Two ways to measure error
For regression, both metrics average how far predictions land from the truth, but they aggregate differently.
- Mean absolute error averages the absolute size of each error. Every miss counts in proportion to its size.
- Root mean squared error squares each error before averaging, then takes the square root. Squaring inflates large errors.
How they differ
RMSE punishes outliers harder. A single prediction that is far off moves RMSE much more than MAE because the error is squared. RMSE is always at least as large as MAE, and the gap between them grows when errors vary widely in size.
- Use MAE when all errors matter equally and outliers should not dominate.
- Use RMSE when large errors are especially costly and you want them penalized extra.
Both share the units of the target, so they are easy to interpret directly.
Key idea
MAE averages absolute errors so each miss counts in proportion, while RMSE squares errors first and so penalizes large mistakes and outliers much more heavily.