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theptrk/python-sklearn-linear-regression.ipynb

Created June 20, 2022 05:06
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python-sklearn-linear-regression.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/theptrk/c7f6529275eb6faacbe17206e9b20c21/python-sklearn-linear-regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d6635a14",
"metadata": {
"id": "d6635a14"
},
"outputs": [],
"source": [
"# Jovian Commit Essentials\n",
"# Please retain and execute this cell without modifying the contents for `jovian.commit` to work\n",
"!pip install jovian --upgrade -q\n",
"import jovian\n",
"jovian.set_project('python-sklearn-linear-regression')\n",
"jovian.set_colab_id('18O3H0wlRl4fEQ4vBB2LiYAWUlzhfL0Ra')"
]
},
{
"cell_type": "markdown",
"id": "0e28a1a1",
"metadata": {
"id": "0e28a1a1"
},
"source": [
"# Linear Regression with Scikit Learn - Machine Learning with Python\n",
"\n",
"This tutorial is a part of [Zero to Data Science Bootcamp by Jovian](https://zerotodatascience.com) and [Machine Learning with Python: Zero to GBMs](https://jovian.ai/learn/machine-learning-with-python-zero-to-gbms)\n",
"\n",
"![](https://i.imgur.com/1EzyZvj.png)\n"
]
},
{
"cell_type": "markdown",
"id": "262ff34b",
"metadata": {
"id": "262ff34b"
},
"source": [
"The following topics are covered in this tutorial:\n",
"\n",
"- A typical problem statement for machine learning\n",
"- Downloading and exploring a dataset for machine learning\n",
"- Linear regression with one variable using Scikit-learn\n",
"- Linear regression with multiple variables \n",
"- Using categorical features for machine learning\n",
"- Regression coefficients and feature importance\n",
"- Other models and techniques for regression using Scikit-learn\n",
"- Applying linear regression to other datasets"
]
},
{
"cell_type": "markdown",
"id": "b9cdc017",
"metadata": {
"id": "b9cdc017"
},
"source": [
"### How to run the code\n",
"\n",
"This tutorial is an executable [Jupyter notebook](https://jupyter.org) hosted on [Jovian](https://www.jovian.ai). You can _run_ this tutorial and experiment with the code examples in a couple of ways: *using free online resources* (recommended) or *on your computer*.\n",
"\n",
"#### Option 1: Running using free online resources (1-click, recommended)\n",
"\n",
"The easiest way to start executing the code is to click the **Run** button at the top of this page and select **Run on Binder**. You can also select \"Run on Colab\" or \"Run on Kaggle\", but you'll need to create an account on [Google Colab](https://colab.research.google.com) or [Kaggle](https://kaggle.com) to use these platforms.\n",
"\n",
"\n",
"#### Option 2: Running on your computer locally\n",
"\n",
"To run the code on your computer locally, you'll need to set up [Python](https://www.python.org), download the notebook and install the required libraries. We recommend using the [Conda](https://docs.conda.io/projects/conda/en/latest/user-guide/install/) distribution of Python. Click the **Run** button at the top of this page, select the **Run Locally** option, and follow the instructions.\n",
"\n",
"> **Jupyter Notebooks**: This tutorial is a [Jupyter notebook](https://jupyter.org) - a document made of _cells_. Each cell can contain code written in Python or explanations in plain English. You can execute code cells and view the results, e.g., numbers, messages, graphs, tables, files, etc., instantly within the notebook. Jupyter is a powerful platform for experimentation and analysis. Don't be afraid to mess around with the code & break things - you'll learn a lot by encountering and fixing errors. You can use the \"Kernel > Restart & Clear Output\" menu option to clear all outputs and start again from the top."
]
},
{
"cell_type": "markdown",
"id": "878f37c0",
"metadata": {
"id": "878f37c0"
},
"source": [
"## Problem Statement\n",
"\n",
"This tutorial takes a practical and coding-focused approach. We'll define the terms _machine learning_ and _linear regression_ in the context of a problem, and later generalize their definitions. We'll work through a typical machine learning problem step-by-step:\n",
"\n",
"\n",
"> **QUESTION**: ACME Insurance Inc. offers affordable health insurance to thousands of customer all over the United States. As the lead data scientist at ACME, **you're tasked with creating an automated system to estimate the annual medical expenditure for new customers**, using information such as their age, sex, BMI, children, smoking habits and region of residence. \n",
">\n",
"> Estimates from your system will be used to determine the annual insurance premium (amount paid every month) offered to the customer. Due to regulatory requirements, you must be able to explain why your system outputs a certain prediction.\n",
"> \n",
"> You're given a [CSV file](https://raw.githubusercontent.com/JovianML/opendatasets/master/data/medical-charges.csv) containing verified historical data, consisting of the aforementioned information and the actual medical charges incurred by over 1300 customers. \n",
"> <img src=\"https://i.imgur.com/87Uw0aG.png\" width=\"480\">\n",
">\n",
"> Dataset source: https://github.com/stedy/Machine-Learning-with-R-datasets\n",
"\n",
"\n",
"**EXERCISE**: Before proceeding further, take a moment to think about how can approach this problem. List five or more ideas that come to your mind below:\n",
" \n",
" 1. ???\n",
" 2. ???\n",
" 3. ???\n",
" 4. ???\n",
" 5. ???\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "05be9ff5",
"metadata": {
"id": "05be9ff5"
},
"source": [
"## Downloading the Data\n",
"\n",
"To begin, let's download the data using the `urlretrieve` function from `urllib.request`."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "c44ead68",
"metadata": {
"id": "c44ead68"
},
"outputs": [],
"source": [
"#restart the kernel after installation\n",
"!pip install pandas-profiling --quiet"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "2fb08156",
"metadata": {
"id": "2fb08156"
},
"outputs": [],
"source": [
"medical_charges_url = 'https://raw.githubusercontent.com/JovianML/opendatasets/master/data/medical-charges.csv'"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "178a1b4a",
"metadata": {
"id": "178a1b4a"
},
"outputs": [],
"source": [
"from urllib.request import urlretrieve"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "8df68352",
"metadata": {
"scrolled": true,
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "8df68352",
"outputId": "557626e7-976c-4694-bdd7-c7d96c7a5b3e"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"('medical.csv', <http.client.HTTPMessage at 0x7febf0857850>)"
]
},
"metadata": {},
"execution_count": 4
}
],
"source": [
"urlretrieve(medical_charges_url, 'medical.csv')"
]
},
{
"cell_type": "markdown",
"id": "549e8d02",
"metadata": {
"id": "549e8d02"
},
"source": [
"We can now create a Pandas dataframe using the downloaded file, to view and analyze the data."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "9f0716e7",
"metadata": {
"id": "9f0716e7"
},
"outputs": [],
"source": [
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "201518f6",
"metadata": {
"id": "201518f6"
},
"outputs": [],
"source": [
"medical_df = pd.read_csv('medical.csv')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "4cd12809",
"metadata": {
"scrolled": false,
"colab": {
"base_uri": "https://localhost:8080/",
"height": 206
},
"id": "4cd12809",
