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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": 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": 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",
"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",
"X=df[['engine-size']]\n",
"Y=df['price']\n",
"lm1.fit(X,Y)"
]
},
{
"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": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-7963.338906281042"
]
},
"execution_count": 17,
"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": 18,
"metadata": {},
"outputs": [],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"yhat=lm1.intercept_+(lm1.coef_*X)"
]
},
{
"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": 19,
"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": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 20,
"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": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-15806.62462632922"
]
},
"execution_count": 21,
"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": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([53.49574423, 4.70770099, 81.53026382, 36.05748882])"
]
},
"execution_count": 22,
"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": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute\n",
"X=df[['normalized-losses','highway-mpg']]\n",
"Y=df['price']\n",
"lm2=LinearRegression()\n",
"lm2.fit(X,Y)"
]
},
{
"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": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.49789586, -820.45434016])"
]
},
"execution_count": 25,
"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": 26,
"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": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 48253.83709371277)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"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": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 47414.1)"
]
},
"execution_count": 28,
"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": 30,
"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": 30,
"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": 31,
"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": 32,
"metadata": {},
"outputs": [],
"source": [
"Y_hat = lm.predict(Z)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"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": 34,
"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": 35,
"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": 36,
"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": 42,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"54\n"
]
},
{
"data": {
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9KFz2GPUHHJ/q5LRacK75Rr+S49vA9DOH2nwqxphWsxJJIrJyqBt+LvmV7/LZyuWd7s7e5po3xrQHy0gStHP4uQQkm9Wv389971Vx1bMrO01mYnPNG2Pag2UkCQp068vy4uM5U96im+7sVHf2wbnmp04qtWotY0ybWUbSDmpGXUwP2cXZvnc63Z29zTVvjElU0jMSEfGJyGIRedEt9xaR10RkpXvvFbLtNBFZJSKfiMjJIeHjRaTCrZvuptzFTcv7hAufLyKDkv19wjlg+ES29RrNVd1fZ/rkwXZRNsZklI4okVwNrAhZvg54XVWHAq+7ZURkBN5UuSOBU4C7RcTn4twDTMWbx32oWw9wGbBVVYcAdwC3JPerRKbjptC7vpIJTYtTlQRjjEmJpGYkIlIOfAv4W0jwGcBM93kmMDkkfJaq1qvqamAVMFFESoEiVZ2n3rzAD7WIE9zXU8CJwdJKR9t14En4u/WlcNkjqTi8McakTLJLJH8CfgkEQsL2U9UqAPfez4WXAetCtqt0YWXuc8vwZnFUtQnYDpS0TISITBWRhSKysLq6OsGvFIEvl7oR55O/7h2yt32enGMYY0waSlpGIiLfBjap6