How this calculator works
Each prediction is paired with its corresponding actual value. Squaring its error gives extra weight to large misses; averaging gives MSE. RMSE restores the original unit, while MAE averages ordinary absolute distances. Signed bias uses prediction minus actual, so positive bias indicates overprediction on average. The divisor is the number of evaluated pairs, without a fitted-parameter degrees-of-freedom correction.
Formula
e_i = predicted_i - actual_i; MSE = Σe_i²/n; RMSE = sqrt(MSE); MAE = Σ|e_i|/n; bias = Σe_i/n.
Worked example
Actual values 2, 4, 6 and predictions 1, 5, 8 give errors -1, 1, 2. MSE = (1 + 1 + 4)/3 = 2 and RMSE = sqrt(2).
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Frequently asked questions
Can MSE be negative?
No. It averages squared errors. Zero means every evaluated prediction equals its actual value.
Why is MSE not in the original unit?
Squaring the error squares the unit. RMSE is the companion measure in the original unit.
Is this the residual mean square used in regression tests?
This page divides by n for prediction evaluation. Regression inference may use n minus the number of fitted parameters instead.