Bivariate Linear Models in Biometry

This paper focuses on the estimation of parameters in the bivariate linear model, especially in the context of bivariate size-shape relationships or allometry. Existing estimation procedures (regression, major axis, reduced major axis) all depend on a priori assumptions on the ratio of the residuals, usually called “errors,” in both variables. These assumptions are reviewed and evaluated. The Bartlett method is not independent of assumptions on the residuals as has been often claimed. A method which does not require assumptions on the ratio of residuals, providing data from a third variable are available, is given. All of the methods discussed are illustrated with data measured on planktonic Foraminifera.