Root Mean Squared Error

machine-learning statistics regression

Definition

Root Mean Squared Error

The Root Mean Squared Error (RMSE) is a standard evaluation metric for regression tasks that represents the quadratic mean of the differences between predicted and observed values. Formally:

$$\text{RMSE}=\sqrt{\frac{1}{m}\sum _{i=1}^m(y_i-{\hat{y}}_i{)}^2}$$

RMSE shares the same units as the target variable $y$, making it more interpretable than MSE while maintaining the property of penalising larger errors more heavily.