Root Mean Square Error tutorial – MATLAB

Here’s how to calculate the root mean square error.

Assume you have one set of numbers that represent the Actual values you want to predict.

Actual = [1 2 3 4];

Then assume you have another set of numbers that Predicted the actual values.

Predicted = [1 3 1 4];

How do you evaluate how close Predicted values are to the Actual values?

Well you could use the root mean square error (RMSE) to give a sense of the Predicted values error.

Here’s some MATLAB code that does exactly that.

% rmse tutorial.
 
% The actual values that we want to predict.
Actual = [1 2 3 4];
 
% The values we actually predicted.
Predicted = [1 3 1 4]; 
 
% One way is to use the Root Mean Square function and pass in the "error" part.
rmse = rms(Predicted-Actual)
 
% That's it! You're done. 
% But for those of you who are the curious type, 
% here's how to calculate the root-mean-square-error by hand.
 
% First calculate the "error".
err = Actual - Predicted;
 
% Then "square" the "error".
squareError = err.^2;
 
% Then take the "mean" of the "square-error".
meanSquareError = mean(squareError);
 
% Then take the "root" of the "mean-square-error" to get 
% the root-mean-square-error!
 
rootMeanSquareError = sqrt(meanSquareError)
 
% That's it! You have calculated the RMSE by hand.
 
% So, this is true.
rootMeanSquareError == rmse

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