PROC GLMSELECT was used for building a model predicting the natural log of a baseball player's salary from certain performance and longevity statistics. The model used backward elimination using SBC…

Question

Options

• ARemoving nAtBat had the largest effect on the parameter estimate of nHits.
• BThe p-value for nAtBat was largest.
• CRemoving nAtBat yielded the largest improvement to SBC.
• DThe p-value for nAtBat was smallest.

• A
  6% (1)
• B
  88% (15)
• C
  6% (1)

Explanation

In backward elimination, variables are removed one at a time based on which variable contributes least to the model - and in standard backward elimination (when using a criterion like p-value to choose which variable to drop), the variable with the largest p-value (i.e., least statistically significant) is removed at each step, making B correct.

Why the distractors are wrong:

• A is wrong because backward elimination does not consider the effect on other variables' parameter estimates - that's a concern in collinearity analysis, not model selection.
• C is wrong because SBC is the stopping criterion (the model is kept if removing a variable doesn't improve SBC enough), not the step-by-step selection rule for which variable to drop; the variable removed is chosen by its p-value.
• D is wrong because the smallest p-value indicates the most significant variable - that's the last one you'd want to remove.

Memory tip: Think "backward = backwards significance" - you remove the variable that is least significant (largest p-value) at each step, stopping when no removal improves the criterion (SBC here). The p-value picks who leaves; SBC decides when to stop.

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