Beginner's Guide to Linear Regression in Python – Simple, Step‑by‑Step

Overview Linear regression is a staple of predictive analytics. In this guide we’ll build a simple linear model from scratch using only NumPy for vectorised math and tqdm for a progress bar. By the end you’ll understand the math behind gradient descent, see how the code maps to the theory, and be able to extend the approach to more complex scenarios. 1️⃣ Introduction Suppose you have five measurements of how far a ball travels ( y ) when it’s kicked from various distances ( x ). You want a model that can predict the expected distance for any new kick. The simplest assumption is a linear relationship: y \;\approx\; m\,x + b where m is the slope and b the intercept. To find the best m and b we minimise the Mean Squared Error (MSE) between predictions and observed values, using gradient descent as the optimisation routine. 2️⃣ What the Code Does (High‑Level View) Step What happens Why it matters 1 Load the data into NumPy arrays. Enables fast, vectorised calculations. 2 Initialise the mod