Principal component regression (PCR) and partial least squares regression (PLSR)

This chapter summarizes ordinary least squares regression, with emphasis on the variance problem caused by collinear predictor variables. It presents a theoretical and optimal estimation solution to this problem, and the relations to Kalman filtering as well as to principal component regression (PCR) and partial least squares regression (PLSR). The chapter then focuses on the theory behind the biased multivariate calibration methods PCR and PLSR. It discusses the PLSR residual issue in process monitoring and PLSR score-loading correspondence. The chapter also summarizes established PCR and PLSR practices with reference to the literature; and introduces some emerging methods in food science. Ergon has shown that a multiresponse PCR model with a common number of components for all responses, as well as a PLSR model for several responses (PLS2), without loss of predictive power can be compressed into a model with as many components as responses.