Comparison of Linear Regression Models for Quantitative Geochemical Analysis: An Example Using X-Ray Fluorescence Spectrometry |
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| Authors: | Mirna Guevara Surendra P Verma Fernando Velasco-Tapia Rufino Lozano-Santa Cruz Patricia Girón |
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| Institution: | Centro de Investigación en Energía, UNAM, Privada Xochicalco s/no. Col. Centro, Apartado Postal 34, Temixco, Mor. 62580, Mexico;Centro de Investigación en Ingeniería y Ciencia Aplicada, UAEM, Av. Universidad no. 1001, Col. Chamilpa, Cuernavaca, Mor. 62210, Mexico;Facultad de Ciencias de la Tierra, UANL, Carretera Linares-Cerro Prieto km 8, Apartado Postal 104, Linares, N.L 67700, Mexico;Instituto de Geología, UNAM, Ciudad Universitaria, Apartado Postal 40-276, Mexico, D.F. 04510, Mexico |
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| 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 (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. |
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| Keywords: | analytical calibration linear regression geochemical reference materials analytical geochemistry error propagation |
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