# In case of multiple output in ANN ,what does R value represent?

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Sunita on 6 Dec 2023
Commented: Aiswarya on 13 Dec 2023
I have 4 inputs and 3 outputs , I am getting only one regression (R-value) , how this is calculated out of 3 outputs?

Aiswarya on 11 Dec 2023
Hi Sunita,
I understand that you want to know how R is calculated for a multiple output ANN(Artificial Neural Network). The formula for calculating the R value is provided in the following documentation:
The R value for multiple outputs can be calculated as follows (where y_predicted and y_actual will be matrices):
% Sum of squared errors
SSE = sum((y_predicted - y_actual).^2,"all")
% Total sum of squares
SST = sum((y_actual - mean(y_actual)).^2,"all");
% Normalized Mean Square Error
NMSE = SSE/SST
% R squared
Rsquared = 1 - NMSE
You may also refer to this MATLAB answer for MSE calculation for multiple output neural network :
Sunita on 11 Dec 2023
Thank you for your response. I'm curious about the R-value displayed when there are three predicted outputs (columns 1, 2, and 3). does the R-value shown correspond to column 1, 2, or 3?
Aiswarya on 13 Dec 2023
It basically represents the cumulative of all three predicted outputs, as mentioned in the sum (SSE and SST), the 'all' term refers to summing up across all dimensions (considering the 3 outputs as different dimensions). So, as answer to your question it represents all the output columns.