how to do whitening transformation of adjusted r squared in matlab

To perform a whitening transformation on the adjusted R-squared in MATLAB, you first need to calculate the adjusted R-squared value. Once you have the adjusted R-squared value, you can apply the whitening transformation using the following steps:

1. Calculate the adjusted R-squared value using the formula:

   adj_r_squared = 1 - ((1 - r_squared) * (n - 1)) / (n - p - 1)

   where r_squared is the ordinary R-squared value, n is the number of observations, and p is the number of predictors in the model.

2. Apply the whitening transformation using the formula:

   whitened_r_squared = sqrt(adj_r_squared * (n - p - 1))

   The whitening transformation involves taking the square root of the product of the adjusted R-squared value and (n - p - 1), where n is the number of observations and p is the number of predictors.

Here's an example MATLAB code snippet to perform the whitening transformation on the adjusted R-squared:

main.m
% Calculate the adjusted R-squared value
r_squared = 0.7;  % Replace with your actual R-squared value
n = 100;  % Replace with the number of observations
p = 5;  % Replace with the number of predictors

adj_r_squared = 1 - ((1 - r_squared) * (n - 1)) / (n - p - 1);

% Apply the whitening transformation
whitened_r_squared = sqrt(adj_r_squared * (n - p - 1));

% Display the results
disp(['Adjusted R-squared: ', num2str(adj_r_squared)]);
disp(['Whitened R-squared: ', num2str(whitened_r_squared)]);
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Make sure to replace r_squared, n, and p with your actual values in the code.

Please note that the whitening transformation of the adjusted R-squared may not be a common statistical technique. If you have a specific reason to apply this transformation, ensure that it is appropriate for your analysis.