A Calibration Tutorial for Spectral Data. Part 1: Data Pretreatment and Principal Component Regression Using Matlab

Abstract

Regression and calibration play an important role in analytical chemistry. All analytical instrumentation is dependent on a calibration that uses some regression model for a set of calibration samples. The ordinary least squares (OLS) method of building a multivariate linear regression (MLR) model has strict limitations. Therefore, biased or regularised regression models have been introduced. Some selected ones are ridge regression (RR), principal component regression (PCR) and partial least squares regression (PLS or PLSR). Also, artificial neural networks (ANN) based on back-propagation can be used as regression models. In order to understand regression models more is needed than just a set of statistical parameters. A deeper understanding of the underlying chemistry and physics is always equally important. For spectral data this means that a basic understanding of spectra and their errors is useful and that spectral representation should be included in judging the usefulness of the data treatment. A “constructed” spectrometric example is introduced. It consists of real spectrometric measurements in the range 408–1176 nm for 26 calibration samples and 10 test samples. The main response variable is litmus concentration, but other constituents such as bromocresolgreen and ZnO are added as interferents and also the pH is changed. The example is introduced as a tutorial. All calculations are shown in detail in Matlab. This makes it easy for the reader to follow and understand the calculations. It also makes the calculations completely traceable. The raw data are available as a file. In Part 1, the emphasis is on pretreatment of the data and on visualisation in different stages of the calculations. Part 1 ends with principal component regression calculations. Partial least squares calculations and some ANN results are presented in Part 2.