MATLAB: How is the coefficient ‘R’ calculated in regression plots in neural network toolbox

neural network performancenon-linear regression

Could anyone please explain how is the coefficient 'R' computed for regression plots in neural network toolbox…and is it known as 'Correlation Coefficient'

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 t   = target
 y   = output
 Cyt = corrcoef(y,t)
 R   = Cyt(2,1)

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MATLAB: Please i need help on how to determine R squared for training, validation, testing and ALL in neural network with a simple code.

"..........Each time I click on plotregression, I see thier R2......"

Hello, point of correction; regression plots of your modeled network show the correlation coefficient,"R" (a measure of the magnitude and direction of linear association between the defined variables), but not the coefficient of determination, "Rsquared / R2" (a measure of the magnitude of variability modeled by the network in your output,'y'). However, R=squareroot(R2). Added to that, a number of answers have been previously given on how to obtain this correlation coefficient you desire. Please refer to the links below:

https://mathworks.com/matlabcentral/answers/47208-corrcoef-plotregression-which-algorithm-plotregression-use

https://mathworks.com/matlabcentral/answers/121706-how-is-the-coefficient-r-calculated-in-regression-plots-in-neural-network-toolbox

Alternatively you could refer to the matlab documentation in the link below, with an example of obtaining the correlation coefficient from the general or "All" plot:

https://mathworks.com/help/deeplearning/ref/regression.html

MATLAB: Calculating the Regression Coefficient

For simple linear regression in the least-square sense, you could do something like this:

% Calculating the regression coefficient
close all
x = linspace(0,1,100);         % Data from your first column/independent variable
y = x + rand(1, length(x));    % Data from your second column/dependent variable
% Compute the mean of your data
yhat = mean(y);
xhat = mean(x);
% Compute regression coefficients in the least-square sense
b = (x - xhat)*(y' - yhat)/sum((x - xhat).^2); % Regression coefficient
a = yhat - b*xhat;                             % Y-intercept
% Plot data
figure()
scatter(x, y);
hold on
plot(x, a + b*x, 'r');
legend(['b = ' num2str(b)]); % Your regression coefficient is b

For more details on the math, you could check the link below:

https://www.bmj.com/about-bmj/resources-readers/publications/statistics-square-one/11-correlation-and-regression

Hope this helps!

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MATLAB: Please i need help on how to determine R squared for training, validation, testing and ALL in neural network with a simple code.

MATLAB: Calculating the Regression Coefficient

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