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This article shows how to transform residuals from regression on an arbitrary set of k regressors to a set of values having the same joint distribution as the residuals from regression on a different set L of k regressors. Let d′ denote the value of the statistic \ (zₓ-zₓ-₁) ^2/\ zₓ^2 calculated from these values. It is shown that for a suitable choice of L the distribution of d′ is the same as that of dₔ, the significance values of which are tabulated in 1.
J. Durbin (1970) studied this question.