"outputId": "8765383d-e788-4605-94c2-ede6e80f4e45"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" age sex bmi children smoker region charges\n",
"0 19 female 27.900 0 yes southwest 16884.92400\n",
"1 18 male 33.770 1 no southeast 1725.55230\n",
"2 28 male 33.000 3 no southeast 4449.46200\n",
"3 33 male 22.705 0 no northwest 21984.47061\n",
"4 32 male 28.880 0 no northwest 3866.85520"
],
"text/html": [
"\n",
" <div id=\"df-e1929889-ae03-4b26-a9bb-b84ee87fa75a\">\n",
" <div class=\"colab-df-container\">\n",
" <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>age</th>\n",
" <th>sex</th>\n",
" <th>bmi</th>\n",
" <th>children</th>\n",
" <th>smoker</th>\n",
" <th>region</th>\n",
" <th>charges</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>19</td>\n",
" <td>female</td>\n",
" <td>27.900</td>\n",
" <td>0</td>\n",
" <td>yes</td>\n",
" <td>southwest</td>\n",
" <td>16884.92400</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>18</td>\n",
" <td>male</td>\n",
" <td>33.770</td>\n",
" <td>1</td>\n",
" <td>no</td>\n",
" <td>southeast</td>\n",
" <td>1725.55230</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>28</td>\n",
" <td>male</td>\n",
" <td>33.000</td>\n",
" <td>3</td>\n",
" <td>no</td>\n",
" <td>southeast</td>\n",
" <td>4449.46200</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>33</td>\n",
" <td>male</td>\n",
" <td>22.705</td>\n",
" <td>0</td>\n",
" <td>no</td>\n",
" <td>northwest</td>\n",
" <td>21984.47061</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>32</td>\n",
" <td>male</td>\n",
" <td>28.880</td>\n",
" <td>0</td>\n",
" <td>no</td>\n",
" <td>northwest</td>\n",
" <td>3866.85520</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-e1929889-ae03-4b26-a9bb-b84ee87fa75a')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
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" </svg>\n",
" </button>\n",
" \n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" flex-wrap:wrap;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
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" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-e1929889-ae03-4b26-a9bb-b84ee87fa75a button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-e1929889-ae03-4b26-a9bb-b84ee87fa75a');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
" </div>\n",
" "
]
},
"metadata": {},
"execution_count": 8
}
],
"source": [
"medical_df.head()"
]
},
{
"cell_type": "markdown",
"id": "b51fe0a5",
"metadata": {
"id": "b51fe0a5"
},
"source": [
"The dataset contains 1338 rows and 7 columns. Each row of the dataset contains information about one customer. \n",
"\n",
"Our objective is to find a way to estimate the value in the \"charges\" column using the values in the other columns. If we can do so for the historical data, then we should able to estimate charges for new customers too, simply by asking for information like their age, sex, BMI, no. of children, smoking habits and region.\n",
"\n",
"Let's check the data type for each column."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ec3846db",
"metadata": {
"id": "ec3846db",
"outputId": "922d311c-e531-4c91-92be-3fb4534513af"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'pandas.core.frame.DataFrame'>\n",
"RangeIndex: 1338 entries, 0 to 1337\n",
"Data columns (total 7 columns):\n",
" # Column Non-Null Count Dtype \n",
"--- ------ -------------- ----- \n",
" 0 age 1338 non-null int64 \n",
" 1 sex 1338 non-null object \n",
" 2 bmi 1338 non-null float64\n",
" 3 children 1338 non-null int64 \n",
" 4 smoker 1338 non-null object \n",
" 5 region 1338 non-null object \n",
" 6 charges 1338 non-null float64\n",
"dtypes: float64(2), int64(2), object(3)\n",
"memory usage: 73.3+ KB\n"
]
}
],
"source": [
"medical_df.info()"
]
},
{
"cell_type": "markdown",
"id": "f7daf1ef",
"metadata": {
"id": "f7daf1ef"
},
"source": [
"Looks like \"age\", \"children\", \"bmi\" ([body mass index](https://en.wikipedia.org/wiki/Body_mass_index)) and \"charges\" are numbers, whereas \"sex\", \"smoker\" and \"region\" are strings (possibly categories). None of the columns contain any missing values, which saves us a fair bit of work!\n",
"\n",
"Here are some statistics for the numerical columns:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "601dd869",
"metadata": {
"id": "601dd869",
"outputId": "32ee9272-542d-4fa5-9734-9eaea1831184"
},
"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>age</th>\n",
" <th>bmi</th>\n",
" <th>children</th>\n",
" <th>charges</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td>1338.000000</td>\n",
" <td>1338.000000</td>\n",
" <td>1338.000000</td>\n",
" <td>1338.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td>39.207025</td>\n",
" <td>30.663397</td>\n",
" <td>1.094918</td>\n",
" <td>13270.422265</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td>14.049960</td>\n",
" <td>6.098187</td>\n",
" <td>1.205493</td>\n",
" <td>12110.011237</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td>18.000000</td>\n",
" <td>15.960000</td>\n",
" <td>0.000000</td>\n",
" <td>1121.873900</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td>27.000000</td>\n",
" <td>26.296250</td>\n",
" <td>0.000000</td>\n",
" <td>4740.287150</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td>39.000000</td>\n",
" <td>30.400000</td>\n",
" <td>1.000000</td>\n",
" <td>9382.033000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td>51.000000</td>\n",
" <td>34.693750</td>\n",
" <td>2.000000</td>\n",
" <td>16639.912515</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td>64.000000</td>\n",
" <td>53.130000</td>\n",
" <td>5.000000</td>\n",
" <td>63770.428010</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" age bmi children charges\n",
"count 1338.000000 1338.000000 1338.000000 1338.000000\n",
"mean 39.207025 30.663397 1.094918 13270.422265\n",
"std 14.049960 6.098187 1.205493 12110.011237\n",
"min 18.000000 15.960000 0.000000 1121.873900\n",
"25% 27.000000 26.296250 0.000000 4740.287150\n",
"50% 39.000000 30.400000 1.000000 9382.033000\n",
"75% 51.000000 34.693750 2.000000 16639.912515\n",
"max 64.000000 53.130000 5.000000 63770.428010"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"medical_df.describe()"
]
},
{
"cell_type": "markdown",
"id": "7fddbb64",
"metadata": {
"id": "7fddbb64"
},
"source": [
"The ranges of values in the numerical columns seem reasonable too (no negative ages!), so we may not have to do much data cleaning or correction. The \"charges\" column seems to be significantly skewed however, as the median (50 percentile) is much lower than the maximum value.\n",
"\n",
"\n",
"> **EXERCISE**: What other inferences can you draw by looking at the table above? Add your inferences below:\n",
">\n",
"> 1. ???\n",
"> 2. ???\n",
"> 3. ???\n",
"> 4. ???\n",
"> 5. ???\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "2992f6a2",
"metadata": {
"id": "2992f6a2"
},
"source": [
"Let's save our work before continuing."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9b6f83e4",
"metadata": {
"id": "9b6f83e4"
},
"outputs": [],
"source": [
"!pip install jovian --quiet"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "cb29b7c9",
"metadata": {
"id": "cb29b7c9"
},
"outputs": [],
"source": [
"import jovian"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4040cd9d",
"metadata": {
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"name": "stderr",
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"text": [
