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.