Regression metrics calculator: MAE, MSE, RMSE and R²

Worked result

MAE 0.5; MSE 0.375; RMSE approximately 0.612372435696; R² approximately 0.948608137045.

1. Subtract each actual value from its prediction.
2. Average absolute errors for MAE and squared errors for MSE.
3. Take the square root of MSE; compare squared error with the target mean baseline for R².

Evaluate four actual–prediction pairs

Use actual values 3, -0.5, 2 and 7 with predictions 2.5, 0, 2 and 8. This is a small arithmetic example, not a trained-model benchmark.

Prediction errors = -0.5, 0.5, 0, 1
Absolute error total = 2
Squared error total = 1.5
MAE = 2/4 = 0.5
MSE = 1.5/4 = 0.375
RMSE = √0.375 ≈ 0.612372435696
Target mean = 2.875; SST = 29.1875
R² = 1 − 1.5/29.1875 ≈ 0.948608137045

MAE and RMSE use the target’s original units. MSE uses squared units. A high score on these four illustrative rows says nothing about generalization to new data.

Prediction errors and a mean-baseline comparison

MAE weights each absolute error linearly, while squaring in MSE increases the influence of larger errors. RMSE returns squared-error loss to the original target units. Compare metrics on the same target scale and evaluation data.

R² compares squared prediction error with the error from predicting the actual-target mean. It may be negative. If the actual targets are all constant, the denominator is zero and the ordinary R² formula is undefined; this tool does not apply a library-specific finite-score replacement.

eᵢ = predictedᵢ − actualᵢ
MAE = Σ|eᵢ|/n
MSE = Σeᵢ²/n; RMSE = √MSE
R² = 1 − Σeᵢ²/Σ(actualᵢ − mean(actual))²

Input limits and common mistakes

Provide at least one pair for error metrics and at least two nonconstant actual values for R². Each row must have exactly two finite numbers. Weights, multi-output aggregation and missing values are not supported.

These are evaluation losses divided by n, not the residual mean-square estimator divided by n minus fitted parameters. Use an appropriate held-out or cross-validation design before interpreting predictive performance. No causal or model-quality verdict is generated.

Questions about mae, mse, rmse and r²

Sources and verification

These references explain the formulas or formats. The worked examples above were created for this tool and checked against independent calculations or format round trips. AI-assisted development does not imply a named human expert review.

• scikit-learn: regression metrics — MAE, squared error, R² and constant-target conventions.

Published 2026-10-23. Examples are illustrations, not measurements of a service or claims about search rankings.

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Further reading

• MAE, MSE, RMSE et R² : exemple calculé et Python (French)