MAE, RMSE, and R²

Numeric errors tell different stories

Mean absolute error (MAE) averages absolute prediction errors and stays in target units. Root mean squared error (RMSE) squares errors before averaging and takes the square root, so large misses count much more. Choose RMSE when large errors are disproportionately costly; choose MAE for a more robust typical error.

R-squared (R²) compares squared error against predicting the target mean. 1 is perfect, 0 is no better than that mean baseline, and negative values mean worse than the baseline. It is unitless but does not tell whether errors are operationally acceptable.

errors model A: 2, 2, 2, 10 -> MAE 4.0, RMSE 5.3
errors model B: 4, 4, 4,  4 -> MAE 4.0, RMSE 4.0
same MAE; RMSE exposes A's large miss

Warning: Comparing R² across different populations or target ranges can mislead. Always report an error metric in real units alongside it.

Tip: Slice residuals by target range and subgroup. A good overall MAE can hide severe underprediction for the largest, most expensive cases.