partial least squares regression (plsr) of x and y in matlab

To perform Partial Least Squares Regression (PLSR) of X and Y in MATLAB, you can use the built-in function plsregress.

Here is an example of how to use plsregress:

main.m
% Generate sample data
X = rand(100, 10); % X matrix with 100 observations and 10 predictor variables
Y = rand(100, 1); % Y vector with 100 observations

% Perform PLSR
numComponents = 3; % Number of components to extract
[XL, YL, XS, YS, beta, PCTVAR, MSE] = plsregress(X, Y, numComponents);

% Extract regression coefficients
coef = [beta(1, :); PCTVAR']*YS/std(Y) + mean(Y);

% Print results
disp('Regression Coefficients:')
disp(coef)
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In the above example, plsregress is used to perform PLSR on the X matrix and Y vector. The numComponents parameter specifies the number of components to extract.

After performing PLSR, the function returns several outputs:

• XL, YL: Scores of the latent variables for X and Y.
• XS, YS: Standardized predictor and response variables.
• beta: Regression coefficients for each component.
• PCTVAR: Percentage of the total variance explained by each component.
• MSE: Mean squared error.

The regression coefficients, denoted as coef in the example, can be computed using the beta, PCTVAR, YS, and standardization factors. Note that mean(Y) and std(Y) are used to convert the coefficients to the original scale of Y.

Make sure you have the Statistics and Machine Learning Toolbox installed, as plsregress is part of that toolbox.