Problems with logarithmic transformations in regression

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.