Abstract We present in this article several results that characterize the set of all weighted regressions. The set of weighted regression estimates is the set of all generalized least squares estimates for covariance matrices that have positive weights on the diagonal and have zeroes elsewhere. The study of sets of estimates is a method for dealing with distributional uncertainty, which does not require the strong assumption of a particular distribution. We show that the set of weighted regressions is the union of the bounded convex polytopes formed by the hyperplanes on which residuals are zero. For the two-dimensional case, we provide a simple method for outlining the set and give an efficient method for selecting the weighted regressions that determine the convex hull of the set. Finally, we discuss two examples that illustrate the use of these results.
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