PLS-regression: a basic tool of chemometrics

Ž . Ž PLS-regression PLSR is the PLS approach in its simplest, and in chemistry and technology, most used form two-block . predictive PLS . PLSR is a method for relating two data matrices, X and Y, by a linear multivariate model, but goes beyond traditional regression in that it models also the structure of X and Y. PLSR derives its usefulness from its ability to analyze data with many, noisy, collinear, and even incomplete variables in both X and Y. PLSR has the desirable property that the precision of the model parameters improves with the increasing number of relevant variables and observations. This article reviews PLSR as it has developed to become a standard tool in chemometrics and used in chemistry and engineering. The underlying model and its assumptions are discussed, and commonly used diagnostics are reviewed together with the interpretation of resulting parameters. Ž . Two examples are used as illustrations: First, a Quantitative Structure–Activity Relationship QSAR rQuantitative StrucŽ . ture–Property Relationship QSPR data set of peptides is used to outline how to develop, interpret and refine a PLSR model. Second, a data set from the manufacturing of recycled paper is analyzed to illustrate time series modelling of process data by means of PLSR and time-lagged X-variables. q 2001 Elsevier Science B.V. All rights reserved.