Question

Suppose that Case i is an outlier in the sense that an amount δ is added to its expected value. Let u i be the unit vector with 1 in the ith position and zeros elsewhere and write the revised model is y = Xβ + δu i + e. Weisberg (1985) calls this the mean shift outlier model. Using standard methodology, develop the test statistic for the hypothesis, H 0 : δ = 0 and show that the resulting t-statistic, with n − m− 2 degrees of freedom, is equivalent to the Studentized residual. Hint: Use the ideas developed in the discussion of added-variable plots to show that ˆ δ = r i(i) and that the residual sum of squares is given by RSS (i)

Suppose that Case i is an outlier in the sense that an amount 5 is added to its expected value. Let u i be the unit vector with 1 in the ith position and zeros elsewhere and write the revised model is Weisberg (1985) calls this the mean shift outlier model. Using standard methodology, develop the test statistic for the hypothesis, H 0: δ-0 and show that the resulting t-statistic, with n -m -2 degrees of freedom, is equivalent to the Studentized residual. Hint: Use the ideas developed in the discussion of added-variable plots to show that ^ δ-r i(i) and that the residual sum of squares is given by RSS (i)

Answer 1

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