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Comparison of Linear Regression Models for Quantitative Geochemical Analysis: An Example Using X‐Ray Fluorescence Spectrometry
Author(s) -
Guevara Mirna,
Verma Surendra P.,
VelascoTapia Fernando,
LozanoSanta Cruz Rufino,
Girón Patricia
Publication year - 2005
Publication title -
geostandards and geoanalytical research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.037
H-Index - 73
eISSN - 1751-908X
pISSN - 1639-4488
DOI - 10.1111/j.1751-908x.2005.tb00900.x
Subject(s) - calibration , mathematics , statistics , ordinary least squares , maximum likelihood
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 (WLS), 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.