qJ4o4QJ0yjh0eI0D1C9T1UnqOqEkpJ98pl2s3P4ed5UvBUPJe0YxhiTbpJZIjkKOF1E1gCzgBNE5BFgo6uuwr1vcttXAgND4pcD6114eZjwZnFEJBvoCaRsON5AQQk7h3ybgk+fR3ZvTVUyjDGmQyUtI1HVaaparqqD8BrR31DVi4EXgClusynA8+7zC8D5rifWgXiN6gtc9VeNiExy7R+XtIgT3NfZ7hgpnbawbvQUsvy7KVzxZCqTYYwxHSYVz5HcDJwkIiuBk9wyqroMmA0sB14GrlDV4LC6l+M12K8CPgPmuPAZQImIrAJ+jusBlkpNvYexu+xICpc9Cv6GVCfHGGOSTlJ8A9/hxowZo3PmzIm9YQLy1r5Nycs/Zuvxt7Br6OlJPZYxxnSEsrKyRao6Idw6e7I9CeoHHk1j8WAKK2ZChmXUxpjMYxlJMkgWdaMvIXfzcnKr3k91aowxJqksI0mSnUNPx5/fi+5LH0h1UowxJqksI0mW7HzqRl5E/tq5ZG9dlerUGGNM0lhGkkQ7R15IwJdP4dIHU50UY4xJGstIkiiQ34tdB59Jt5UvkLVzU+wIxhjTCVlGkmS1o6dAoInCjx5NdVI6VEVVXaebetgY0zaWkSSZv+cB7D7wJAqXz0Ia2v+imo4X7IqqOq56dmWnm3rYGNM2lpF0gNoxPyCrYQfdPm7fYVPS9YK9uLKGRr8SUDrV1MPGmLaxjKQDNPYbQ33p4XSvmNmuw6ak6wV7XHkPcnxCltDpph42xrSeZSQdpHbsj/DVbaBg1Yvtts90vWCPLi1k+plDmTqplOlnDrWph43p4rJTnYBMsdA3jrEFQyhceB+7hp4BWb7YkWIIXrAXV9YwrrxHWl2wR5cWplV6jDHJYyWSDlBRVcdVz63idztOpXvdF2xc8lK77Xt0aSGXHN7fLtrGmJSxjKQDBNsyXvJPZI3uR//lM2wwR2NMl2EZSQcItmWo+JgR+A6lOz8h98t5ccdPxy6+xhgTlMw52/NFZIGIfCgiy0TkRhd+g4h8KSJL3Ou0kDjTRGSViHwiIieHhI8XkQq3brqbKRE3m+ITLny+iAxK1vdJRGjj8zHfuRR/t770WHJfXHHTtYuvMcYEJbNEUg+coKpjgLHAKSIyya27Q1XHutdLACIyAm9K3pHAKcDdIhJskb4HmIo3/e5Qtx7gMmCrqg4B7gBuSeL3SUiwLWNkeW9qD/0Beevnk7vhAyB6iSNdu/gaY0xQMudsV1WtdYs57hWtYeAMYJaq1qvqarxpdSeKSClQpKrz3HzsDwGTQ+LMdJ+fAk4MllbS2c7h53pDzC++N2aJI127+BpjTFBS20hExCciS4BNwGuqOt+tulJElorI30WklwsrA9aFRK90YWXuc8vwZnFUtQnYDpSEScdUEVkoIgurq6vb58slQHO6UTf6++Sve4f1ny6MWuKwZzKMMekuqRmJqvpVdSxQjle6GIVXTTUYr7qrCrjdbR6uJKFRwqPFaZmO+1R1gqpOKCnZJ59JibqRFxLILeK07U/ELHFYF19jTDrrkF5bqroNmAucoqobXQYTAO4HJrrNKoGBIdHKgfUuvDxMeLM4IpIN9AS2JOdbtC/N7U7dqIvZb8Ob3Di+ngkDe3D1MeWWWRhjOp1k9trqKyLF7nMB8A3gY9fmEXQm8JH7/AJwvuuJdSBeo/oCVa0CakRkkmv/uAR4PiTOFPf5bOAN147SKdSO+h5Nvm4ULb6XhetquPPtyi7TK8u6LBuTOZI5REopMNP1vMoCZqvqiyLysIiMxauCWgP8GEBVl4nIbGA50ARcoap+t6/LgQeBAmCOewHMAB4WkVV4JZHzk/h92p3mF7Ogz2RO2fA4g6nkM385iytrOn2pJNiBoNGv5Pg2WNuOMV1c0jISVV0KjAsT/r0ocW4CbgoTvhAYFSZ8N3BOYilNrd1jfsCuDc9wVfYz/EKv7hK9ssJ1WbaMxJiuy55sT7FDBpWxcegFfNs3nxnfyOoSF1zrsmxMZrGMJA10O/JHaE4B49c+mOqktAvrsmxMZrGMJA0E8ntRN/Ji8j9/mewtK1OdnHZhXZaNyRyWkaSJukO/j+YU0OODu1OdFGOMaRXLSNJEIL8XdaO+R8HnL5Nd/XGqk5Mw6/5rTOawjCSN1B56KYHcHvRY+OdUJyUhNmKxMZnFMpI0onk9qT30Ugq+eIOcTUv3hHe2u3sbsdiYzGIZSZqpG3UJ/vxe9Fg4Heicd/fW/deYzJLMJ9tNG2huIbVjf0TP924lt+p9FlcO7HQP9wW7/y6urGFceY+0T68xJjFWIklDdSMu8GZRfP9OxpV1t7t7Y0xasxJJOsrOp+awn1L87o1MaFrI9DMP71R39zbWljGZxUokaWrnId+lqWh/ihbcwej+BZ3q4T5rbDcms7QqIxGRXiJyaLISY0Jk5bDj8KvJ2fIpBateTHVqWsUa243JLDEzEhGZKyJFItIb+BB4QET+mPykmd0HnUJDyXCvB5e/ISnHSEbXYhtry5jMEk+JpKeq7gDOAh5Q1fF4k1SZZJMsar52Ldk1X1K4Yna77z6ZXYttrC1jMkc8GUm2m9XwXKBz1bF0AfVlR1I/YBLdP7gbaaht131bW4Yxpj3Ek5HcCLwCrFLV90XkICDmELUiki8iC0TkQxFZJiI3uvDeIvKaiKx0771C4kwTkVUi8omInBwSPl5EKty66W7KXdy0vE+48PkiMqiV3z/9ibDja7/At3sr3Zf8rV13bW0Zxpj2EDUjcdPkDlTVQ1X1pwCq+rmqfjeOfdcDJ6jqGGAscIqITAKuA15X1aHA624ZERmBN1XuSOAU4G53fIB7gKl487gPdesBLgO2quoQ4A7glri+dSfT2HckO4d8m+4VD5JVu6Hd9mttGcaY9hA1I3Fzpp/elh2rJ1gXk+NeCpwBzHThM4HJ7vMZwCxVrVfV1cAqYKKrVitS1XmqqsBDLeIE9/UUcGKwtNLV1Bx+DWiAIjd0SnuxtgxjTKLiqdr6t4jcJSJfF5HDgq94di4iPhFZAmwCXlPV+cB+qloF4N77uc3LgHUh0StdWJn73DK8WRxVbQK2AyVh0jFVRBaKyMLq6up4kp52/D3KvGHmP32uSwwzb4zpOuLJSI7Eq276LXC7e90Wz85V1a+qY4FyvNLFqCibhytJaJTwaHFapuM+VZ2gqhNKSvbJZzqNmnFT0bwiit77X9B9vqYxxqREzCFSVPX4RA+iqttEZC5e28ZGESlV1SpXbbXJbVYJDAyJVg6sd+HlYcJD41SKSDbQE9iSaHrTleb1pOawy+k572by1r1F/f7HpTpJxhgT35PtIvItEfmliPx38