"\u001b[31m[jovian] Error: The current API key is invalid or expired.\u001b[0m\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[jovian] Please enter your API key ( from https://jovian.ai/ ):\u001b[0m\n",
"API KEY: ········\n",
"[jovian] Updating notebook \"aakashns/python-sklearn-linear-regression\" on https://jovian.ai/\u001b[0m\n",
"[jovian] Committed successfully! https://jovian.ai/aakashns/python-sklearn-linear-regression\u001b[0m\n"
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"data": {
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"'https://jovian.ai/aakashns/python-sklearn-linear-regression'"
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"source": [
"jovian.commit()"
]
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{
"cell_type": "markdown",
"id": "2581f84b",
"metadata": {
"id": "2581f84b"
},
"source": [
"## Exploratory Analysis and Visualization\n",
"\n",
"Let's explore the data by visualizing the distribution of values in some columns of the dataset, and the relationships between \"charges\" and other columns.\n",
"\n",
"We'll use libraries Matplotlib, Seaborn and Plotly for visualization. Follow these tutorials to learn how to use these libraries: \n",
"\n",
"- https://jovian.ai/aakashns/python-matplotlib-data-visualization\n",
"- https://jovian.ai/aakashns/interactive-visualization-plotly\n",
"- https://jovian.ai/aakashns/dataviz-cheatsheet"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "f2e85bc8",
"metadata": {
"id": "f2e85bc8"
},
"outputs": [],
"source": [
"!pip install plotly matplotlib seaborn --quiet"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "66d82725",
"metadata": {
"id": "66d82725"
},
"outputs": [],
"source": [
"import plotly.express as px\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"id": "60caa58a",
"metadata": {
"id": "60caa58a"
},
"source": [
"The following settings will improve the default style and font sizes for our charts.\n",
"\n",
"> Indented block\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "8ffedac7",
"metadata": {
"id": "8ffedac7"
},
"outputs": [],
"source": [
"sns.set_style('darkgrid')\n",
"matplotlib.rcParams['font.size'] = 14\n",
"matplotlib.rcParams['figure.figsize'] = (10, 6)\n",
"matplotlib.rcParams['figure.facecolor'] = '#00000000'"
]
},
{
"cell_type": "markdown",
"id": "e17a8220",
"metadata": {
"id": "e17a8220"
},
"source": [
"### Age\n",
"\n",
"Age is a numeric column. The minimum age in the dataset is 18 and the maximum age is 64. Thus, we can visualize the distribution of age using a histogram with 47 bins (one for each year) and a box plot. We'll use plotly to make the chart interactive, but you can create similar charts using Seaborn."
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "1252a914",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "1252a914",
"outputId": "702ee6cd-e39b-41df-a7b5-cca2efb29773"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"count 1338.000000\n",
"mean 39.207025\n",
"std 14.049960\n",
"min 18.000000\n",
"25% 27.000000\n",
"50% 39.000000\n",
"75% 51.000000\n",
"max 64.000000\n",
"Name: age, dtype: float64"
]
},
"metadata": {},
"execution_count": 26
}
],
"source": [
"medical_df.age.describe()"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "fa559500",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 542
},
"id": "fa559500",
"outputId": "5b0e53ae-e764-481c-efa3-e04d9fd66667"
},
"outputs": [
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"source": [
"fig = px.histogram(medical_df, \n",
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"The distribution of ages in the dataset is almost uniform, with 20-30 customers at every age, except for the ages 18 and 19, which seem to have over twice as many customers as other ages. The uniform distribution might arise from the fact that there isn't a big variation in the [number of people of any given age](https://www.statista.com/statistics/241488/population-of-the-us-by-sex-and-age/) (between 18 & 64) in the USA.\n",
"\n",
"\n",
"\n",
"> **EXERCISE**: Can you explain why there are over twice as many customers with ages 18 and 19, compared to other ages?\n",
">\n",
"> ???\n"
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"### Body Mass Index\n",
"\n",
"Let's look at the distribution of BMI (Body Mass Index) of customers, using a histogram and box plot."
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],
"source": [
"fig = px.histogram(medical_df, \n",
" x='bmi', \n",
" marginal='box', \n",
" color_discrete_sequence=['red'], \n",
" title='Distribution of BMI (Body Mass Index)')\n",
"fig.update_layout(bargap=0.1)\n",
"fig.show()"
]
},
{
"cell_type": "markdown",
"id": "028fe64f",
"metadata": {
"id": "028fe64f"
},
"source": [
"The measurements of body mass index seem to form a [Gaussian distribution](https://en.wikipedia.org/wiki/Normal_distribution) centered around the value 30, with a few outliers towards the right. Here's how BMI values can be interpreted ([source](https://study.com/academy/lesson/what-is-bmi-definition-formula-calculation.html)):\n",
"\n",
"![](https://i.imgur.com/lh23OiY.jpg)\n",
"\n",
"> **EXERCISE**: Can you explain why the distribution of ages forms a uniform distribution while the distribution of BMIs forms a gaussian distribution?\n",
">\n",
"> ???"
]
},
{
"cell_type": "markdown",
"id": "a6a6b297",
"metadata": {
"id": "a6a6b297"
},
"source": [
"### Charges\n",
"\n",
"Let's visualize the distribution of \"charges\" i.e. the annual medical charges for customers. This is the column we're trying to predict. Let's also use the categorical column \"smoker\" to distinguish the charges for smokers and non-smokers."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "56afc784",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 542
},
"id": "56afc784",
"outputId": "d485e811-9611-441c-c682-3a9f3903963d"
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"outputs": [
{
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"source": [
"fig = px.histogram(medical_df, \n",
" x='charges', \n",
" marginal='box', \n",
" color='smoker', \n",
" color_discrete_sequence=['green', 'grey'], \n",
" title='Annual Medical Charges')\n",
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"source": [
"We can make the following observations from the above graph:\n",
"\n",
"* For most customers, the annual medical charges are under \\\\$10,000. Only a small fraction of customer have higher medical expenses, possibly due to accidents, major illnesses and genetic diseases. The distribution follows a \"power law\"\n",
"* There is a significant difference in medical expenses between smokers and non-smokers. While the median for non-smokers is \\\\$7300, the median for smokers is close to \\\\$35,000.\n",
"\n",
"\n",
"> **EXERCISE**: Visualize the distribution of medical charges in connection with other factors like \"sex\" and \"region\". What do you observe?"
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"cell_type": "code",
"execution_count": 15,
"id": "ca6c00ba",
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""
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"cell_type": "code",
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""
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"id": "810f3059"
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"source": [
"### Smoker\n",
"\n",
"Let's visualize the distribution of the \"smoker\" column (containing values \"yes\" and \"no\") using a histogram."
