Regression models are often used for estimating net outputs of a biological system. In many cases both heteroscedasticity and asymmetry of the errors are encountered. Properly accounting for the effects of these types of errors can substantially improve the estimation of regression coefficients and prediction intervals. Transformations, such as those proposed by Box and Cox (1964), are used extensively to obtain homoscedasticity and symmetry of errors. One of the major drawbacks of transformation methods is that when both heteroscedasticity and asymmetry are present, a transformation that corrects for both may not exist. A regression method based on modeling the error distribution using Johnson's (1949) S_U distribution is proposed and referred to as S_U regression. This new regression technique is compared with the weighted and unweighted transformation of both sides methods using two forestry datasets. For both datasets the assumption of S_U distributed errors was appropriate, but neither of the transformation of both sides methods was able to achieve symmetric residuals. Clear improvements in the prediction intervals for S_U regression were demonstrated in a cross-validated simulation.

Key Words
Prediction intervals; Transformation of both sides.

Michael S. Williams is Mathematical Statistician, Multiresource Inventory Techniques, Rocky Mountain Forest and Range Experiment Station, USDA Forest Service, 240 W. Prospect, Fort Collins, CO 80526-2098 (e-mail: s28a@mhs-fswa.attmail.com).