Exact presentation of multivariate calibration model as univariate calibration graph

A proof is given that a recently introduced univariate presentation of a multivariate calibration model is exact, i.e., there are no approximations involved. The proof is based on: (1) previously proposed definitions of multivariate net analyte signal and multivariate calibration factors (sensitivity in classical model and inverse sensitivity in inverse model) and (2) the geometrical property of the true regression vector in inverse multivariate calibration that it must be proportional to the true multivariate net analyte signal Vector of a particular sample. The extension of the proof to multiway calibration is briefly discussed. A practical example from near-infrared (NIR) spectroscopy is used to illustrate that the proposed univariate presentation may give more meaning to the term 'spectral overlap'. (C) 2000 Elsevier Science B.V. All rights reserved.