A MATLAB Toolbox for Multivariate Regression Coupled with Variable Selection

Multivariate regression is a fundamental supervised chemometric approach that defines the relationship between a set of independent variables and a quantitative response. It enables the subsequent prediction of the response for future samples, thus avoiding its experimental measurement. Regression approaches have been widely applied for data analysis in different scientific fields. In this paper, we describe the regression toolbox for MATLAB, which is a collection of modules for calculating some well-known regression methods: Ordinary Least Squares (OLS), Partial Least Squares (PLS), Principal Component Regression (PCR), Ridge and local regression based on sample similarities, such as Binned Nearest Neighbours (BNN) and k-Nearest Neighbours (kNN) regression methods. Moreover, the toolbox includes modules to couple regression approaches with supervised variable selection based on All Subset models, Forward Selection, Genetic Algorithms and Reshaped Sequential Replacement. The toolbox is freely available at the Milano Chemometrics and QSAR Research Group website and provides a graphical user interface (GUI), which allows the calculation in a user-friendly graphical environment.