How to calculate the determination coefficient R^2 with two matrix ?

hello I have two matrices A(i,j) and B (i,j). How to calculate for each i the covariance (A,B)? also calculate the determination coefficientR ^2?

Answer 1

[Ayush Modi]

Hi Albert,

You can calculate the covariance between two matrices A and B using "cov" function. To calculate covariance for each row, iterate over each row using a loop. Here is the sample code:

A = [1 9 3; 4 5 6; 7 8 6]; % Replace with your matrix A
B = [6 8 7; 6 5 4; 3 2 1]; % Replace with your matrix B

[numRows, numCols] = size(A);

covarianceValues = zeros(numRows, 1);
R2Values = zeros(numRows, 1);

% Loop through each row
for i = 1:numRows
    % Extract the i-th row from A and B
    Ai = A(i, :);
    Bi = B(i, :);
    
    covMatrix = cov(Ai, Bi);
    
    covarianceValues(i) = covMatrix(1, 2);
    

To calculate the determination coefficient R^2, you can calculate the standard deviation of each row using "std" function and apply the formula for 'r'.

    sigmaA = std(Ai);
    sigmaB = std(Bi);
    
    % Calculate the determination coefficient R^2
    R2Values(i) = (covarianceValues(i) / (sigmaA * sigmaB))^2;
end

disp(covarianceValues);

    4.0000
   -1.0000
    0.5000

disp('Determination coefficient R^2 for each row:');

Determination coefficient R^2 for each row:

disp(R2Values);

    0.9231
    1.0000
    0.2500

Note - covariance matrix covMatrix returned by the cov function contains the variances of Ai and Bi on the diagonal and the covariance between Ai and Bi off the diagonal.

Refer to the following documentation for more information on the function:

cov - https://www.mathworks.com/help/matlab/ref/cov.html

std - https://www.mathworks.com/help/matlab/ref/std.html

[albert Kinda]

Thanks but how can get RMSE?

[Torsten]

Use

https://uk.mathworks.com/help/matlab/ref/rmse.html

@Ayush Modi thought your aim was to compute Pearson's correlation coefficient (@Ayush Modi why squared ?):

https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

[albert Kinda]

The correlation coefficient is the covariance divided by the two standard deviations marginal

The determination coefficient is the square of the correlation coefficient

[Torsten]

You asked for RMSE in your comment, not for the correlation coefficient or the coefficient of determination.

Better you just write down the mathematical formula of what you want if a, b are vectors of the same size. This will avoid confusion about terminology .