Estimation of Weighting Factors in Linear Regression and Analysis of Variance

It frequently happens that data to be treated by regression methods or analysis of variance are subject to marked heterogeneity in the error variance. Weighting of the observations, in the least squares sense, is then appropriate but requires that values of the relative weighting factors be available. A method is presented for deriving weight estimates from the residuals of an analysis carried out with any preliminary set of weights. The method is iterative and may therefore be applied with an initial set of unit weights for all observations. Specifically, the method is concerned with column weighting in two-way tables, treated in accordance with an additive model or a more general linear regression model. The effectiveness of the method has been tested by Monte-Carlo techniques. An application of the method to an interlaboratory study of a test method is discussed.