Regression metrics cheat sheet

Metric	Formula	Units	Use when	Watch out
MAE	$\frac{1}{n}\sum\lvert y - \hat{y}\rvert$	target units	every unit of error costs the same; outliers shouldn't dominate	not differentiable at 0 (fine for reporting)
MSE	$\frac{1}{n}\sum(y - \hat{y})^2$	squared units	training loss; large errors are especially bad	hard to interpret
RMSE	$\sqrt{\text{MSE}}$	target units	report MSE in readable units	dominated by a few big misses
R²	$1 - \frac{\sum(y-\hat{y})^2}{\sum(y-\bar{y})^2}$	none	compare against predicting the mean	can be negative on test data; not comparable across datasets
MAPE	$\frac{100\%}{n}\sum\left\lvert\frac{y - \hat{y}}{y}\right\rvert$	percent	relative error across scales	explodes near $y = 0$ ; asymmetric
Huber loss	quadratic near 0, linear beyond δ		robust training loss	choose δ

Worked example. Errors $[-10, 10, -10, 10, -5]$ : MAE 9.0, RMSE 9.2. Change one error to 100: MAE 28.0, RMSE 45.6. RMSE reacts five times more.

Always also: plot residuals versus predictions (curvature means a missing nonlinearity; a fan shape means non-constant variance), and compare against a baseline (mean, last value, seasonal naive).

Lessons: Linear regression · Regularization and regression metrics