Linear Regression as a Model

The same affine computation can predict a continuous quantity.

Suppose x is the number of hours a machine has run and y_hat is its predicted energy use:

y_hat = wx + b

Here the output is a prediction, not a class score. If w = 1.5 and b = 2, then for x = 4:

y_hat = 1.5 * 4 + 2 = 8

This is linear regression with one feature. The weight says that each additional hour changes the prediction by 1.5 units. The bias is the prediction at x = 0. Whether that intercept has a sensible real-world interpretation depends on whether zero hours is meaningful and represented by the data.

Several Features Use the Same Rule

For a feature vector x and weight vector w:

y_hat = x · w + b

Let:

x = [3, 2]
w = [4, -1]
b = 5

Then:

y_hat = 3 * 4 + 2 * (-1) + 5
      = 12 - 2 + 5
      = 15

The arithmetic is the affine map from the previous lesson. “Regression” names the task: predicting a numerical target. Training still needs a dataset and a loss; this page only defines the model's prediction.