University of Hertfordshire

Least Squares Percentage Regression

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Original languageEnglish
Pages (from-to)526-534
JournalJournal of Modern Applied Statistical Methods
Journal publication dateNov 2008
Publication statusPublished - Nov 2008


In prediction, the percentage error is often felt to be more meaningful than the absolute error. We therefore extend the method of least squares to deal with percentage errors, for both simple and multiple regression. Exact expressions are derived for the coefficients, and we show how such models can be estimated using standard software. When the relative error is normally distributed, least squares percentage regression is shown to provide maximum likelihood estimates. The multiplicative error model is linked to least squares percentage regression in the same way that the standard additive error model is linked to ordinary least squares regression.

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