partial least squares regression (plsr) in matlab

To perform Partial Least Squares Regression (PLSR) in MATLAB, you can use the plsregress function from the Statistics and Machine Learning Toolbox.

Here is an example of how to use plsregress:

main.m
% Load sample data
load sample_data.mat

% Set the number of components for PLSR
numComponents = 2;

% Perform PLSR using plsregress
[X_loadings, Y_loadings, X_scores, Y_scores, beta, ~, ~, ~] = plsregress(X, Y, numComponents);

% Display the regression coefficients
disp('PLSR Coefficients:')
disp(beta)

% Predict Y using the PLSR model
Y_pred = [ones(size(X, 1), 1), X] * beta;

% Calculate the coefficient of determination (R-squared)
R2 = 1 - sum((Y - Y_pred).^2) / sum((Y - mean(Y)).^2);
disp('R-squared:')
disp(R2)
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In this example, X and Y are the predictor and response variables, respectively. The numComponents parameter specifies the number of components to use in the PLSR model.

The function returns several outputs, including the loadings (X_loadings, Y_loadings), scores (X_scores, Y_scores), regression coefficients (beta), and additional information that is not relevant for this example.

Note that you need to have the Statistics and Machine Learning Toolbox installed to use the plsregress function.