Simplified Algorithm for Single Dependent Variable Partial Least Squares Regression

In this article, I provide a detailed explanation of my custom implementation of a partial least squares regression model for single dependent variables. This model utilizes a simplified algorithmic approach that enables both predictive modeling and identification of outliers. Partial least squares regression represents a crucial statistical methodology that helps uncover relationships between variables, thereby enhancing data analysis and prediction accuracy. The implementation employs a computationally efficient algorithm that calculates latent variables through iterative decomposition of predictor and response matrices. The article thoroughly examines the model's theoretical foundations, algorithmic structure, and practical applications, supplemented with concrete examples to facilitate better understanding and implementation. The code implementation includes key functions for data preprocessing, covariance matrix computation, component extraction, and regression coefficient calculation. Special attention is given to the outlier detection mechanism, which leverages residual analysis and leverage values to identify anomalous data points. Furthermore, I discuss the model's advantages and limitations, particularly focusing on its computational efficiency compared to standard PLS implementations and its sensitivity to data scaling. The article concludes with proposed enhancements, including potential integration of cross-validation techniques and kernel-based extensions for nonlinear relationships. This comprehensive treatment aims to provide valuable insights and references for effectively understanding and applying partial least squares regression in practical scenarios.