Building Partial Least Squares Models with MATLAB Code Implementation

This section demonstrates how to implement partial least squares modeling using MATLAB programming. The PLS algorithm effectively handles multicollinearity in datasets by projecting both predictor and response variables into new latent spaces, making it particularly useful for analyzing high-dimensional data with correlated variables. The provided code includes detailed inline comments explaining each variable declaration, matrix operation, and function call. Key computational steps such as covariance matrix decomposition, weight vector calculation, and score extraction are annotated with mathematical explanations. For instance, comments clarify how the NIPALS algorithm iteratively extracts components by maximizing covariance between X and Y matrices. These annotations document the program's logical flow, variable purposes, and implementation strategies - including critical functions like plsregress for core calculations and cross-validation techniques for model optimization. Through this commented implementation, users can understand both the statistical methodology and programming approaches, thereby enhancing their data analysis capabilities and software development skills for scientific computing tasks.