A note on millers's empirical weights for heteroscedastic linear regression

For heteroscedastic simple linear regression when the variances are proportional to a power of the mean of the response variable, Miller (1986) recommends the following procedure: do a weighted least squares regression with the weights (empirical weights) estimated by the inverse of the appropriate power of the response variable. The practical appeal of this approach is its simplicity.

In this article some of the consequences of this simple procedure are considered. Specifically, the effect of this procedure on the bias of the point estimators of the regression coefficients and on the coverage probabilities of their corresponding confidence intervals is examined. It is found that the performance of the process of employing empirical weights in a weighted least squares regression depends on : (1) the particular regression parameter (slope or intercept) of interest, (2) the appropriate power of the mean of the response variable involved, and (3) the amount of variation in the data about the true regression line.