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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.The outlying tendency of any case in a multiple regression of p predictors may be estimated by drawing all subsets of size p from the remaining cases and fitting the model. Each such subset yields an elemental residual for the case in question, and a suitable summary statistic of them can be used as an estimate of the case's outlying tendency. We propose two such summary statistics: an unweighted median, which is of bounded influence, and a weighted median, which is more efficient but less robust. The computational load of the procedure is reduced by using random samples in place of the full set of subsets of size p. As a byproduct the method yields useful information on the influence (or leverage) of cases and the mutual masking of high leverage points.