]
},
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"cell_type": "code",
"execution_count": 28,
"id": "b742e0d1",
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"output_type": "execute_result",
"data": {
"text/plain": [
"no 1064\n",
"yes 274\n",
"Name: smoker, dtype: int64"
]
},
"metadata": {},
"execution_count": 28
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"source": [
"medical_df.smoker.value_counts()"
]
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"id": "131851de",
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],
"source": [
"px.histogram(medical_df, x='smoker', color='sex', title='Smoker')"
]
},
{
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"id": "55bcfcbc",
"metadata": {
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"It appears that 20% of customers have reported that they smoke. Can you verify whether this matches the national average, assuming the data was collected in 2010? We can also see that smoking appears a more common habit among males. Can you verify this?\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "08e5c1ff",
"metadata": {
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"source": [
"> **EXERCISE**: Visualize the distributions of the \"sex\", \"region\" and \"children\" columns and report your observations. "
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "3a13c26d",
"metadata": {
"id": "3a13c26d"
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"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "807ab8d4",
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"id": "807ab8d4"
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"source": [
""
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},
{
"cell_type": "code",
"execution_count": 17,
"id": "5f7b0736",
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"id": "5f7b0736"
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"source": [
""
]
},
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"id": "f19bf6f1",
"metadata": {
"id": "f19bf6f1"
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"source": [
"Having looked at individual columns, we can now visualize the relationship between \"charges\" (the value we wish to predict) and other columns.\n",
"\n",
"### Age and Charges\n",
"\n",
"Let's visualize the relationship between \"age\" and \"charges\" using a scatter plot. Each point in the scatter plot represents one customer. We'll also use values in the \"smoker\" column to color the points."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "5d6d5d24",
"metadata": {
"colab": {
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"height": 542
},
"id": "5d6d5d24",
"outputId": "0fd0f0d3-3099-412c-a7c5-317b64911b73"
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"source": [
"fig = px.scatter(medical_df, \n",
" x='age', \n",
" y='charges', \n",
" color='smoker', \n",
" opacity=0.8, \n",
" hover_data=['sex'], \n",
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"We can make the following observations from the above chart:\n",
"\n",
"* The general trend seems to be that medical charges increase with age, as we might expect. However, there is significant variation at every age, and it's clear that age alone cannot be used to accurately determine medical charges.\n",
"\n",
"\n",
"* We can see three \"clusters\" of points, each of which seems to form a line with an increasing slope:\n",
"\n",
" 1. The first and the largest cluster consists primary of presumably \"healthy non-smokers\" who have relatively low medical charges compared to others\n",
" \n",
" 2. The second cluster contains a mix of smokers and non-smokers. It's possible that these are actually two distinct but overlapping clusters: \"non-smokers with medical issues\" and \"smokers without major medical issues\".\n",
" \n",
" 3. The final cluster consists exclusively of smokers, presumably smokers with major medical issues that are possibly related to or worsened by smoking.\n",
" \n",
"\n",
"> **EXERCISE**: What other inferences can you draw from the above chart?\n",
">\n",
"> ???"
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"### BMI and Charges\n",
"\n",
"Let's visualize the relationship between BMI (body mass index) and charges using another scatter plot. Once again, we'll use the values from the \"smoker\" column to color the points."
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"source": [
"fig = px.scatter(medical_df, \n",
" x='bmi', \n",
" y='charges', \n",
" color='smoker', \n",
" opacity=0.8, \n",
" hover_data=['sex'], \n",
" title='BMI vs. Charges')\n",
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"It appears that for non-smokers, an increase in BMI doesn't seem to be related to an increase in medical charges. However, medical charges seem to be significantly higher for smokers with a BMI greater than 30.\n",
"\n",
"What other insights can you gather from the above graph?"
]
},
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"> **EXERCISE**: Create some more graphs to visualize how the \"charges\" column is related to other columns (\"children\", \"sex\", \"region\" and \"smoker\"). Summarize the insights gathered from these graphs.\n",
">\n",
"> *Hint*: Use violin plots (`px.violin`) and bar plots (`sns.barplot`)\n"
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""
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""
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"source": [
"### Correlation\n",
"\n",
"As you can tell from the analysis, the values in some columns are more closely related to the values in \"charges\" compared to other columns. E.g. \"age\" and \"charges\" seem to grow together, whereas \"bmi\" and \"charges\" don't.\n",
"\n",
"This relationship is often expressed numerically using a measure called the _correlation coefficient_, which can be computed using the `.corr` method of a Pandas series."
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"source": [
"medical_df.charges.corr(medical_df.age)"
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"source": [
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"To compute the correlation for categorical columns, they must first be converted into numeric columns."
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"source": [
"smoker_values = {'no': 0, 'yes': 1}\n",
"smoker_numeric = medical_df.smoker.map(smoker_values)\n",
"medical_df.charges.corr(smoker_numeric)"
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"\n",
"\n",
"\n",
"Here's how correlation coefficients can be interpreted ([source](https://statisticsbyjim.com/basics/correlations)):\n",
"\n",
"* **Strength**: The greater the absolute value of the correlation coefficient, the stronger the relationship.\n",
"\n",
" * The extreme values of -1 and 1 indicate a perfectly linear relationship where a change in one variable is accompanied by a perfectly consistent change in the other. For these relationships, all of the data points fall on a line. In practice, you won’t see either type of perfect relationship.\n",
"\n",
" * A coefficient of zero represents no linear relationship. As one variable increases, there is no tendency in the other variable to either increase or decrease.\n",
" \n",
" * When the value is in-between 0 and +1/-1, there is a relationship, but the points don’t all fall on a line. As r approaches -1 or 1, the strength of the relationship increases and the data points tend to fall closer to a line.\n",
"\n",
"\n",
"* **Direction**: The sign of the correlation coefficient represents the direction of the relationship.\n",
"\n",
" * Positive coefficients indicate that when the value of one variable increases, the value of the other variable also tends to increase. Positive relationships produce an upward slope on a scatterplot.\n",
" \n",
" * Negative coefficients represent cases when the value of one variable increases, the value of the other variable tends to decrease. Negative relationships produce a downward slope.\n",
"\n",
"Here's the same relationship expressed visually ([source](https://www.cuemath.com/data/how-to-calculate-correlation-coefficient/)):\n",
"\n",
"<img src=\"https://i.imgur.com/3XUpDlw.png\" width=\"360\">\n",
"\n",
"The correlation coefficient has the following formula:\n",
"\n",
"<img src=\"https://i.imgur.com/unapugP.png\" width=\"360\">\n",
"\n",
"You can learn more about the mathematical definition and geometric interpretation of correlation here: https://www.youtube.com/watch?v=xZ_z8KWkhXE\n",
"\n",
"Pandas dataframes also provide a `.corr` method to compute the correlation coefficients between all pairs of numeric columns."
]
},
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"execution_count": 23,
"id": "53b625c7",
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"height": 175
},
"id": "53b625c7",
"outputId": "3a6312f4-4678-4f48-8345-52616746474f"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" age bmi children charges\n",
"age 1.000000 0.109272 0.042469 0.299008\n",
"bmi 0.109272 1.000000 0.012759 0.198341\n",
"children 0.042469 0.012759 1.000000 0.067998\n",
"charges 0.299008 0.198341 0.067998 1.000000"
],
"text/html": [
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" <th>children</th>\n",
" <th>charges</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>age</th>\n",
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" <td>0.042469</td>\n",
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" <tr>\n",
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" <td>1.000000</td>\n",
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" <td>0.198341</td>\n",
" </tr>\n",
" <tr>\n",
" <th>children</th>\n",
" <td>0.042469</td>\n",
" <td>0.012759</td>\n",
" <td>1.000000</td>\n",
" <td>0.067998</td>\n",
" </tr>\n",
" <tr>\n",
" <th>charges</th>\n",
" <td>0.299008</td>\n",
" <td>0.198341</td>\n",
" <td>0.067998</td>\n",
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" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-a2aed05d-7457-4c9a-9e17-62a318695c86');\n",
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]
},
"metadata": {},
"execution_count": 23
}
],
"source": [
"medical_df.corr()"
]
},
{
"cell_type": "markdown",
"id": "69108b01",
"metadata": {
"id": "69108b01"
},
"source": [
"The result of `.corr` is called a correlation matrix and is often visualized using a heatmap."
