Linear Regression From Scratch!
Building Your Machine Learning Foundation
Welcome to the first chapter of what I hope will become your go-to resource for understanding linear regression from the ground up and prepare you to level up in the ML and AI world.
Whether you're a computer science student, an aspiring data scientist, or simply curious about how predictions work in our data-driven world, this book will guide you through the concepts, mathematics, and practical applications of linear regression in a clear, engaging way.
In this book, we'll move beyond dealing with machine learning algorithms as magical black boxes.
Instead, we'll build a solid understanding of the basics that will become the foundation for all your future learning in AI and machine learning.
By starting with linear regression—perhaps the most fundamental predictive modeling technique—you'll develop the intuition and skills needed to tackle more complex models with confidence.
Let's begin our exploration of how simple mathematical relationships can help us make powerful predictions that drive real-world decision-making.
Chapter 1: Introduction to Linear Regression
🎯Learning Objectives
Understand what prediction means in the context of data
Recognize why linear regression is a fundamental skill in machine learning
Learn the historical context and basic concepts of linear regression
Explore real-world applications where linear regression provides value
Appreciate the benefits of learning linear regression from scratch
The Power of Prediction
Imagine this: you're thinking about opening a small ice cream shop.
Before you put your savings into it, you'd probably want to know how much money you might make.
Now, you've noticed something interesting… when it's hot outside, people buy more ice cream. Makes sense!
What if you could use tomorrow's weather forecast to predict how much ice cream you'll sell? That would be super helpful for planning, wouldn't it?
This is what prediction is all about.
We use the information we already have (like temperature) to make predictions about things we don't know yet (like how much ice cream we'll sell).
Pretty simple, huh?
Linear regression is one of the simplest yet most powerful ways to make these kinds of predictions. Think of it as drawing a straight line through a bunch of points on a graph.
Something like:
That line represents your best estimate of the relationship between two things – in our case, temperature and ice cream sales.
🤔 Before reading further, look at the graph above, then try to answer the following:
If the temperature tomorrow will be 24°C, roughly how much would you predict in ice cream sales? What about if it's 30°C?
The Need for Prediction
We're surrounded by data everywhere these days., aren't we?
Just think about it – a single online store might track thousands of customer clicks every hour.
Hospitals collect hundreds of measurements for each patient.
Weather stations are constantly monitoring what's happening in the atmosphere.
But here's the thing – having all this data doesn't automatically tell us what to do.
We need to turn all those numbers into insights we can actually use:
If you're running a store, you want to know what products to stock next month
If you're a doctor, you need to figure out how a patient might respond to a treatment
If you're a farmer, you're trying to decide the best time to plant your crops
and so on…
This is where prediction comes in – it's like building a bridge between having a pile of data and making smart decisions—and linear regression is one of the most straightforward ways to build that bridge.
🌎Real-World Connection
Your phone's weather app predicts a 70% chance of rain tomorrow. This prediction comes from models analyzing atmospheric data.
The app turns complex weather data into a simple prediction you can use to decide whether to bring an umbrella.
Historical Foundations
The idea of finding patterns in data isn't new – people have been doing it for ages!
But modern linear regression really got its start in the early 1800s when a mathematician named Adrien-Marie Legendre introduced something called the "method of least squares."
Don't worry about that name for now – it's basically just a fancy way of finding the line that best fits a set of points.
Later on, a statistician named Francis Galton was studying heights of parents and their children.
He noticed something interesting: really tall parents tended to have tall children, but usually not quite as tall as them, and very short parents typically had children who were short, but not as short as the parents.
He called this tendency "regression toward the mean" – and that's actually where we get the term "regression" from!
The core idea is pretty simple: we're trying to find a straight line that comes as close as possible to our data points. This line shows us a pattern or relationship that helps us make predictions.
I know I may sound like I'm repeating the same concept over and over, but this will help you build a strong understanding of the idea before we move on to the next level!
Real-World Applications
Trust me, once you start looking around you, you'll see linear regression practically everywhere!
Here are just a few places it shows up:
In Business and Economics:
Want to know if your marketing is working? Linear regression can help you figure out how your ad spending affects your sales.
Wondering how much a house is worth? Linear regression can help predict prices based on things like size, location, and number of bathrooms.
Curious about how interest rates might affect consumer spending? Yep, linear regression can help with that, too!
In Healthcare:
How long might it take a patient to recover? Linear regression can help estimate recovery time based on treatment methods and patient characteristics.
Wondering how diet affects health outcomes? Linear regression can help identify those relationships.
Trying to understand how diseases spread? Linear regression is often part of the toolkit.
In Environmental Science:
Concerned about pollution and health? Linear regression helps model those relationships.
Trying to predict your crop yield based on rainfall and temperature? Linear regression can help you find the answer!
Trying to predict energy consumption based on the weather? You guessed it – linear regression!
In Sports Analytics:
Want to predict an athlete's performance based on their training? Linear regression can help.
Curious about which game factors contribute most to winning? Linear regression can help sort that out.
Trying to figure out a player's value based on their stats? Linear regression is your friend.
In each case, we're not just finding out that two things are related – we're figuring out how they're related so we can use one to predict the other.
💡Application Spotlight
Netflix uses regression-based models to predict how many stars you might give a movie based on your previous ratings and the ratings of similar users. This helps them recommend movies you'll likely enjoy!
Why Learn Linear Regression from Scratch?
You might be thinking, "Wait a minute. There are tons of tools and libraries that can do linear regression for me with just a few lines of code.
Why should I bother learning how it works from scratch?"
That's a fair question! Here's why it's totally worth your time:
1. It's Like Building the Foundation of a House. Linear regression concepts form the foundation for lots of advanced machine-learning techniques.
