Problems with Logarithmic Transformations in Regression

Abstract

The power model is widely used in engineering as the structure for empirical models. The coefficients are fitted using a logarithmic transformation of the data. The logarithmic transformation leads to a biased model, which is not usually corrected for. Even when the traditional approach to eliminating the bias is used, only the intercept coefficient is changed; the other coefficients are not corrected, so they remain biased estimators. A numerical method for fitting the coefficients of the power model is discussed; the method enables the coefficients to be fit so they provide unbiased estimates and a minimum‐error variance in the y‐space, rather than the log y‐space. The numerical method is easily modified to fit the coefficients using an objective function based on the relative errors. Examples using actual engineering data are provided.