Using the Studentized residuals ti to determine influential points in a multiple regression model with k independent variable and n observations and letting t_n-k-2 denote the upper critical value of a two-tail t test with a 0.10 level of significance, X_iis an influential point if A) $ \left|t_{i}\right|t_{n-k-1} $. C) $ \left|t_{i}\right|t_{n-k-2} $.

Question

Using the Studentized residuals ti to determine influential points in a multiple regression model with k independent variable and n observations and letting t_n-k-2 denote the upper critical value of a two-tail t test with a 0.10 level of significance, X_iis an influential point if A) $ \left|t_{i}\right|< t_{n-k-2} $. B) $ \left|t_{i}\right|>t_{n-k-1} $. C) $ \left|t_{i}\right|< t_{n-k-1} $. D) $ \left|t_{i}\right|>t_{n-k-2} $.

Quizplus · Accepted Answer

According to the definition of a studentized residual, ti measures the discrepancy between the observed value of the dependent variable and the predicted value based on the regression model, adjusted for the standard error of the estimate. Therefore, a large positive (or negative) value of ti indicates that the corresponding observation has a larger (or smaller) effect on the estimated regression coefficients and thus may be considered an influential point.

The critical value tn-k-2 is the value that separates the extreme end of the t-distribution with 0.10 probability in each tail. Therefore, if ti > tn-k-2, we can reject the null hypothesis that the corresponding observation has no effect on the regression coefficients at the 0.10 level of significance, and conclude that it is an influential point. Conversely, if ti < tn-k-2, we fail to reject the null hypothesis and cannot claim that the observation is influential.

Hence, the correct choice is D, ti > tn-k-2.

Using the Studentized Residuals Ti to Determine Influential Points in a Multiple