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "c94049f3",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 398
},
"id": "c94049f3",
"outputId": "3c51fbd4-1231-4f24-94c8-a86965dc08ad"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 720x432 with 2 Axes>"
],
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"sns.heatmap(medical_df.corr(), cmap='Reds', annot=True)\n",
"plt.title('Correlation Matrix');"
]
},
{
"cell_type": "markdown",
"id": "68de3f2a",
"metadata": {
"id": "68de3f2a"
},
"source": [
"**Correlation vs causation fallacy:** Note that a high correlation cannot be used to interpret a cause-effect relationship between features. Two features $X$ and $Y$ can be correlated if $X$ causes $Y$ or if $Y$ causes $X$, or if both are caused independently by some other factor $Z$, and the correlation will no longer hold true if one of the cause-effect relationships is broken. It's also possible that $X$ are $Y$ simply appear to be correlated because the sample is too small. \n",
"\n",
"While this may seem obvious, computers can't differentiate between correlation and causation, and decisions based on automated system can often have major consequences on society, so it's important to study why automated systems lead to a given result. Determining cause-effect relationships requires human insight."
]
},
{
"cell_type": "markdown",
"id": "324e1d52",
"metadata": {
"id": "324e1d52"
},
"source": [
"Let's save our work before continuing."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "72623ae5",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 169
},
"id": "72623ae5",
"outputId": "37c914c8-eea5-4064-db48-bbed55f35a94"
},
"outputs": [
{
"output_type": "error",
"ename": "NameError",
"evalue": "ignored",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-25-7f2017c1a3df>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mjovian\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcommit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mNameError\u001b[0m: name 'jovian' is not defined"
]
}
],
"source": [
"jovian.commit()"
]
},
{
"cell_type": "markdown",
"id": "eab02335",
"metadata": {
"id": "eab02335"
},
"source": [
"## Linear Regression using a Single Feature\n",
"\n",
"We now know that the \"smoker\" and \"age\" columns have the strongest correlation with \"charges\". Let's try to find a way of estimating the value of \"charges\" using the value of \"age\" for non-smokers. First, let's create a data frame containing just the data for non-smokers."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "fc5f95a2",
"metadata": {
"id": "fc5f95a2"
},
"outputs": [],
"source": [
"non_smoker_df = medical_df[medical_df.smoker == 'no']"
]
},
{
"cell_type": "markdown",
"id": "47dae464",
"metadata": {
"id": "47dae464"
},
"source": [
"Next, let's visualize the relationship between \"age\" and \"charges\""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b6e218f7",
"metadata": {
"id": "b6e218f7",
"outputId": "5c13ae86-9912-44a0-f2fb-0368e680d1fe"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.title('Age vs. Charges')\n",
"sns.scatterplot(data=non_smoker_df, x='age', y='charges', alpha=0.7, s=15);"
]
},
{
"cell_type": "markdown",
"id": "2baffd91",
"metadata": {
"id": "2baffd91"
},
"source": [
"Apart from a few exceptions, the points seem to form a line. We'll try and \"fit\" a line using this points, and use the line to predict charges for a given age. A line on the X&Y coordinates has the following formula:\n",
"\n",
"$y = wx + b$\n",
"\n",
"The line is characterized two numbers: $w$ (called \"slope\") and $b$ (called \"intercept\"). \n",
"\n",
"### Model\n",
"\n",
"In the above case, the x axis shows \"age\" and the y axis shows \"charges\". Thus, we're assume the following relationship between the two:\n",
"\n",
"$charges = w \\times age + b$\n",
"\n",
"We'll try determine $w$ and $b$ for the line that best fits the data. \n",
"\n",
"* This technique is called _linear regression_, and we call the above equation a _linear regression model_, because it models the relationship between \"age\" and \"charges\" as a straight line. \n",
"\n",
"* The numbers $w$ and $b$ are called the _parameters_ or _weights_ of the model.\n",
"\n",
"* The values in the \"age\" column of the dataset are called the _inputs_ to the model and the values in the charges column are called \"targets\". \n",
"\n",
"Let define a helper function `estimate_charges`, to compute $charges$, given $age$, $w$ and $b$.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5a718186",
"metadata": {
"id": "5a718186"
},
"outputs": [],
"source": [
"def estimate_charges(age, w, b):\n",
" return w * age + b"
]
},
{
"cell_type": "markdown",
"id": "f58fc89c",
"metadata": {
"id": "f58fc89c"
},
"source": [
"The `estimate_charges` function is our very first _model_.\n",
"\n",
"Let's _guess_ the values for $w$ and $b$ and use them to estimate the value for charges."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3f171033",
"metadata": {
"id": "3f171033"
},
"outputs": [],
"source": [
"w = 50\n",
"b = 100"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d98596e8",
"metadata": {
"id": "d98596e8"
},
"outputs": [],
"source": [
"ages = non_smoker_df.age\n",
"estimated_charges = estimate_charges(ages, w, b)"
]
},
{
"cell_type": "markdown",
"id": "33ca95fc",
"metadata": {
"id": "33ca95fc"
},
"source": [
"We can plot the estimated charges using a line graph."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2ca70529",
"metadata": {
"id": "2ca70529",
"outputId": "51930c59-0746-47fa-ba0d-2206b10f938d"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(ages, estimated_charges, 'r-o');\n",
"plt.xlabel('Age');\n",
"plt.ylabel('Estimated Charges');"
]
},
{
"cell_type": "markdown",
"id": "8ad1a4b5",
"metadata": {
"id": "8ad1a4b5"
},
"source": [
"As expected, the points lie on a straight line. \n",
"\n",
"We can overlay this line on the actual data, so see how well our _model_ fits the _data_."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6c410ea9",
"metadata": {
"id": "6c410ea9",
"outputId": "0dd655bb-ef3a-4aa2-a133-4b64e36c8363"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"target = non_smoker_df.charges\n",
"\n",
"plt.plot(ages, estimated_charges, 'r', alpha=0.9);\n",
"plt.scatter(ages, target, s=8,alpha=0.8);\n",
"plt.xlabel('Age');\n",
"plt.ylabel('Charges')\n",
"plt.legend(['Estimate', 'Actual']);"
]
},
{
"cell_type": "markdown",
"id": "6d44f8f9",
"metadata": {
"id": "6d44f8f9"
},
"source": [
"Clearly, the our estimates are quite poor and the line does not \"fit\" the data. However, we can try different values of $w$ and $b$ to move the line around. Let's define a helper function `try_parameters` which takes `w` and `b` as inputs and creates the above plot."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "49e0cdcf",
"metadata": {
"id": "49e0cdcf"
},
"outputs": [],
"source": [
"def try_parameters(w, b):\n",
" ages = non_smoker_df.age\n",
" target = non_smoker_df.charges\n",
" \n",
" estimated_charges = estimate_charges(ages, w, b)\n",
" \n",
" plt.plot(ages, estimated_charges, 'r', alpha=0.9);\n",
" plt.scatter(ages, target, s=8,alpha=0.8);\n",
" plt.xlabel('Age');\n",
" plt.ylabel('Charges')\n",
" plt.legend(['Estimate', 'Actual']);"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "65976fd3",
"metadata": {
"id": "65976fd3",
"outputId": "d688f257-25e0-4034-ced9-2b1ff100d20a"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"try_parameters(60, 200)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c3fb1453",
"metadata": {
"scrolled": false,
"id": "c3fb1453",
"outputId": "a66305fc-74dd-4e63-ce3a-ece98b7ad7eb"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"try_parameters(400, 5000)"
]
},
{
"cell_type": "markdown",
"id": "0ed3893a",
"metadata": {
"id": "0ed3893a"
},
"source": [
"> **EXERCISE**: Try various values of $w$ and $b$ to find a line that best fits the data. What is the effect of changing the value of $w$? What is the effect of changing $b$?"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6b46dcb9",
"metadata": {
"id": "6b46dcb9"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5a96801d",
"metadata": {
"id": "5a96801d"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "43d0490f",
"metadata": {
"id": "43d0490f"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "452c291c",
"metadata": {
"id": "452c291c"
},
"source": [
"As we change the values, of $w$ and $b$ manually, trying to move the line visually closer to the points, we are _learning_ the approximate relationship between \"age\" and \"charges\". \n",
"\n",
"Wouldn't it be nice if a computer could try several different values of `w` and `b` and _learn_ the relationship between \"age\" and \"charges\"? To do this, we need to solve a couple of problems:\n",
"\n",
"1. We need a way to measure numerically how well the line fits the points.\n",
"\n",
"2. Once the \"measure of fit\" has been computed, we need a way to modify `w` and `b` to improve the the fit.\n",
"\n",
"If we can solve the above problems, it should be possible for a computer to determine `w` and `b` for the best fit line, starting from a random guess."
