Calculation and Miscalculation of the Allometric Equation as a Model in Biological Data

Abstract

The allometric equation Y = βXα is widely used as a regression model in biology. The common procedure for fitting this model by the method of least squares involves the logarithmic transformation of both variables: log Y = log β + α log X. This transformation procedure results in a least squares solution which only approximates β and α and often the approximation is a poor one. That erroneous conclusions may arise from the use of the logarithmic transformation is demonstrated with an example, and a preferred procedure is recommended.