Calculate root mean squared error between predicted and actual values.
Root Mean Squared Error (RMSE) is the square root of MSE: RMSE = √MSE = √[(1/n) × Σ(y_i − ŷ_i)²]. Taking the square root brings the error back into the same units as the target variable, making RMSE much easier to interpret than MSE while retaining the same sensitivity to large errors (since the squaring happens before the square root). RMSE is one of the most widely reported regression metrics because it balances interpretability with a meaningful penalty for large mistakes.
RMSE = sqrt((1/n) * sum((y_i - y_hat_i)^2))
RMSE is in the same units as the original target variable (since taking a square root undoes the squaring), making it directly interpretable — e.g. 'predictions are off by about $450 on average' — whereas MSE's squared units have no intuitive meaning.
Yes, for the same set of errors, RMSE is always greater than or equal to MAE, because squaring disproportionately amplifies larger errors before the square root is taken — the gap between them grows when errors are inconsistent in size.
A large gap suggests the presence of some particularly large errors (outliers) in the predictions, since RMSE is much more sensitive to big mistakes than MAE is.