]
},
{
"cell_type": "markdown",
"id": "c0a905ea",
"metadata": {
"id": "c0a905ea"
},
"source": [
"### Loss/Cost Function\n",
"\n",
"We can compare our model's predictions with the actual targets using the following method:\n",
"\n",
"* Calculate the difference between the targets and predictions (the differenced is called the \"residual\")\n",
"* Square all elements of the difference matrix to remove negative values.\n",
"* Calculate the average of the elements in the resulting matrix.\n",
"* Take the square root of the result\n",
"\n",
"The result is a single number, known as the **root mean squared error** (RMSE). The above description can be stated mathematically as follows: \n",
"\n",
"<img src=\"https://i.imgur.com/WCanPkA.png\" width=\"360\">\n",
"\n",
"Geometrically, the residuals can be visualized as follows:\n",
"\n",
"<img src=\"https://i.imgur.com/ll3NL80.png\" width=\"420\">\n",
"\n",
"Let's define a function to compute the RMSE."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b69db3e3",
"metadata": {
"id": "b69db3e3"
},
"outputs": [],
"source": [
"!pip install numpy --quiet"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "498d84d9",
"metadata": {
"id": "498d84d9"
},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e5cb0cab",
"metadata": {
"id": "e5cb0cab"
},
"outputs": [],
"source": [
"def rmse(targets, predictions):\n",
" return np.sqrt(np.mean(np.square(targets - predictions)))"
]
},
{
"cell_type": "markdown",
"id": "7e6d4cf1",
"metadata": {
"id": "7e6d4cf1"
},
"source": [
"Let's compute the RMSE for our model with a sample set of weights"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5e5941fb",
"metadata": {
"id": "5e5941fb"
},
"outputs": [],
"source": [
"w = 50\n",
"b = 100"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "edb05a32",
"metadata": {
"id": "edb05a32",
"outputId": "2b86a8f7-8e86-4c82-fb89-f462a08a1f31"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"try_parameters(w, b)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "642e7247",
"metadata": {
"id": "642e7247"
},
"outputs": [],
"source": [
"targets = non_smoker_df['charges']\n",
"predicted = estimate_charges(non_smoker_df.age, w, b)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4401f23c",
"metadata": {
"id": "4401f23c",
"outputId": "5ca5dfdf-c1fc-40e2-d318-c74d4fa9bd91"
},
"outputs": [
{
"data": {
"text/plain": [
"8461.949562575493"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rmse(targets, predicted)"
]
},
{
"cell_type": "markdown",
"id": "996b8371",
"metadata": {
"id": "996b8371"
},
"source": [
"Here's how we can interpret the above number: *On average, each element in the prediction differs from the actual target by \\\\$8461*. \n",
"\n",
"The result is called the *loss* because it indicates how bad the model is at predicting the target variables. It represents information loss in the model: the lower the loss, the better the model.\n",
"\n",
"Let's modify the `try_parameters` functions to also display the loss."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "15dbbaf1",
"metadata": {
"id": "15dbbaf1"
},
"outputs": [],
"source": [
"def try_parameters(w, b):\n",
" ages = non_smoker_df.age\n",
" target = non_smoker_df.charges\n",
" predictions = estimate_charges(ages, w, b)\n",
" \n",
" plt.plot(ages, predictions, 'r', alpha=0.9);\n",
" plt.scatter(ages, target, s=8,alpha=0.8);\n",
" plt.xlabel('Age');\n",
" plt.ylabel('Charges')\n",
" plt.legend(['Prediction', 'Actual']);\n",
" \n",
" loss = rmse(target, predictions)\n",
" print(\"RMSE Loss: \", loss)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bfadd017",
"metadata": {
"id": "bfadd017",
"outputId": "27fc444d-6a4e-4537-ab9c-528ad7b03da9"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RMSE Loss: 8461.949562575493\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"try_parameters(50, 100)"
]
},
{
"cell_type": "markdown",
"id": "3d1cf458",
"metadata": {
"id": "3d1cf458"
},
"source": [
"> **EXERCISE**: Try different values of $w$ and $b$ to minimize the RMSE loss. What's the lowest value of loss you are able to achieve? Can you come with a general strategy for finding better values of $w$ and $b$ by trial and error?"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "aaa548a2",
"metadata": {
"id": "aaa548a2"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a72060a8",
"metadata": {
"id": "a72060a8"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3639a5ac",
"metadata": {
"id": "3639a5ac"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "1c562b45",
"metadata": {
"id": "1c562b45"
},
"source": [
"### Optimizer\n",
"\n",
"Next, we need a strategy to modify weights `w` and `b` to reduce the loss and improve the \"fit\" of the line to the data.\n",
"\n",
"* Ordinary Least Squares: https://www.youtube.com/watch?v=szXbuO3bVRk (better for smaller datasets)\n",
"* Stochastic gradient descent: https://www.youtube.com/watch?v=sDv4f4s2SB8 (better for larger datasets)\n",
"\n",
"Both of these have the same objective: to minimize the loss, however, while ordinary least squares directly computes the best values for `w` and `b` using matrix operations, while gradient descent uses a iterative approach, starting with a random values of `w` and `b` and slowly improving them using derivatives. \n",
"\n",
"Here's a visualization of how gradient descent works:\n",
"\n",
"![](https://miro.medium.com/max/1728/1*NO-YvpHHadk5lLxtg4Gfrw.gif)\n",
"\n",
"Doesn't it look similar to our own strategy of gradually moving the line closer to the points?\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "b5060d75",
"metadata": {
"id": "b5060d75"
},
"source": [
"### Linear Regression using Scikit-learn\n",
"\n",
"In practice, you'll never need to implement either of the above methods yourself. You can use a library like `scikit-learn` to do this for you. "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5861457f",
"metadata": {
"id": "5861457f"
},
"outputs": [],
"source": [
"!pip install scikit-learn --quiet"
]
},
{
"cell_type": "markdown",
"id": "6c79c881",
"metadata": {
"id": "6c79c881"
},
"source": [
"Let's use the `LinearRegression` class from `scikit-learn` to find the best fit line for \"age\" vs. \"charges\" using the ordinary least squares optimization technique."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1bd6a91c",
"metadata": {
"id": "1bd6a91c"
},
"outputs": [],
"source": [
"from sklearn.linear_model import LinearRegression"
]
},
{
"cell_type": "markdown",
"id": "68cf1399",
"metadata": {
"id": "68cf1399"
},
"source": [
"First, we create a new model object."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8b690c0c",
"metadata": {
"id": "8b690c0c"
},
"outputs": [],
"source": [
"model = LinearRegression()"
]
},
{
"cell_type": "markdown",
"id": "1e56b468",
"metadata": {
"id": "1e56b468"
},
"source": [
"Next, we can use the `fit` method of the model to find the best fit line for the inputs and targets."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3a1a957f",
"metadata": {
"id": "3a1a957f",