BVHnL4iUuw+F+A9e/Ix8AIwxW02BXjefX4BON/1xDoQr1F9gav+qhGRSa7945IWcYL7Oht4w7WjdFl1Iy6gqecgiubdCoHGVCfHGGPierL9XuA84Gd4VUnnAAfEse9S4E0RWQq8j9dG8iJwM3CSiKwETnLLqOoyYDawHHgZuMI19gNcDvwNrwH+M2COC58BlIjIKuDnuB5gXZovl+2TfknO9tUULp+V6tQYYwwS6wZeRJaq6qEh792BZ1T1mx2TxPY1ZswYnTNnTuwN05kqvV/6Ibmbl7HxvDlofq/YcYwxJgFlZWWLVHVCuHXxVG3tcu87RWQA0Agc2F6JM20gwo4jfoU01NBj0V9SnZqwOtv0wMaYtotnPpIXXVvH/wIf4PWKat9HrE2rNfUexs5DzqFw+Sx2Dj+Xpt7DUp2kPSqq6rjymU9p8kO2r4q7zhpmz6kY04XFLJGo6v+o6jZVfRqvbeQQVf2v5CfNxFJz+NVobnd6/vsPadUdeM6Kahr93h1Ho99bNsZ0XREzEhG5WES+FxqmqvXAuSJyYdJTZmIK5Pdix4Sfkbf+PfJXv5rq5IRo+XhPlxxswBjjRCuRXAs8FyZ8lltn0sDO4efR2Ptgit67BWnaFTtCBzh1eG9yfILgDQZ56vDeqU6SMSaJomUkPlXdZ1xxF5aTvCSZVsnKZvtRvyG7toruS+5PdWoAb/yuu84ayo+PKOWus2wwSGO6umiN7TkiUqiqzbrdiEgPIDe5yTKt0VB6ODsHf4vuH85g57DJ+Iv2T3WSGF1aaBmIMRkiWolkBvBU6Bwf7vMst86kkR2Tfolm5dDzX79Lq4Z3Y0zXFzEjUdXb8IYieUtEqkVkM/AW8KKq/m9HJdDEJ1DYj5oJPyN/3Tvkr3kt1ckxxmSQWPOR3KuqB+B1+z1QVQ9Q1Xs6JmmmtepGXkRj74Pp+e8/II32IKAxpmPENWijqtaGa3g3aSYrm21HX4+vbgM9Ft2d6tQYYzJEXBmJ6Twa+4+j7uDvUlgxk+zqT1KdHGNMBoj2QOI57t3G1epkdnztWgJ5RRS/898Q8MeOYIwxCYhWIpnm3p/uiISY9qP5vdhxxDRyNy2lmw01b4xJsmjPkVSLyJvAgSLyQsuVqnp68pJlErVryLcpWPk8Re/fwe5BJxLo3r9Dj19RVcfiyhrGlfew50mM6eKilUi+hVcq2czeudpDX1GJyEAReVNEVojIMhG52oXfICJfisgS9zotJM40EVklIp+IyMkh4eNFpMKtm+5mSsTNpviEC58f+sxLxhNh+9HXQ8BPz3//rkMPXVFVx1XPruS+96q46tmVNpS8MV1ctOdIGlT1PeBIVX0Lbwj5Rar6lluOpQm4VlWHA5OAK0RkhFt3h6qOda+XANy684GReHO73y0iPrf9PcBUvOl3h7r1AJcBW1V1CHAHcEvc3zwD+IsGUjv+CgrWvE7+56902HEXV9bQ6FcCCo1+ZXGldfgzpiuLp9fWfiKyGPgIWC4ii0RkVKxIqlqlqh+4zzXACqAsSpQzgFmqWq+qq/Gm1Z0oIqVAkarOc/OxPwRMDokz031+CjgxWFoxntpDp9DQZwQ9//U/yO6tHXLMceU9yPEJWeIN2jiuvEeHHNcYkxrxZCT3AT93DyPujzfy732tOYirchoHzHdBV4rIUhH5u4gE54ktA9aFRKt0YWXuc8vwZnFUtQnYDpSEOf5UEVkoIgurqzNsboysHLYdexNZu7fTc97NHXLI0aWFXH1MORMG9uDqY8qtjcSYLi6ejKRQVd8MLqjqXCDuK4Ob4/1p4BpV3YFXTTUYGAtUsbe9JVxJQqOER4vTPED1PlWdoKoTSkr2yWe6vKaSQ6gd9yO6rXyBvLXx1EompqKqjjvfrmThuhrufLvS2kiM6eLiyUg+F5H/EpFB7vX/gNXx7FxEcvAykUdV9RkAVd2oqn5VDQD3AxPd5pXAwJDo5cB6F14eJrxZHBHJBnoCW+JJW6apGfcTGnsNofidG5CG5LZZWBuJMZklnozkB0Bf4Bn36gNcGiuSa6uYAaxQ1T+GhJeGbHYmXtsLwAvA+a4n1oF4jeoLVLUKqBGRSW6fl+ANJhmMM8V9Pht4w7WjmJZ8uV4V185NFCW5isvaSIzJLNGeIwFAVbcCV7Vh30cB3wMqRGSJC/s1cIGIjMWrgloD/NgdZ5mIzAaW4/X4ukJVg49lXw48CBQAc9wLvIzqYRFZhVcSOb8N6ezUWvO8RmO/Q6kd8yN6LPkruwd9g/oDjk9KmkaXFjL9zKH2HIkxGUIy7QZ+zJgxOmfOnNgbdgLB5zUa/UqOT5h+ZhyzEfob6PvsOWTt2sKmc15A83tF394YY4CysrJFqjoh3DobtLETa1NbhC+XrcfdTNbubd4kWMYYkyDLSDqxtrZFNPUZTs34n9Lts5fI/+ylJKfSGNPVxcxIRGSYiLwuIh+55UNdzy2TYsG2iKmTSuOr1gpRO/ZHNPQ7lOJ3biSrdkMSU2mM6eriKZHcjzfmViOAqi4lAxu109Xo0kIuObx/6xu0s7LZevytEGii19xpoIHkJNAY0+XFk5F0U9UFLcKakpEY07H8PQ9gx5HTyFv/HoUVM2NHaIWKqjoeen+DPYxoTAaI2f0X2Cwig3FPjIvI2XhPpJsuYOfB3yVv7VyKFtxB/YBJNPUZnvA+m/cm29DqarfgPqz7sDGdQzwlkiuAvwKHiMiXwDV4z3WYrkCE7cf8D4H8Ynq9fi3SuDPhXSb6ZLsNQ29M5xIzI1HVz1X1G3hPtx+iqker6pqkp8x0mEB+L7YefyvZ29dQ9O+bEt5fok+2L66soaHJZURNNsSKMekunl5bvxeRYlWtU9UaEeklIvYAQhfTUDaJ2rFTKfzkGfJX/SOhfSXSmwygqCB7z8ibAbdsjElf8VRtnaqq24ILbsiU0yJvbjqrmglX0LDfWIrfuR7fjnWxI0TR5t5kwI5dTXuGdRa3bIxJX/FkJD4RyQsuiEgBkBdle9NZZeWw9YTbQHz0+ud/sKxyS0p6Xo0r70Futlc1lpttgz4ak+7iqTN4BHhdRB7A67n1A/bOSmi6GH+PMrYd93t6v3olX714Pfc1/qDNPa/aKtagj9ajy5j0Es/ov7eKSAVwIl5Nw/+oasdNAG463O5BJzK/33lcuOkJ3pNDeNF/JIsrazr0oj26tDDs8Sqq6rjymZU0+ZVs3wbuOqvjMjhjTHhxtWKqaujQ7SYDbD/8P1j04hL+kHM/K/2DGFc+LNVJAmDOii00+r2m+Ea/MmfFFstIjEmxiG0kIvKue68RkR0hrxoR2dFxSTSpMKqsJzUn/RHJyefJ4r9waNrMUNxy2oPMmgbBmHQUMSNR1aPdew9VLQp59VDVoo5LokmVYQcdxM6T/0Rh3RcUv/VrSIO5a04dXkKOz6tjzfF5y8aY1Iraa0tEsoKj/raWiAwUkTdFZIWILBORq114bxF5TURWuvdeIXGmicgqEflERE4OCR8vIhVu3XQ35S5uWt4nXPh8ERnUlrSayBrKJrFj4rUUrH6V7h/OSHVyGF1ayF1nDePHR5Ry11nDrFrLmDQQNSNR1QDwoYjs34Z9NwHXqupwYBJwhYiMAK4DXlfVocDrbhm37nxgJHAKcLeI+Ny+7gGm4s3jPtStB7gM2KqqQ4A7gFvakE4TQ92hl7LroFPo8f4d5FX+K9XJSegZFWNM+4vnOZJSYJmbk+SF4CtWJFWtUtUP3OcaYAVQBpzB3u7DM4HJ7vMZwCxVrVfV1cAqYKKIlAJFqjpPvXmBH2oRJ7ivp4ATg6UVk7g9I/hu2Mm2Y39HU/Fger1+Lb7tX6Q6acaYNBJPr60bEz2Iq3IaB8wH9lPVKvAyGxHp5zYrA94LiVbpwhrd55bhwTjr3L6aRGQ7UAJsbnH8qXglGsrKyjCxhRvBd+zJf6Hvs+fQ+5Ur2Dz5cTTXHhQ0xkTvtZUvItcA5wCHAP9S1beCr3gPICLdgaeBa1Q1Wm+vcCUJjRIeLU7zANX7VHWCqk4oKbHG2XiEG8HXXzSQLSfdSfb2L+j1xn9CwJ/qZBpj0kC0qq2ZwASgAjgVuL21OxeRHLxM5FFVfcYFb3TVVbj3TS68EhgYEr0cWO/Cy8OEN4sjItlAT2BLa9Np9hVpBN+GAV9j+1G/Jn/tWxQt+GOKU2mMSQfRqrZGqOpoABGZAbScJTEq11YxA1ihqqFXnBeAKcDN7v35kPDHROSPwAC8RvUFqup3z65MwqsauwT4c4t9zQPOBt5w7SgmTpGGG4k2TMnOEReQs2Ul3Zf+naaeB7Bz+Ln77Pe5jzYzd9U2jhtSzORRfTrkuxhjUiNaRtIY/ODaH1q776OA7wEVIrLEhf0aLwOZLSKXAWvxqs5Q1WUiMhtYjtfj6wpVDdadXA48CBTgPWEffMp+BvCwiKzCK4nYXPKtEGsmw0jDlABsP/LX+Goq6fnub/H3KKO+/Kg96577aDO3vuGNHrxgrTeXiGUmxnRd0TKSMSFPsAtQ4JYF0FgPJarqu4RvwwBv3K5wcW4C9plZSVUXAqPChO/GZUSm9cK1g8TdpTYrm60n/pE+L1xEr9euYfMZj9LU2xtGZe6qbc02nbtq2z4ZiQ28aEzXEe3Jdl+Lp9mz7cn2rmVceQ98WYIAvqzWD9euud3Zcso9aHY+vef8hKy6jQAcN6S42XYtl+OZSndP12ObZjfp7FybRMXzHInp0rTFe/wqqup4YEUW8yf8iayG7ZTM+THSUMPgkgJ87pfly4LBJQXN4sWaStfmbO84dq5Ne7CMJIMtrqzBH/CyEH+AVs2NHnoBuvRNHx8cdivZWz+j96s/Y+na6j3Dcqnuu99YU+mGq3LrDDrjnX1nPdcmvVhGksEidfGNR8sL0D8bRrLt2N+Rt34+F391GzlZGrHKLNZUuomkK5ZkXew76519Ms+1yRxxzUdiuqbRpYVcfUz5nm66rWn09i5AG1yPL+8CtKv0DLJ2baZ0/m1cnxXgN/4fRIybm908bst0RZshsa1i9VJLREIdF1IoWefaZBbLSDJYRVUdd75dSaNf+XB9LYNLCuK+kES6ANWNuYzlq7/kwk2Ps0W780f/eftcVOO5eEXretxWybzYh8tYO4tknGuTWSwjyWCJXlgjXYB2TPw5jz+/kSuzn6eGQsaV/zzuuMmUzIu93dmbTGYZSQZL1oX1sy27ua3xB3RnJ9OyH+Ptj/aD0qntsm+I/QxKW57WN8a0nWUkGSzRC2ukYVDmrtpGgCz+o/Gn5NHIN1ffwbYVxWGHUmmtWO0ciTytn8x0GdOVWa+tDNfWSaKCw6AsWFvDrW+s47mP9o7cH3wAsYlsrmy8ii+KJ9HznRso+OTZPdvE6j0VaX2sZ1BirU8W60ZrMpmVSEybzF68aZ/lYKkk+B4sreQcci/1r/yU4rd+AyIs6HFSm0sVsZ5BibU+WTpzY7sxibKMxCTF5FF9mlV3bT35Lnq9ciXFc3+Nf/9qGv2HRWzkj9YJIPgMSnCimpbPoMRanyzW/mIymVVtmTY5d1y/qMstaXYBW07+C/UDj+a0tbfxvex/RnwILtpDcuPKe5Dt88YHy44QNzfbi5ub3bElA5tL3mQqK5GYiKL1jhpcUkAWXvVRFvuOpxVWdj5bTvozvf95NTeu/TvH7J9H02GX7bPv2Hf3kccHs5KBMR3PMhITVqxeSI8u2kDAfQ645Zu/PTj2jrPz2HLSdHq9+StO/PweavaDmv4/gxbz3UTqXbW4soYmvxsfzE/YZ1/sATtjOlbSqrZE5O8isklEPgoJu0FEvhSRJe51Wsi6aSKySkQ+EZGTQ8LHi0iFWzfdzbyIiOSJyBMufL6IDErWd8lEsXohrd1aH3U5aq8sXy5bT7iNuoPPoscH91A07w+ggX23CyNVjenGmMiS2UbyIHBKmPA7VHWse70EICIj8GY3HOni3C0iPrf9PcBUvKl3h4bs8zJgq6oOAe4AbknWF8lEsQbz279XXsTluAYwzPKx/ZjfUTt6Ct0/epjiN34J/oaY6QptPO/IxnRjTGRJy0hU9W286W/jcQYwS1XrVXU1sAqYKCKlQJGqznNzsT8ETA6JM9N9fgo4MVhaMYkLtjVMnVQa9uG6i8b3J8ud7SzxloPifqZChB2TfsWOiT+n22f/oOTlHyMNtVHTFVoCUaxEYkw6SEWvrStFZKmr+urlwsqAdSHbVLqwMve5ZXizOKraBGwHSsIdUESmishCEVlYXV3dft+ki4vVC8mXhRsqvnl4q4YmF6F27I/YetwfyF2/kD7/dwlZdZsibh5rCHpjTMfr6IzkHmAwMBaoAm534eFKEholPFqcfQNV71PVCao6oaQkbF6Tsdo6P0doo3eTv/nkVbFKM+HsGjaZLafcjW/HF/R97jyyqz8Ou10qu/caY8Lr0HoBVd0Y/Cwi9wMvusVKYGDIpuXAehdeHiY8NE6liGQDPYm/Ks2Q2PhQoY3e4aqY2tJzqn7g19l8+qOUvPwT+rxwEVtP/CP1+x+7z36te68x6aVDSySuzSPoTCDYo+sF4HzXE+tAvEb1BapaBdSIyCTX/nEJ8HxInCnu89nAG64dxcQpkfGhQquYsmi/KqamkkP4avITNBUdQO9Xfkrh0gehxZ/VHvwzJr0ks/vv48A84GARqRSRy4BbXVfepcDxwH8AqOoyYDawHHgZuEJV/W5XlwN/w2uA/wyY48JnACUisgr4OXBdsr5LV5XINKuhVUw5YaqYEpnSNlC4H9WnP8zuA06g53u3UDx3GjTVx44Yh844r3qiMvE7m44lmXYTP2bMGJ0zZ07sDTNEtKfX2zrvR/MqM2n7kOoaoPsH91C06C4a+h7Klm9OJ1C4X+v3097p6kQy8Tub5CgrK1ukqhPCrbOxtkxY8TwLEqmKqT2Gcq+oquOhhZuYN+D7bDlpOtlbV9H36bPI/fK9hDoIZNpQ75n4nU3Hs074GSxaY3s80/BGKpEk+vT5vuk6knFnzqbXa1dR8o/LqPCfx31N3ybHl9WqO+xkD/UeqwSXCja8vekIlpFksGiZRawLUEVVHVc+s5Imv5Lt28BdZ+29oCc6lHvYdB0+mM2TZ7PtuV/wi22PM46P+WXTj1s1z3wye3yl6wyJ1svNdATLSDJYtMwi1gVozootNPq9ckejX5mzYkuzTCg3u+13wZHSpbmFrD36f5n93F+4zvcI/8idxtr8m4H+0XcYIlkDOsZTgksVG8TSJJtlJBksVmYR7QK0ZWdDxOVE74Kjxf9sy24eaPomC/zD+HPOdCbMu5y63VOpGf9TyMpp1XHak1UhmUxmGUmGa/vdasuBBeIbBj7RdM1dtQ2AZTqI7zTcxF+KH+W4xfeSV/kuW4+/FX/xgW0+ZiKsCslkMuu1ZdqoZbfxjulGftyQ4j2f6yhg+WE3suUbd+LbUUnfp8+i8KNH4h6SPpxEnrmwByVNprISiWmT3t1yoy4ny+CSAnxZ4A94g0UOLilgd+k3aeg/luK3/h89/30T+atfYdsxv8Pf84BW7TtdG8yNSXdWIjERRbs7P3V4b7LdOPLZWcKpw3t3SJoWV9YQcAUODewdLDLQrR9bTvkrW4/9PTnVn9D3qckULn0AAvH3GLNnLoxpG8tITFhe995P+eu8Kq585tOwmYmIIu69o0R9RkWEXQefydvHzuazwsPo+d6t9H32XHI2VezZJFrmmMiQMcZkMqvaMmHNWVFNoxvtrNHvLYdW8yyurMEfcHOnB8LPnZ4MsZ5Rqaiq46o522j0X8Fp2V/jtrpH6PPceewccQHvDfwhV/1jY8SqK2swN6ZtrERiIojeKytVd++x5iPZOzyL8FLj4dw97AHqRl5EtxWzOOL1MzlLXwcNRBy6JVaD+XMfbeaa51bx3Eebk/L9jOmMrERiwjp1eG9eXF5NU0DDtoGk6u491nFbVn3ld+/JjlG/Yech36Xp1ev5Q9PfuND3T25qupiigoH77D+a5z7azK1veBN5LljrZUKTR/VJ9CsZ0+lZRmIiitUGkqonpqMd99NNu8IuN5UcwkOD/0TVgqf5Zc4sZuX+jpUfvUF2+W9oKj4oruMGn2EJXbaMJLp0HH/MtD+r2jJhhWsD6RwiP98ybmARL2cdzTcabud2/3kcuPND+j75HXq+9Rt8teuJZWjfgqjLNu9Hc/GMIG26BiuRmLA665Afpw4v4R8rqmnyQ7bPWw4KrRYbVf6fbC7+Gd0X30fh8sfptvL/qBtxPgtLL+S9zflh76Dr6gMRl+0ZlH2l8/hjpn0lc4bEv4vIJhH5KCSst4i8JiIr3XuvkHXTRGSViHwiIieHhI93syquEpHpbspd3LS8T7jw+SIyKFnfJRMFL7pTJ5V2qovi6NJC7jprGD8+opS7zhoWdvywYGN6oKCEHUdOY9P5L7Nz6Ol0W/YYR7x6OgPe/z2/e2ZemDvoyKWd9piDpaux7tSZI5lVWw8Cp7QIuw54XVWHAq+7ZURkBHA+MNLFuVtEfC7OPcBUvHnch4bs8zJgq6oOAe4AbknaN8lQXXHIj3C9rvzdB7D92N9x0/4zeMZ/NBf43uD17GsonjuN7K2r9mw3rF+3ZvsKXU50DpauqLPejJjWS9qvXVXfDlNKOAM4zn2eCcwFfuXCZ6lqPbDazcM+UUTWAEWqOg9ARB4CJuPN234GcIPb11PAXSIimmlzB5tmolUxxep1tbKxLzOafsRdTZP5YfZLXFg7l7wnX2P3/sdSO+oSXl3RvOfaqx9X74mf6BwsXZUNYZ8ZOrqxfT9VrQJw7/1ceBmwLmS7ShdW5j63DG8WR1WbgO1ACWGIyFQRWSgiC6urq9vpq5h0FK2KKVyvq1C9u3n3VV/SlxubpvDbQQ+zY/yV5GyqoM9Ll3H71qu40Pc63dgNwPodjXvixnq+BTKzMT4Tv3MmSpfyd8un32DvzV248Ghx9g1UvQ+4D2DMmDFWYunColUxDe1bsKckElwOderwEv5vefWeASGPGXUQtaWjqR3zQwo+n0PBezP4PTOYlv0Yz/uPZNv+5+yJG+v5lkxsjM/E75ypOrpEslFESgHc+yYXXgmEPh1WDqx34eVhwpvFEZFsoCewJWkpN62SqjvRSM+RAKzbWt9sXctlgCzx7lCyQm9TsvPYNWwyfO8F/nrgnbzrm8h5Oe9w5ec/oc/TZ1H40cNk7d4aNV2hJaWGDGmMt0EwM0dHZyQvAFPc5ynA8yHh57ueWAfiNaovcNVfNSIyyfXWuqRFnOC+zgbesPaR9JDa5wci96z6qq6x2ZqWyzGfnRHhOyd9kzE/vJfN33uL7Uf+BkTo+e/f0+/hY8h5fiobFjzFdc9W7POdQ0tKSmY0xluvrcyRtF+ziDyO17DeR0QqgeuBm4HZInIZsBY4B0BVl4nIbGA50ARcoapuyEAux+sBVoDXyD7Hhc8AHnYN81vwen2ZNJDK5weiPUcysDiPFRt3NlsOFc+zM899tJm5q7Zx3JBiJo+6mLpRF5Nd/Qmr33mM4Rv/yQk5H7BT81j7ztcoOOx0du9/LJrbnffW7Gi2n/fW7OjyT8XbIJiZI5m9ti6IsOrECNvfBNwUJnwhMCpM+G5cRmTSSyofZgw+RxLu4rWtRU+qlsuxLnyRen01lRzMoiE/4/y1p3O4fMJ3fPM4q+4DCt94G83KoX7A15i0ZTifyygqtS8Am1uUhroq67WVGbp++dp0uFTfiUa6eMVqbI8WF2D24k37LId2/4UsFuhwFjYN58uR0/jh/hvIX/0a+Wvn8tPd7/LTPFgVGMA7gdH4en4daShHc+0iazo/y0hMUqTjnWhdvT/qciK87r8hpbCBPWnoP4CG/oex44hf8cDL8wh89gZfz6rgfN+bFKx9BZ15PY19R1JfejgNpRNo6DcWzS9u0/FtcESTSpaRmC4n8kU1+hwrsRx1UE/WLNrUbDlodGkhVx9Tvqf9pOXFfO6Wnqz0n8YM/2nk0cAZxav5r+EbyF3/Pt0rHkI+nAFAY/FgGvuNoaHfKBr7jqax9zDw5UbNKLzZLFfS5FeyfRu46yzrZmsZa8eyjMR0KdGeXSjMa95JseVyLNFKNBVVddzx1jqa/LD4yxoGlxQ0u4B9Vbu3PaaeXF7dPYJrDvf6h0jTLnI2VZC7cTG5Gz4gb+2bdPv0GQA0K4ea7gdSt60//sBAZi8cSN7JX2fYgQeCN+wcc1ZsodHv9Qlr9CtzVmzJ6ItnPBlr804TXbvTQ0ewjMR0KdF6jC2urG2xbe0+8aPfyUYu0cSamnhQ73yWrK9rthyk2QU0DJhIw4CJLkDx1XxJzlcV5FSv4KvPPuQoWcpZ2W976/95M4Gc7jQVD6Kp5yCO2dgTySpirfZjnfZja13zzg2ZdtGMlbHaBGXtzzIS06VE6zHWpzCn2bYtl2M9iT2sX/PG+ebL0avNLj+qjJ88+eme4RouP6qMiETwF5XjLypn9+BTWTXQS1d3/3aG+77k1+MaOMC/Dt+OL8jd8AGTa6s4K3fv8zJNVdnweH/83Uv5orEY34ZcRmsxn1T2ZOG2oUwaPohAfi8CecWQnRc5HZ1W5GeJwCYoSwbLSEyXEq3H2EXj9+Nfa7bvGQLlovH7NYsbfPpc2TtOV2j8aAMznjq8t3t+Rcn27Ts18WfVu5o9kPhZ9a64q5+af6cJFJcWsj1k/VVPfsSWDV+wv2yiXL5iXI/tnLpfA77aKnpsWcoU3xbyxXU3Xu5eTiC7AM3tQSCvB5pbRCCnEHWvQE43NDsfzSlAffmoLw+yc9GsHDQrB3zuXXyQ5UPFB5K156W4YQKQPdVwqHpnQEEIfg6EhAeQ4LIGAO+zaCDMtu69hUuL6glkb8AfAMnKYkpxOXlffLYnnRf23Ulg3WYayKGRbM4cUI6v5kvUl+t93+wCyGr7pTET22csIzFdTqQeY6NLC7n7u+GfMYHYQ8GPK+9Btm/DnswitLTjPb8Sucvzi8uq91luzV1wtF5wlbWwQQfwuQ4A4J/+HI44wXv06roXP+ftz7dRRB19ZAcnDPDz03F5ZO3eRlb9NrJ2b0MaashqqCGrfgdZ9duR2vVkNdYhjbuQpl1IoHM989IbmB76p1vYfP1kYHJoQWyJe4XQrBw0p5uXseZ29zLW3B4E8np6GW9+sVeqy++Fv6A3gYISAgV9+HBrDlc991nGjS9mGYnpcqLdEUa7IMc3FLy2eI9v330Ks6MuJ2JnQyDi8qRBRbz9+XZ20J0d2p2zDx7I7oNaWY0TaET8DYi/AZp2I4FGxN8IgSYvk1E/EvBDoAlQCPi90kazkkMIEYKlFK/UkhUS5n3WYMkG8UoSgtvWt7d0I8HOEi2rFVscW/2IKmjTnnRKoNF9L++74a9H/PVI024v83SZaFZjHdJQS1ZDLVm7qsnetpqsBi/DDaevZPO6r5gNWb2p0t70nD+IbkOH4O9RTlPR/vh7lIEvt3XnvxOwjMR0KYmMOLvPsyAtnsgPNxZXvPu+aHx/3l29g4B6A0JeNL5/a79aRIEWF+rQ5ccWbWy27rFFG1vfHuCqsjSnfe+sO3UVUKDJK8Ht3krWrmqydlXj27WZ6k1fsvTTz+nHFkZnrWH/zYvI2rS3RKcI/h4DaOp5IE3FB9JUPJim3kNp7DUEzStKKEmpPJ+WkZguJZFxvmI9kZ/o0C++LFC/996ehvTJZ8n6nc2Wg6pqGppt23I5VTr9sy9Z2QQKehMo6A29Bu8JzgcKhtfxtvsN5fYvIGvXZnw7viR7x1qyd6zFt/0LsrevptvHH5DVtPfv1lRYSmOf4TSVDKehzwga+40m0K1vXMlJ9ZD9lpGYLiXRi3206qlEhn5JpDQTy+VHlXP5U5/uKe1cftTemRdyfcKugDZbTgdd+dmXlr+hQLd+BLr1o7H/uOYbquKrqyJ7y6fkbFlJdvUn5FR/TP7aua5zgctc+h1KQ//DaOh/GI0lh4TtCJDKgVLBMhLTxSR7nK+2Dv2SzIEsR5cWcs/Z4TsR+APNq71aLqdO9C66GUEEf/cB+LsPoH7/4/YGN+4ku/oTcjd9SM5XFeRuXELB6lcACGR3o6F0PA2lE6kvm0RjyXDI8qV0oFSwjMR0Qek4zleqMrjueT627PQ3W04H0Yb7z3Sa043G/uOalWCyajeQu/ED8qoWkrt+AUXrbgfAn1dMffmRTCw/mntPm8D8r3JS0kYimTYX1JgxY3TOnDmxNzSmE4nU0Br6FDfAL08Y2K4P3yXy1HynbmxPsaydX5G3fj55694lr/Jf+HZtRhEa9xvD7v2PZ9eBJ+EvPrBdj1lWVrZIVSeEW5eSjERE1gA1gB9oUtUJItIbeAIYBKwBzlXVrW77acBlbvurVPUVFz6evZNevQRcHWuWRMtITFfTvKFV9mlojXWxb+sFPZ5MyjKLDqBKTvVy8r6YS/4Xb5K7eRkAjb2Gsuugk9k1+LR2yVSiZSSprNo6XlU3hyxfB7yuqjeLyHVu+VciMgJv9sORwADgnyIyzM2geA8wFXgPLyM5hb0zKBrTaul64YuWrlgNrZNH9YlYWkikt0+shyxT3ZOoq4n4GxChsc9IGvuMpHb8FWTVVlGw+jXyV79Kj0V/oWjRXTT0GcmuId9m15DTCHTr1+5pS6c2kjPwpuYFmAnMBX7lwmepaj2w2k2tO9GVaopUdR6AiDyE99CqZSSmTdL1whcrXYk0tCbS2yfW2GWp7knUlbTmtxnoXkrd6EuoG30JWXWbKPjsJQpWvUjP925BfTnsHHlRu6cvVRmJAq+KiAJ/VdX7gP1UtQpAVatEJJhtluGVOIIqXVij+9wyfB8iMhWv5EJZWZTB8kxGS9cLX6x0JdKQn0gmFGvsslT3JOpK2vrbDBT2o+7Q71N36PfxbVvtPfeSBKnKSI5S1fUus3hNRD6Osm24ju8aJXzfQC+jug+8NpLWJtZkhnS98MWTrrb2VEskE4o1dlmqp1zuStrjt9neje+hUpKRqOp6975JRJ4FJgIbRaTUlUZKgeBUdJXAwJDo5cB6F14eJtyYNknXC1+6PhsTT9x07IrdGaXrbzOowzMSESkEslS1xn3+JvBb4AVgCnCze3/eRXkBeExE/ojX2D4UWKCqfhGpEZFJwHzgEuDPHfttTFeTrhe+dE2X6Tjp/BtIRYlkP+BZ8UbwzAYeU9WXReR9YLaIXAasBc4BUNVlIjIbbxaFJuAK12ML4HL2dv+dgzW0G2NMh+vwjERVPwfGhAmvBk6MEOcm4KYw4QuBUe2dRmOMMfFr53FIjTHGZBrLSIwxxiTEMhJjjDEJsYzEGGNMQjJu9F8R+Qr4oo3R+wCbY27V8SxdrWPpar10TZulq3USSdcBqhp2ysaMy0gSISILI41+mUqWrtaxdLVeuqbN0tU6yUqXVW0ZY4xJiGUkxhhjEmIZSevcl+oERGDpah1LV+ula9osXa2TlHRZG4kxxpiEWInEGGNMQiwjMcYYkxDLSCIQkb+LyCYR+Sgk7AYR+VJElrjXaSlI10AReVNEVojIMhG52oX3FpHXRGSle++VJulK6TkTkXwRWSAiH7p03ejCU32+IqUr5b8xlw6fiCwWkRfdckrPV5R0pfx8icgaEalwx1/owlJ+viKkKynny9pIIhCRY4Ba4CFVHeXCbgBqVfW2FKarFChV1Q9EpAewCG+u+u8DW1T1ZhG5Duilqr9Kg3SdSwrPmXjzFRSqaq2I5ADvAlcDZ5Ha8xUpXaeQ4t+YS9/PgQlAkap+W0RuJYXnK0q6biD1/5NrgAmqujkkLOXnK0K6biAJ58tKJBGo6tvAllSnoyVVrVLVD9znGmAF3lz1ZwAz3WYz8S7i6ZCulFJPrVvMcS8l9ecrUrpSTkTKgW8BfwsJTun5gojpSlcpP18dyTKS1rtSRJa6qq+UFO+DRGQQMA5vhsj9VLUKvIs60C9N0gUpPmeuOmQJ3vTNr6lqWpyvCOmC1P/G/gT8EgiEhKX8fEVIF6T+fCnwqogsEpGpLiwdzle4dEESzpdlJK1zDzAYGAtUAbenKiEi0h14GrhGVXekKh0thUlXys+ZqvpVdSxQDkwUkbSYDC1CulJ6vkTk28AmVV3UkceNJUq6Uv77Ao5S1cOAU4ErXLV4OgiXrqScL8tIWkFVN7p//gBwPzAxFelwdepPA4+q6jMueKNrpwi2V2xKh3SlyzlzadkGzMVrh0j5+QqXrjQ4X0cBp7v69VnACSLyCKk/X2HTlQbnC1Vd7943Ac+6NKT6fIVNV7LOl2UkrRD8YThnAh9F2jaJaRBgBrBCVf8YsuoFYIr7PAV4Ph3SlepzJiJ9RaTYfS4AvgF8TOrPV9h0pfp8qeo0VS1X1UHA+cAbqnoxKT5fkdKV6vMlIoWucwkiUgh806Uh1b+vsOlK1vnq8DnbOwsReRw4DugjIpXA9cBxIjIWr+5xDfDjFCTtKOB7QIWrXwf4NXAzMFtELgPWAuekSbouSPE5KwVmiogP78Zptqq+KCLzSO35ipSuh9PgNxZOqn9fkdya4vO1H/Csdx9FNvCYqr4sIu+T2vMVKV1J+X1Z919jjDEJsaotY4wxCbGMxBhjTEIsIzHGGJMQy0iMMcYkxDISY4wxCbGMxBi8YV0kZKTnkPDfisg3YsS9QUR+kbzUGZPe7DkSY6JQ1f9OdRqMSXdWIjFmL5+I3C/e/CCvikiBiDwoImcDiMhpIvKxiLwrItPFzYnhjBCRuSLyuYhc5bb/ZcjnO0TkDff5RDfsCCJyj4gslOZzkpwoIs8GdywiJ4nIM7TgSkIzXVrXiMhZInKreHNQvOyGrAnOS3GLePOfLBCRIS58sIi8JyLvu5JXbctjGBMPy0iM2Wso8BdVHQlsA74bXCEi+cBfgVNV9Wigb4u4hwAn441ddL27iL8NfN2tnwB0d+FHA++48N+o6gTgUOBYETkUeAMYLiLBY1wKPBAhzYPxhlY/A3gEeFNVRwO7XHjQDlWdCNyFN4ouwJ3Anap6OLA++qkxJjLLSIzZa7WqLnGfFwGDQtYdAnyuqqvd8uMt4v5DVevdJEKb8IaoWASMd2Me1QPz8DKUr7M3IzlXRD4AFgMjgRHqDTfxMHCxG4/rCGBOhDTPUdVGoALwAS+78IoW6X885P0I9/kI4En3+bEI+zcmJmsjMWav+pDPfqAgZFlaGTdbVRvdaLWXAv8GlgLH45UiVojIgcAvgMNVdauIPAjku308APwfsBt4UlWbROQK4EdufXCK1HoAVQ2ISKPuHfMoQPP/b43w2ZiEWYnEmPh8DBwk3qRdAOfFGe9tvMzibbxSyE+AJe6CXwTUAdtFZD+8eSOAPUOArwf+H/CgC/uLqo51r9ZWRZ0X8j7PfX6PvdV357dyf8bsYSUSY+KgqrtE5KfAyyKyGVgQZ9R3gN8A81S1TkR2uzBU9UMRWQwsAz4H/tUi7qNAX1Vd3g5fIU9E5uPdPF7gwq4BHhGRa4F/ANvb4TgmA9nov8bESUS6q2qtm3vlL8BKVb0jice7C1isqjMS3M8aYIJrvwkN7wbsUlUVkfOBC1T1jESOZTKTlUiMid+PRGQKkIvXOP7XZB1IRBbhVXtdm6xjAOOBu1zGuA34QRKPZbowK5EYY4xJiDW2G2OMSYhlJMYYYxJiGYkxxpiEWEZijDEmIZaRGGOMScj/B41kdnX8dWerAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"PlotPolly(p, x, y, 'highway-mpg')"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.55663829e+00, 2.04754306e+02, -8.96543312e+03, 1.37923594e+05])"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.polyfit(x, y, 3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p>We can already see from plotting that this polynomial model performs better than the linear model. This is because the generated polynomial function \"hits\" more of the data points.</p>\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": 46,
"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": 47,
"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": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"PolynomialFeatures(degree=2, include_bias=True, interaction_only=False)"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pr=PolynomialFeatures(degree=2)\n",
"pr"
]
},
{
"cell_type": "code",
"execution_count": 49,
"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": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 4)"
