RMSEä

RMSEä, in practice often written as RMSE, is a standard metric used to quantify the accuracy of predictions from regression models. It measures the average magnitude of the errors between predicted values and observed values, giving larger errors more weight due to the squaring step. In Finnish contexts, RMSEä is commonly used as the term for this measure.

Formula and interpretation: RMSEä = sqrt( (1/n) * sum_{i=1}^n (y_i - ŷ_i)^2 ), where y_i are observed values and ŷ_i are predictions. The result shares the same units as the target variable, which aids interpretability. A smaller RMSEä indicates a better fit, with zero representing a perfect prediction. Because it is the square root of the mean squared error, RMSEä penalizes larger errors more heavily than smaller ones.

Relation to other metrics: RMSEä is the square root of MSE, and is often preferred when the goal is to have error measures in interpretable units. It is complementary to metrics like MAE (mean absolute error) and R-squared, each providing different perspectives on model performance. RMSEä can be sensitive to outliers since large residuals have a disproportionate effect.

Practical usage and limitations: RMSEä is widely used in model evaluation, cross-validation, and hyperparameter tuning for regression tasks. It is informative when the target variable has a meaningful unit and similar error scales across observations. However, it does not convey directionality of errors and can be distorted by outliers or skewed error distributions. When comparing models, RMSEä should be computed on the same dataset and with the same units.