Least Squares Percentage Regression

Abstract

The percentage error, or error relative to the observed value is usually felt to be more meaningful than the absolute error - yet is rarely used in the fitting of least squares regression models. We therefore explore least squares regression based on the error relative to the observed value of the dependent variable - hence percentage least squares. We are able to derive exact expressions for the regression coefficients when the model is linear in these coefficients. Such a formula is not available in the more widely known method of minimizing the mean absolute percentage error (MAPE). Another advantage of our approach over MAPE is that the solution is unique. For the practising analyst we demonstrate that percentage regression models can easily be fitted using ordinary regression software, as well as spreadsheets, by simple transformation of the data. The method can therefore easily be taught to college students.