The PLS multivariate regression model:: testing the significance of successive PLS components

In this paper we write the PLS multivariate regression model in terms of a redundancy index and obtain some properties of the successive PLS components, We study their significance in the model and build tests of hypotheses to this effect. A stopping rule is given to obtain the right number of PLS components, and a numerical measure is defined to assess the overall quality of the PLS regression. Finally, an algorithm is given explicitly as it was coded in S-Plus and is applied in some chosen examples. Copyright (C) 2001 John Wiley & Sons, Ltd.