Refer to the exhibit. SAS output from the RSQUARE selection method, within the REG procedure, is shown. The top two models in each subset are given. Based on the exhibit, which statement is true?

Question

Options

• AThe AIC champion model is more parsimonious than the SBC champion.
• BThe SBC champion model is more parsimonious than the AIC champion.
• CThe R-Square champion model is the most parsimonious.
• DAdjusted R-Square and R-Square agree on the champion model.

• A
  9% (3)
• B
  69% (24)
• C
  3% (1)
• D
  20% (7)

Explanation

SBC imposes a larger penalty on model complexity than AIC. Specifically, SBC's penalty term is ln(n) × k versus AIC's 2k, where k is the number of parameters. Because ln(n) exceeds 2 for any sample size greater than ~7, SBC penalizes extra predictors more harshly - so its champion model will contain fewer variables and be more parsimonious than the AIC champion.

Why the distractors fail:

• A has the relationship backwards: AIC's softer penalty means it tolerates more complexity, so the AIC champion is less parsimonious than SBC's.
• C is the opposite of true - R-Square never decreases as predictors are added, so the RSQUARE champion is always the full model, making it the least parsimonious.
• D is unlikely to hold: Adjusted R-Square corrects for the number of predictors while R-Square does not, so they frequently disagree, especially when comparing models of different sizes.

Memory tip: Think "S > A" - SBC's penalty is Stricter, so it picks Smaller models. If you remember that SBC's penalty grows with sample size (ln n) while AIC's is fixed (2), the parsimony ordering follows naturally.

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