Partial Least Squares Overviewoverview see also
Partial Least Squares OverviewPartial least squares (PLS) is a biased, non-least squares regression procedure that relates a set of predictor variables to multiple response variables. Use PLS with ill-conditioned data, when predictors are highly collinear or predictors outnumber observations and ordinary least squares regression either fails or produces coefficients with high standard errors.
Minitab uses the nonlinear iterative partial least squares (NIPALS) algorithm developed by Herman Wold [42]. The algorithm reduces the number of predictors using a technique similar to principal components analysis to extract a set of components that describes maximum correlation among the predictors and response variables. It then performs least squares regression on these uncorrelated components. In addition, cross-validation is often used to select the components that maximize the model's predictive ability. To perform partial least squares regression, see Stat > Regression > Partial Least Squares. See [17] for a tutorial on PLS.