MATLAB-Based Multivariate Linear Regression with Leave-One-Out Cross-Validation Prediction Package

This MATLAB-based package provides researchers with robust tools for multivariate linear regression analysis and Leave-One-Out Cross-Validation prediction. The core implementation utilizes MATLAB's matrix operations for efficient computation of regression coefficients through the normal equation method (using the backslash operator or pinv() function for numerical stability). The package analyzes the influence of multiple independent variables on a single dependent variable, helping users understand variable relationships and predict future data trends. It includes comprehensive data preprocessing functions for handling missing values, outlier detection, and data normalization using z-score or min-max scaling methods. Key algorithmic features include: - Implementation of LOOCV where each observation serves as validation data once - Calculation of prediction error metrics (MSE, RMSE, R-squared) - Statistical significance testing for regression coefficients The package offers extensive visualization capabilities, generating diagnostic plots including: - Residual plots for error analysis - Actual vs. predicted value scatter plots - Coefficient importance bar charts - QQ-plots for normality assessment The modular code structure allows easy customization of regression models and validation procedures. This powerful, user-friendly tool enables researchers to conduct comprehensive multivariate regression analysis and prediction with statistical rigor and visual interpretability.