CHAPTER 4: Ordinary Multiple Linear Regression and Principal Components Regression

Calibration based on a classical univariate regression requires completely selective measurements. Therefore, predictions may be biased severely when this requirement is not fulfilled. Multivariate regression is presented as a means to overcome these limitations. Three different approaches to multivariate calibration are presented: the classical least‐squares model, the inverse least‐squares model, and the regression on principal components. Their advantages (mainly their ability to yield correct predictions for non‐selective measurements) and limitations are discussed. This introduction to multivariate calibration offers a basis for understanding the partial least‐squares model described in Chapter 5.