Statistical properties of linearization of the Arrhenius equation via the logarithmic transformation

The temperature dependence of a rate constant is usually described by the Arrhenius equation. It can be transformed into a linear model by the logarithmic transformation of the dependent variable. The parameter vector in the linearized model is then often estimated by the ordinary least squares esti...

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Bibliographic Details
Published inChemometrics and intelligent laboratory systems Vol. 39; no. 1; pp. 69 - 75
Main Authors Klicka, Roman, Kubácek, Lubomir
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.1997
Subjects
Arrhenius equation
Least squares estimation
Linear regression
Linearization
Logarithmic transformation
Arrhenius equation
Linear regression
Least squares estimation
Logarithmic transformation
Linearization
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Summary:The temperature dependence of a rate constant is usually described by the Arrhenius equation. It can be transformed into a linear model by the logarithmic transformation of the dependent variable. The parameter vector in the linearized model is then often estimated by the ordinary least squares estimator. Theoretical bias and the covariance matrix of the parameter vector in the linearized model are given for this method if the original errors are normally distributed, independent and have a constant variance. The expressions are verified by computer simulation of a numerical example. This true covariance matrix of the parameter vector is compared with that if the change of distribution of errors is neglected. The results are also compared with those obtained by the generalized least squares estimator.
ISSN:0169-7439
1873-3239
DOI:10.1016/S0169-7439(97)00049-X