]
},
"execution_count": 50,
"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": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(201, 15)"
]
},
"execution_count": 51,
"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": 52,
"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": 53,
"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": 54,
"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": 54,
"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": 55,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/preprocessing/data.py:625: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.partial_fit(X, y)\n",
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/sklearn/base.py:465: DataConversionWarning: Data with input dtype int64, float64 were all converted to float64 by StandardScaler.\n",
" return self.fit(X, y, **fit_params).transform(X)\n"
]
},
{
"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": 55,
"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": 56,
"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": 56,
"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": 59,
"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": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Write your code below and press Shift+Enter to execute \n",
"Input1=[('scale',StandardScaler()), ('model',LinearRegression())]\n",
"pipe1=Pipeline(Input1)\n",
"pipe1.fit(Z,y)\n",
"ypipe1=pipe1.predict(Z)\n",
"ypipe1[0:10]"
]
},
{
"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": 60,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The R-square is: 0.4966263556974878\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": 61,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The output of the first four predicted value is: [16231.78938339 16231.78938339 17052.24372355 13833.33798916]\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": 62,
"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": 63,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mean square error of price and predicted value is: 31632832.975589428\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": 64,
"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": 65,
"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": 66,
"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": 67,
"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": 68,
"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": 69,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"20474146.426361218"
]
},
"execution_count": 69,
"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": 70,
"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": 71,
"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": 74,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
" normalize=False)"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X = df[['highway-mpg']]\n",
"Y = df['price']\n",
"lm.fit(X, Y)\n",
"lm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Produce a prediction\n"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([37601.57247984, 36779.83910151, 35958.10572319, 35136.37234487,\n",
" 34314.63896655])"
]
},
"execution_count": 75,
"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": 76,
"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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