On the impact of uncorrelated variation in regression mathematics



The objective of the present study is to investigate if, and if so, how uncorrelated variation relates to regression mathematics as exemplified by partial least squares (PLS) methodology. In contrast to previous methods, orthogonal partial least squares (OPLS) method requires a multi-focus, in the sense that in parallel to calculation of correlation it requires an analysis of orthogonal variation, i.e. the uncorrelated structure in a comprehensive way. Subsequent to the estimation of the correlation is the remaining orthogonal variation, i.e. uncorrelated data, divided into uncorrelated structure and stochastic noise by the ‘OPLS component’. Thus, it appears obvious that it is of interest to understand how the uncorrelated variation can influence the interpretation of the regression model. We have scrutinized three examples that pinpoint additional value from OPLS regarding the modelling of the orthogonal, i.e. uncorrelated, variation in regression mathematics. In agreement with the results, we conclude that uncorrelated variations do impact interpretations of regression analyses output and provides not only opportunities by OPLS but also an obligation for the user to maximize benefit from OPLS. Copyright © 2008 John Wiley & Sons, Ltd.