,
"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": 78,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 78,
"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": 79,
"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": 80,
"metadata": {},
"outputs": [],
"source": [
"new_input=np.arange(1, 100, 1).reshape(-1, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Fit the model \n"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(X, Y)\n",
"lm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Produce a prediction\n"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([37601.57247984, 36779.83910151, 35958.10572319, 35136.37234487,\n",
" 34314.63896655])"
]
},
"execution_count": 82,
"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": 83,
"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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