02.01 · UNIT 01 · Regression and tensor mechanics · Lab

Linear regression: the first complete model

Linear regression learns a straight-line rule for predicting numbers.

PLAIN-LANGUAGE INTRODUCTION

What is this?

Linear regression learns a straight-line rule for predicting numbers.

One simple example

The hidden rule is y=3x−2. When x=4, the target is 10.

One number per example. Here, one input is x=4.

One predicted number. A trained model should return near 10.

This model shows every training step with simple arithmetic.

One straight line cannot represent every curved relationship.

WORK THROUGH THE IDEA

The model uses ŷ = wx+b. The symbol ŷ means predicted output.
Start with w=1 and b=0. For x=4, the prediction is 4.
The target is 10. The squared error is (4−10)² = 36.
Training changes w and b. Good values approach 3 and −2 for this generated data.
Common mistake: low training error alone does not prove good predictions on held-out inputs.