🔬 Root Mean Squared Error (RMSE)

Root Mean Squared Error (RMSE)#

The square root of mean squared error, in the target’s units.

Important

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What it is#

Root mean squared error is the square root of the MSE:

\[\text{RMSE} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}\big(y_i - \hat{y}_i\big)^2}.\]

The root returns the error to the target’s original units, so it reads as a typical error magnitude.

How it behaves#

RMSE keeps MSE’s heavy penalty on large errors and its outlier sensitivity, but is far more interpretable — an RMSE of 5 means predictions are off by about 5 units on average. It ranks models identically to MSE, is always ≥ the MAE, and the RMSE–MAE gap widens as the error variance grows.

When to use it#

Report RMSE for regression when large errors are costly and you want a number in the data’s units; pair it with R² for a scale-free complement. Like R², it also falls as you add variables, so watch overfitting.

Theme: Model Evaluation & Uncertainty · All terminology

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Mind map — connected ideas

Mean Squared Error (MSE) · Mean Absolute Percentage Error (MAPE) · R² (R-squared) · Loss Functions · Regression Models · Average Absolute Error (AAE)

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More in Model Evaluation & Uncertainty

Average Absolute Error (AAE) · Baseline Heuristics · Bootstrap · Bootstrap Confidence Intervals (CIs) · Coverage · Cramér’s V · DeLong’s Test · KS Statistic (Kolmogorov–Smirnov Statistic) · Likelihood Ratio (LR) · Mann–Whitney U Test (also called the Wilcoxon rank-sum test) · MASE (Mean Absolute Scaled Error) · Mean Absolute Error (MAE) · Mean Absolute Percentage Error (MAPE) · Mean Squared Error (MSE)