Python Linear Regression Exercises: Fit, Predict, Evaluate

Exercise: turn a line into a prediction

Write the prediction rule first. The slope controls change per input unit, and the intercept sets the starting height. Test one value before fitting anything.

def predict(x, slope, intercept):
    return slope * x + intercept

print(predict(4, 1.5, 2.0))

A rule you can test

Exercise: fit with centered sums

Center x and y around their means, multiply the paired deviations, and divide by the squared deviations of x. This is the least-squares slope for one input.

xs = [1, 2, 3]
ys = [3, 5, 7]
mean_x = sum(xs) / len(xs)
mean_y = sum(ys) / len(ys)
slope = sum((x - mean_x) * (y - mean_y) for x, y in zip(xs, ys)) / sum((x - mean_x) ** 2 for x in xs)
intercept = mean_y - slope * mean_x
print(slope, intercept)

Fitted by hand

Exercise: compare error with a baseline

A model should beat a simple baseline. Predict the training mean for every input, compute its MSE, then compare the fitted line's MSE. If the line is not better, the extra complexity is not earning its place.

xs = [1, 2, 3]
ys = [2, 4, 5]
mean_y = sum(ys) / len(ys)
baseline_mse = sum((y - mean_y) ** 2 for y in ys) / len(ys)
slope = 1.5
intercept = 2 / 3
model_mse = sum((y - (slope * x + intercept)) ** 2 for x, y in zip(xs, ys)) / len(xs)
print(round(baseline_mse, 2), round(model_mse, 2))

Beat the mean

Exercise: keep prediction inside the evidence

A guard is part of the model's interface. Return a clear result when the input is outside the training range instead of silently extrapolating.

def safe_predict(x, xs, slope, intercept):
    if not min(xs) <= x <= max(xs):
        return None
    return slope * x + intercept

print(safe_predict(3, [1, 2, 3], 2.0, 0.0))
print(safe_predict(4, [1, 2, 3], 2.0, 0.0))

Outside the range, return nothing

Exercise: report the right unit

MSE is in squared output units. Root mean squared error returns to the original unit and is easier to explain. Compute both so the relationship is visible.

import math

mse = 4.0
print(math.sqrt(mse))

Back to the original unit

Your practice checklist

• Write the prediction rule before fitting.
• Check that the denominator of the slope is not zero.
• Compare the fitted model with a mean baseline.
• Report error on data that was not used to fit the line.
• Reject or flag predictions outside the training range.

Common questions

Keep reading:

• Python linear regression from scratch
• Python Model Evaluation Exercises: Beyond Accuracy
• Python Practice for Beginners: A Simple 4-Week Plan