How to find the Relative Root Mean Square Error for the given data?

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Sadiq Akbar
Sadiq Akbar el 6 de Mzo. de 2024
Respondida: Divyam el 30 de Oct. de 2024
I have some data as given below:
u=[-30 30 -50 50];% desired vector
low = [-90 -90 -90 -90];
up = [90 90 90 90];
b = low + (up - low) .* randn(1,4);% Estimated vetors
How will we find the Relative Root Mean Sqaure Error (RRMSE) for this? Further, what does the RRMSE show?
  6 comentarios
Dyuman Joshi
Dyuman Joshi el 7 de Mzo. de 2024
Editada: Dyuman Joshi el 7 de Mzo. de 2024
@Sadiq Akbar, you should read the comments included in the code above.
Sadiq Akbar
Sadiq Akbar el 8 de Mzo. de 2024
Yes, I read and made the dimension of both equal and it worked. But If we want to determine the RMSE and the RRMSE for the above data when u=[-30 30]; Then what is the diffeence between them. Further and most important if we want to draw a plot for both the metrics i.e., RMSE and RRMSE for the above data, then how will be that and what is the difference between both? I mean what extra information is given by RRMSE than RMSE?

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Divyam
Divyam el 30 de Oct. de 2024
To compare by drawing a plot for RMSE and RRMSE, you can simply use a barplot and check the values for each using the code below in addition to the code provided by Manikanta:
metrics = [rmse, rrmse];
metric_names = {'RMSE', 'RRMSE'};
figure;
bar(metrics);
set(gca, 'xticklabel', metric_names);
ylabel('Error');
title('Comparison of RMSE and RRMSE');
The key difference between RMSE and RRMSE is that RRMSE normalizes the RMSE value by dividing RMSE by the mean of the observed values. RRMSE is a better measure for comparing error values across different datasets. RRMSE thus makes the error relative to the size of the data and hence removes the influence of scaling on datasets.
Dataset 1:
observed = [100, 120, 150]
predicted = [98, 123, 147]
RMSE = 2.708
RRMSE = 0.021788
Dataset 2:
observed = [1000, 1200, 1500]
predicted = [980, 1230, 1470]
RMSE = 27.0801
RRMSE = 0.021788
Notice how the values for RMSE in the above example vary heavily with the values in the dataset but RRMSE stays constant despite the scaling.

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