Least Squares Percentage Regression

Abstract

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