What is root mean square error?
Root mean square error (RMSE) is the square root of the average squared difference between a model’s predictions and the actual values. The result is in the same units as the prediction. Because errors are squared before averaging, one large miss raises RMSE far more than several small misses that add up to the same total. Without the final square root, the measure is the mean squared error (MSE), the loss function many regression models minimize during training.
RMSE is always at least as large as mean absolute error (MAE), and the gap between the two shows how uneven the errors are. Similar values mean consistent errors. An RMSE well above the MAE means a few large misses.
Root mean square error in practice
A third-party logistics warehouse assigns dock doors and unloading crews from predicted truck arrival times. Model A has an MAE of 20 minutes and an RMSE of 42 minutes, because it occasionally misses by three hours. Model B has an MAE of 25 minutes and an RMSE of 28 minutes and never misses by more than an hour. MAE favors model A, but the operations manager chose model B, because a three-hour miss leaves a crew idle and a door blocked while other trucks queue. RMSE ranked the two models in the same order as the warehouse’s own costs.
The same sensitivity becomes a weakness when the data contains bad records. A single mistyped arrival time can inflate RMSE, so clean the actual values before comparing models on it.