Comparison of linear regression models for quantitative geochemical analysis: An example using X-ray fluorescence spectrometry

Abstract

This paper presents statistical aspects related to the calibration process and a comparison of different regression approaches of relevance to almost all analytical techniques. The models for ordinary least-squares (OLS), weighted least-squares (WILS), and maximum likelihood fitting (MLF) were evaluated and, as a case study, X-ray fluorescence (XRF) calibration curves for major elements in geochemical reference materials were used. The results showed that WLS and MLF models were statistically more consistent in comparison with the usually applied OLS approach. The use of uncertainty on independent and dependent variables during the calibration process and the calculation of final uncertainty on individual results using error propagation equations are the novel aspects of our work.