`rmse`

Root-mean-square error between two sets of values.

Category: Data Import and Analysis > Descriptive Statistics

Syntax

e = rmse(F, A)

Square root of the mean of (F - A).^2.

Description

rmse is the standard way to summarize how far predictions are from observations. Squaring before averaging punishes large misses more than small ones, so a few big errors raise the RMSE noticeably. It is expressed in the same units as the data, unlike the mean squared error.

For a percentage view of the error relative to the actual values, see mape.

Input arguments

F: Forecast or estimated values.
A: Actual (reference) values, same size as F.

Output arguments

e: The error in the units of the data; 0 means a perfect match.

Example

Error of a fit

actual   = [1 3 5];
forecast = [1 2 3];
rmse(forecast, actual)

Output

ans = 1.2910

rmse