Selection of weights for a weighted regression of tree volume

The construction of regression equations for predicting tree volumes requires the assumption of homogeneity of variance that can be achieved by the method of weighted least squares. Some of the weights have the form (1/D λ H) 2 or (1/D λ ) 2 (where D represents tree diameter at breast height and H represents tree height). Traditionally, λ has been assigned a value of 2. This paper suggests a method to estimate the exponent λ. This is accomplished by finding a maximum log likelihood function for a transformed tree volume regression equation. A proper value of λ is chosen within the confidence interval of λ. The confidence interval is established from the maximum log likelihood function.