Optimised score plot by principal components of predictions

A common problem in statistics/chemometrics is to relate two data matrices (X and Y) to each other, with the purpose of either prediction or interpretation. Usually, one is interested in understanding which directions in Y-space that can be predicted by which directions in X-space. Several methods exist for this, for instance, PLS regression and canonical correlation. The present paper presents a new plot for visualising the relationship between X and Y. The plot is based on a decomposition of the X-space that is optimal with respect to Y-variance. The new procedure can accompany any regression method.