Which characteristic of Studentized residuals indicate potential outliers?

Question

Options

• AOnly studentized residuals greater than negative two
• BOnly studentized residuals less than negative two or greater than two
• COnly studentized residuals greater than two
• DOnly studentized residuals less than two and greater than negative two

• A
  8% (3)
• B
  3% (1)
• C
  86% (32)
• D
  3% (1)

Explanation

There appears to be an error in the marked correct answer. Statistically, B is the correct answer, not C.

Studentized residuals indicate potential outliers when their absolute value exceeds 2 - meaning values less than -2 or greater than 2. Outliers can appear on either end of the distribution, so both tails must be considered; restricting detection to only one side (as C and A do) misses half the possible outliers. Option D is wrong because it describes the normal range (between -2 and 2), which is where non-outliers fall. Option A is wrong because it only flags the negative tail. Option C is wrong because it only flags the positive tail - a value of -3.5 is just as much an outlier as +3.5.

Memory tip: Think of the rule as a two-sided absolute value: |Studentized residual| > 2 raises a flag. If you can't take the absolute value mentally, picture a number line - anything outside the "safe zone" of [-2, 2] is suspect, and that means both extremes.

Note to exam taker: If your source material marks C as correct, it may reflect a textbook error or a poorly worded question. Double-check your course notes, because the universally accepted rule in regression diagnostics captures both tails (answer B).

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