Which SAS program will best identify influential observations in a multiple regression application?

Question

Options

• Aproc reg data = SASUSER.RETAIL; model Purchase = Gender Age Income / lackfit; run;
• Bproc reg data = SASUSER.RETAIL; model Purchase = Gender Age Income / vif; run;
• Cproc reg data = SASUSER.RETAIL plots(only)=(RSTUDENTBYPREDICTED); model Purchase = Gender Age Income; run;
• Dproc reg data = SASUSER.RETAIL plots(only)=(COOKSD); model Purchase = Gender Age Income; run;

• A
  17% (4)
• B
  4% (1)
• C
  71% (17)
• D
  8% (2)

Explanation

Option C is correct because the RSTUDENTBYPREDICTED plot displays externally studentized residuals (which account for the observation's own influence on the model) against predicted values, making it the standard diagnostic tool for visually identifying influential observations - those with unusually large residuals that disproportionately affect the regression results.

Why the distractors are wrong:

• A (lackfit) tests whether the model has a lack of fit against a pure error estimate - it evaluates model adequacy, not individual observation influence.
• B (vif) computes Variance Inflation Factors, a diagnostic for multicollinearity among predictors, not for spotting influential data points.
• D (COOKSD) plots Cook's Distance, which does measure influence, but it summarizes influence as a single scalar per observation; the RSTUDENTBYPREDICTED scatterplot is preferred in this context because it simultaneously reveals both the direction and magnitude of residual influence across the range of predicted values.

Memory tip: Think of the RSTUDENT in option C as "Rogue Student" - a student whose answers (residuals) are so far from the class norm that they skew the teacher's grading curve (the regression model). When you need to find those rogue students visually, you plot them against what the model predicted.

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