When you understand how weights, cost functions, and optimization work in linear regression, you'll have a much easier time tackling complex models like neural networks later on.
It's like learning to walk before you run!
2. You'll Develop a "Feel" for How It Works:
When you build something from scratch, you develop an intuition for how it works. It's like the difference between following a cake recipe and understanding the principles of baking – when something goes wrong, you'll have a much better idea of how to fix it!
3. You Can Customize It to Fit Your Needs:
Once you understand the inner workings, you can modify algorithms to suit your specific problems – something that's hard to do if you're using pre-built tools as "black boxes." It's like knowing how to modify a recipe to suit your taste rather than just heating a frozen meal.
💡 For example, I built SimplerLLM, an open-source Python library that simplifies working with large language models (LLMs).
This is an alternative to using libraries like Langchain and Llamaindex.
Don't worry if you don't know anything about these - this is just an example of how understanding the basics lets you build customized and more straightforward solutions.
4. You'll Appreciate the Trade-offs:
Every approach in machine learning involves trade-offs. By implementing linear regression yourself, you'll experience these trade-offs firsthand and develop a better sense of when to use different approaches. It's like knowing when to use a hammer versus a screwdriver.
5. You Can Explain It to Others:
When you truly understand how a model works, you can explain it clearly to others – an essential skill whether you're working with a team or presenting findings to non-technical stakeholders.
6. Stand Out in the AI Era:
In today's world, where AI tools are becoming accessible to everyone, what distinguishes you as an ML engineer, programmer, or CS student is your depth of understanding and unique advanced skills.
While many can use AI libraries and tools, those who truly understand the core principles and mathematical foundations will be the ones designing, improving, and innovating the next generation of models.
Deep knowledge of fundamentals like linear regression gives you the expertise to go beyond just using AI – you'll be able to create it, optimize it, and apply it in novel ways that others can't.
Albert Einstein
"If you can't explain it simply, you don't understand it well enough."
A Simple Example: The Ice Cream Shop Again!
Let's go back to our ice cream shop example to see how linear regression works in practice.
Say you've been tracking daily temperatures and ice cream sales for the past month. Your data might look something like this:
If you plot these points on a graph, with temperature on the x-axis and sales on the y-axis, you'd probably notice a pattern: higher temperatures generally mean higher sales.
No big surprise there!
Linear regression helps us find the straight line that best represents this relationship.
This line would have an equation like:
Sales = a + b × Temperature
Where:
'a' is what we call the y-intercept (think of it as the sales you might expect on a hypothetical day with 0°C)
'b' is the slope (how much sales increase for each 1°C increase in temperature)
Finding the "best" values for 'a' and 'b' is what linear regression is all about.
Once we have these values, we can predict sales for any temperature. Pretty cool, right?
In Chapter 2, we'll dig into exactly how to find these values, what makes them "best," and how to implement and evaluate the entire process.
Don't worry if it seems a bit mysterious now – we'll break it down step by step!
ℹ️ You might be thinking this prediction with just two factors (temperature and sales) seems relatively simple - we can use a line equation to find any point!
But what happens when we have 3, 4, 5, or more factors affecting our prediction?
Things become quite different then! The basic idea remains the same, but we'll need to expand our approach beyond a simple 2D line! don’t rush; we will see all this later!
✏️ Summary and Key Takeaways
Let's wrap up what we've covered so far:
Prediction means using the information we have to make guesses about things we don't know yet. It's like checking today's weather forecast to decide what to wear tomorrow.
Linear regression is a method for finding patterns in data that can be used for prediction. It's like finding the straight line that best fits your scattered data points.
The technique has historical roots dating back to the 1800s and got its name from the statistical phenomenon of "regression toward the mean."
Linear regression shows up in tons of real-world applications across business, healthcare, science, sports, and more.
Learning linear regression from scratch gives you a solid foundation for more advanced machine-learning techniques and a deeper understanding of how prediction works.
At its core, linear regression finds the line of best fit through data points with an equation that can be used to make predictions.
Exercises and Practice Problems
Ready to try some of this out yourself?
Here are a few exercises to get you thinking:
Think About Your Life: What are three examples from your everyday life where prediction could be valuable? What information would you need to make these predictions? (For example, maybe you want to guess how long your drive to work will take based on what time you leave home)
Collect Some Data: Choose a simple relationship you're curious about – maybe study time vs. test scores or hours of sleep vs. how productive you feel the next day. Collect at least 10 data points and plot them on a graph. Do you see any patterns?
Thought Experiment: If you were trying to predict housing prices in your area, what factors do you think would be most important? How might they relate to the price? Would you expect the relationships to be linear?
Give these a shot, and don't worry if you're not sure about everything yet – we're just getting started!
Have Questions? Feedback? 👇
📌 Join the CS Learning Revolution (read this, please) 👇
Thank you for reading this first chapter!
I'm on a mission to reshape computer science education with a curriculum that truly prepares students for the future, especially with the rapid AI development. The current CS curriculum is almost outdated!
This book is part of that journey.
I'd love to hear your thoughts:
Was this chapter clear and easy to understand?
What concepts would you like explained in more detail?
How could I make these explanations even more beginner-friendly?
Your feedback is invaluable in creating learning resources that work for everyone, not just those with technical backgrounds.
Follow along with more chapters on my Substack, where I'm building this curriculum piece by piece.
Together, we can make technical education more accessible and relevant for tomorrow's challenges.
Ready For Part 2? Check it out here:
The Power of Weights: How Linear Models Make Predictions
Welcome to the second chapter of my new book, "Linear Regression From Scratch!", which I hope will become your go-to resource for understanding linear regression from the ground up and prepare you to level up in the ML and AI world.