Estimation in a Heteroscedastic Regression Model

A method is suggested for obtaining a multiple linear regression equation which permits the variance, as well as the mean, of normally distributed random variables, Y to be a function of known constants X1 … Xp. The method is applicable to large samples, and yields an approximation of maximum likelihood estimates of regression coefficients, which may be used to construct confidence intervals for the parameters of the normal distribution and tolerance intervals for individual Y. A likelihood ratio test may be used to test this model against the usual homoscedastic least squares model. Two exmples of this type of analysis on data from the literature are presented.