Error measurement

Regression error is measured with metrics like MSE and MAE.

MAE and MSE

To measure a regression model, predictions are compared with the true values:

MAE (mean absolute error): mean(|y - ŷ|), in the data's unit.
MSE (mean squared error): mean((y - ŷ)²), penalises large errors more.
RMSE: √MSE, back in the data's unit.

from sklearn.metrics import mean_absolute_error, mean_squared_error
y = [3, 5, 7]
p = [2, 5, 9]
print(mean_absolute_error(y, p))   # 1.0
print(mean_squared_error(y, p))    # 1.666...

The R² score

R² says how much of the variability in y the model explains: 1 is perfect, 0 is as good as "always predict the mean", negative is worse than that.

from sklearn.metrics import r2_score
print(r2_score([3, 5, 7], [3, 5, 7]))   # 1.0
print(r2_score([3, 5, 7], [5, 5, 5]))   # 0.0
print(m.score(X_test, y_test))          # for regression score = R²

R² is unit-free; MAE/RMSE answer "how many TL is it off on average?". Both should be reported together.

Exercise Measure the model

Train the model and get predictions for X. Round MAE, MSE and R² with round(..., 3) and print them on separate lines.

Show example solution

import numpy as np
from sklearn.linear_model import LinearRegression

X = np.array([[1], [2], [3], [4], [5]])
y = np.array([3.1, 4.9, 7.2, 8.8, 11.0])
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score

m = LinearRegression().fit(X, y)
p = m.predict(X)
print(round(mean_absolute_error(y, p), 3))
print(round(mean_squared_error(y, p), 3))
print(round(r2_score(y, p), 3))

Test yourself

If the truth is <code>[10, 20]</code> and the prediction <code>[12, 16]</code>, what is the MAE?
- 3.0
- 10.0
- 2.0
- 6.0
Show answer

3.0 — |10-12| = 2, |20-16| = 4; the mean is (2 + 4) / 2 = 3.

Compute the mean absolute error.

hata = mean______error(y_true, y_pred)

Show answer

hata = mean_absolute_error(y_true, y_pred)

Match the metrics.

MAE

Mean of absolute errors
MSE

Mean of squared errors
RMSE

Square root of MSE
R²

Share of explained variance

Next lesson: Summary - Regression

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