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Least Squares Percentage Regression

Journal of Modern Applied Statistical Methods, 2009

12 Pages Posted: 22 May 2009  

Chris Tofallis

University of Hertfordshire Business School

Date Written: May 18, 2009


When using a model for prediction, or for representing the data, the percentage error may be more important than the absolute error. We therefore present the method of least squares regression based on percentage errors. Exact expressions are derived for the coefficients, and we show how models can be estimated easily using existing regression software. (The proposed method is not to be confused with semi-log regression.)

Least squares percentage regression is linked to the multiplicative error model in the same way that the standard additive error model is linked to ordinary least squares regression. The method should therefore also prove useful when the data does not have constant variance (heteroscedastic data). The coefficients are shown to be unbiased.

When the relative error is normally distributed, least squares percentage regression is shown to provide maximum likelihood estimates.

Keywords: regression, error measures, relative error, percentage regression, weighted least squares, multiplicative error, heteroscedasticity.

JEL Classification: C13, C20, C22

Suggested Citation

Tofallis, Chris, Least Squares Percentage Regression (May 18, 2009). Journal of Modern Applied Statistical Methods, 2009. Available at SSRN: or

Chris Tofallis (Contact Author)

University of Hertfordshire Business School ( email )

College Lane
Hatfield, Hertfordshire AL10 9AB
United Kingdom


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