"outputId": "aefb46a6-4b69-4f34-9715-d33c26c181ba"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Help on method fit in module sklearn.linear_model._base:\n",
"\n",
"fit(X, y, sample_weight=None) method of sklearn.linear_model._base.LinearRegression instance\n",
" Fit linear model.\n",
" \n",
" Parameters\n",
" ----------\n",
" X : {array-like, sparse matrix} of shape (n_samples, n_features)\n",
" Training data\n",
" \n",
" y : array-like of shape (n_samples,) or (n_samples, n_targets)\n",
" Target values. Will be cast to X's dtype if necessary\n",
" \n",
" sample_weight : array-like of shape (n_samples,), default=None\n",
" Individual weights for each sample\n",
" \n",
" .. versionadded:: 0.17\n",
" parameter *sample_weight* support to LinearRegression.\n",
" \n",
" Returns\n",
" -------\n",
" self : returns an instance of self.\n",
"\n"
]
}
],
"source": [
"help(model.fit)"
]
},
{
"cell_type": "markdown",
"id": "f5645a5c",
"metadata": {
"id": "f5645a5c"
},
"source": [
"Not that the input `X` must be a 2-d array, so we'll need to pass a dataframe, instead of a single column."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "21693b2f",
"metadata": {
"id": "21693b2f",
"outputId": "a82908c9-6735-47c9-b125-11adcdbed3b1"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"inputs.shape : (1064, 1)\n",
"targes.shape : (1064,)\n"
]
}
],
"source": [
"inputs = non_smoker_df[['age']]\n",
"targets = non_smoker_df.charges\n",
"print('inputs.shape :', inputs.shape)\n",
"print('targes.shape :', targets.shape)"
]
},
{
"cell_type": "markdown",
"id": "8280d6bb",
"metadata": {
"id": "8280d6bb"
},
"source": [
"Let's fit the model to the data."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c27cf40f",
"metadata": {
"id": "c27cf40f",
"outputId": "c2769846-6185-41bb-d05a-86986bbef96e"
},
"outputs": [
{
"data": {
"text/plain": [
"LinearRegression()"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.fit(inputs, targets)"
]
},
{
"cell_type": "markdown",
"id": "61367053",
"metadata": {
"id": "61367053"
},
"source": [
"We can now make predictions using the model. Let's try predicting the charges for the ages 23, 37 and 61"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5e342060",
"metadata": {
"id": "5e342060",
"outputId": "b528fd8c-5d31-4658-b3f1-3c8e4db88cef"
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 4055.30443855, 7796.78921819, 14210.76312614])"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.predict(np.array([[23], \n",
" [37], \n",
" [61]]))"
]
},
{
"cell_type": "markdown",
"id": "4f00e31a",
"metadata": {
"id": "4f00e31a"
},
"source": [
"Do these values seem reasonable? Compare them with the scatter plot above.\n",
"\n",
"Let compute the predictions for the entire set of inputs"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "705628f0",
"metadata": {
"id": "705628f0"
},
"outputs": [],
"source": [
"predictions = model.predict(inputs)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8eea9cf3",
"metadata": {
"id": "8eea9cf3",
"outputId": "19e3a56b-5f11-4a86-be54-c2c868256ffe"
},
"outputs": [
{
"data": {
"text/plain": [
"array([2719.0598744 , 5391.54900271, 6727.79356686, ..., 2719.0598744 ,\n",
" 2719.0598744 , 3520.80661289])"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"predictions"
]
},
{
"cell_type": "markdown",
"id": "0590d375",
"metadata": {
"id": "0590d375"
},
"source": [
"Let's compute the RMSE loss to evaluate the model."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "cf1677a9",
"metadata": {
"id": "cf1677a9",
"outputId": "9d9d29f3-3bb3-4abd-95ef-9cd4adacacf6"
},
"outputs": [
{
"data": {
"text/plain": [
"4662.505766636395"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rmse(targets, predictions)"
]
},
{
"cell_type": "markdown",
"id": "7d7459a7",
"metadata": {
"id": "7d7459a7"
},
"source": [
"Seems like our prediction is off by $4000 on average, which is not too bad considering the fact that there are several outliers."
]
},
{
"cell_type": "markdown",
"id": "04ef4656",
"metadata": {
"id": "04ef4656"
},
"source": [
"The parameters of the model are stored in the `coef_` and `intercept_` properties."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c47d0e9a",
"metadata": {
"id": "c47d0e9a",
"outputId": "abc93e01-8ce3-49b7-ce31-934c1122153e"
},
"outputs": [
{
"data": {
"text/plain": [
"array([267.24891283])"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# w\n",
"model.coef_"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "34149458",
"metadata": {
"id": "34149458",
"outputId": "7e4fc0fd-3446-446d-d9f6-8499a83d09f9"
},
"outputs": [
{
"data": {
"text/plain": [
"-2091.4205565650864"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# b\n",
"model.intercept_"
]
},
{
"cell_type": "markdown",
"id": "0df2ab81",
"metadata": {
"id": "0df2ab81"
},
"source": [
"Are these parameters close to your best guesses?\n",
"\n",
"Let's visualize the line created by the above parameters."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0fa0b08e",
"metadata": {
"id": "0fa0b08e",
"outputId": "7c8d5f49-037d-4675-ba0f-0572892dfc8a"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RMSE Loss: 4662.505766636395\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"try_parameters(model.coef_, model.intercept_)"
]
},
{
"cell_type": "markdown",
"id": "568d5ea8",
"metadata": {
"id": "568d5ea8"
},
"source": [
"Indeed the line is quite close to the points. It is slightly above the cluster of points, because it's also trying to account for the outliers. \n",
"\n",
"> **EXERCISE**: Use the [`SGDRegressor`](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.SGDRegressor.html) class from `scikit-learn` to train a model using the stochastic gradient descent technique. Make predictions and compute the loss. Do you see any difference in the result?"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ee442a00",
"metadata": {
"id": "ee442a00"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ad6e52f5",
"metadata": {
"id": "ad6e52f5"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3f968e54",
"metadata": {
"id": "3f968e54"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "eaf4b75b",
"metadata": {
"id": "eaf4b75b"
},
"source": [
"> **EXERCISE**: Repeat the steps is this section to train a linear regression model to estimate medical charges for smokers. Visualize the targets and predictions, and compute the loss."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "56e996b8",
"metadata": {
"id": "56e996b8"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "382309ce",
"metadata": {
"id": "382309ce"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a384c438",
"metadata": {
"id": "a384c438"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "47a9b57a",
"metadata": {
"id": "47a9b57a"
},
"source": [
"### Machine Learning\n",
"\n",
"Congratulations, you've just trained your first _machine learning model!_ Machine learning is simply the process of computing the best parameters to model the relationship between some feature and targets. \n",
"\n",
"Every machine learning problem has three components:\n",
"\n",
