# The HPPLS Procedure

#### Principal Components Regression

Like the SIMPLS method, principal component regression (PCR) defines all the scores in terms of the original (centered and scaled) predictors . However, unlike both the PLS and SIMPLS methods, the PCR method chooses the X-weights and X-scores without regard to the response data. The X-scores are chosen to explain as much variation in as possible; equivalently, the X-weights for the PCR method are the eigenvectors of the predictor covariance matrix . Again, the X- and Y-loadings are defined as in PLS; but, as in SIMPLS, it is easy to compute overall model coefficients for the original (centered and scaled) responses in terms of the original predictors .