"1. **Model**\n",
"\n",
"2. **Cost Function**\n",
"\n",
"3. **Optimizer**\n",
"\n",
"We'll look at several examples of each of the above in future tutorials. Here's how the relationship between these three components can be visualized:\n",
"\n",
"<img src=\"https://www.deepnetts.com/blog/wp-content/uploads/2019/02/SupervisedLearning.png\" width=\"480\">"
]
},
{
"cell_type": "markdown",
"id": "415dfbfc",
"metadata": {
"id": "415dfbfc"
},
"source": [
"As we've seen above, it takes just a few lines of code to train a machine learning model using `scikit-learn`."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "27237ffd",
"metadata": {
"id": "27237ffd",
"outputId": "1ac52273-5f6e-461d-e012-428fbed23808"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Loss: 4662.505766636395\n"
]
}
],
"source": [
"# Create inputs and targets\n",
"inputs, targets = non_smoker_df[['age']], non_smoker_df['charges']\n",
"\n",
"# Create and train the model\n",
"model = LinearRegression().fit(inputs, targets)\n",
"\n",
"# Generate predictions\n",
"predictions = model.predict(inputs)\n",
"\n",
"# Compute loss to evalute the model\n",
"loss = rmse(targets, predictions)\n",
"print('Loss:', loss)"
]
},
{
"cell_type": "markdown",
"id": "f05db110",
"metadata": {
"id": "f05db110"
},
"source": [
"Let's save our work before continuing."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a0b6aaaa",
"metadata": {
"scrolled": true,
"id": "a0b6aaaa",
"outputId": "efe5b41c-8852-4704-afda-db8e7879ff66"
},
"outputs": [
{
"data": {
"application/javascript": [
"window.require && require([\"base/js/namespace\"],function(Jupyter){Jupyter.notebook.save_checkpoint()})"
],
"text/plain": [
"<IPython.core.display.Javascript object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[jovian] Updating notebook \"aakashns/python-sklearn-linear-regression\" on https://jovian.ai/\u001b[0m\n",
"[jovian] Committed successfully! https://jovian.ai/aakashns/python-sklearn-linear-regression\u001b[0m\n"
]
},
{
"data": {
"text/plain": [
"'https://jovian.ai/aakashns/python-sklearn-linear-regression'"
]
},
"execution_count": 63,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"jovian.commit()"
]
},
{
"cell_type": "markdown",
"id": "ac1f56e3",
"metadata": {
"id": "ac1f56e3"
},
"source": [
"## Linear Regression using Multiple Features\n",
"\n",
"So far, we've used on the \"age\" feature to estimate \"charges\". Adding another feature like \"bmi\" is fairly straightforward. We simply assume the following relationship:\n",
"\n",
"$charges = w_1 \\times age + w_2 \\times bmi + b$\n",
"\n",
"We need to change just one line of code to include the BMI."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d102c01a",
"metadata": {
"id": "d102c01a",
"outputId": "27d61a54-1346-4a55-eca1-d7540e20b4c0"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Loss: 4662.3128354612945\n"
]
}
],
"source": [
"# Create inputs and targets\n",
"inputs, targets = non_smoker_df[['age', 'bmi']], non_smoker_df['charges']\n",
"\n",
"# Create and train the model\n",
"model = LinearRegression().fit(inputs, targets)\n",
"\n",
"# Generate predictions\n",
"predictions = model.predict(inputs)\n",
"\n",
"# Compute loss to evalute the model\n",
"loss = rmse(targets, predictions)\n",
"print('Loss:', loss)"
]
},
{
"cell_type": "markdown",
"id": "43dde0b3",
"metadata": {
"id": "43dde0b3"
},
"source": [
"As you can see, adding the BMI doesn't seem to reduce the loss by much, as the BMI has a very weak correlation with charges, especially for non smokers."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bed633ab",
"metadata": {
"id": "bed633ab",
"outputId": "6131bace-f993-44b9-c08b-eb80ec84dbdc"
},
"outputs": [
{
"data": {
"text/plain": [
"0.08403654312833268"
]
},
"execution_count": 65,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"non_smoker_df.charges.corr(non_smoker_df.bmi)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "314b2440",
"metadata": {
"id": "314b2440",
"outputId": "0be7796b-93fa-4380-95a5-3f0f0f45b1b8"
},
"outputs": [
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = px.scatter_3d(non_smoker_df, x='age', y='bmi', z='charges')\n",
"fig.update_traces(marker_size=3, marker_opacity=0.5)\n",
"fig.show()"
]
},
{
"cell_type": "markdown",
"id": "56b6b254",
"metadata": {
"id": "56b6b254"
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"source": [
"You can see that it's harder to interpret a 3D scatter plot compared to a 2D scatter plot. As we add more features, it becomes impossible to visualize all feature at once, which is why we use measures like correlation and loss. \n",
"\n",
"Let's also check the parameters of the model."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5c9bfa29",
"metadata": {
"id": "5c9bfa29",
"outputId": "03ac4bc0-8ddf-47b5-be2a-4bd99bb4b010"
},
"outputs": [
{
"data": {
"text/plain": [
"(array([266.87657817, 7.07547666]), -2293.6320906488727)"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.coef_, model.intercept_"
]
},
{
"cell_type": "markdown",
"id": "284763df",
"metadata": {
"id": "284763df"
},
"source": [
"Clearly, BMI has a much lower weightage, and you can see why. It has a tiny contribution, and even that is probably accidental. This is an important thing to keep in mind: you can't find a relationship that doesn't exist, no matter what machine learning technique or optimization algorithm you apply. "
]
},
{
"cell_type": "markdown",
"id": "90530eaf",
"metadata": {
"id": "90530eaf"
},
"source": [
"> **EXERCISE**: Train a linear regression model to estimate charges using BMI alone. Do you expect it to be better or worse than the previously trained models?"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f1b74343",
"metadata": {
"id": "f1b74343"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7a926898",
"metadata": {
"id": "7a926898"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f5085011",
"metadata": {
"id": "f5085011"
},
"outputs": [],
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "fd7cc138",
"metadata": {
"id": "fd7cc138"
},
"source": [
"Let's go one step further, and add the final numeric column: \"children\", which seems to have some correlation with \"charges\".\n",
"\n",
"$charges = w_1 \\times age + w_2 \\times bmi + w_3 \\times children + b$"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c6cd797b",
"metadata": {
"id": "c6cd797b",
"outputId": "854ff296-45b0-4e45-92b7-ee991630306c"
},
"outputs": [
{
"data": {
"text/plain": [
"0.13892870453542194"
]
},
"execution_count": 69,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"non_smoker_df.charges.corr(non_smoker_df.children)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d6396301",
"metadata": {
"id": "d6396301",
"outputId": "ca4a266a-c95b-4573-f2fb-99da38f26814"
},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"alignmentgroup": "True",
"boxpoints": "all",
"fillcolor": "rgba(255,255,255,0)",
"hoveron": "points",
"hovertemplate": "children=%{x}<br>charges=%{y}<extra></extra>",
"legendgroup": "",
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