In SAS, which procedure is most appropriate for building a multivariate regression model when the number of predictors (p=500) greatly exceeds the number of observations (n=200)?
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Short Explanation and Infographic
Here's the deal — b is correct because when p > n, ordinary least squares (OLS) regression is underdetermined and produces infinitely many solutions with perfect fit and no generalization. PROC HPREG with SELECTION=LASSO applies L1 regularization that simultaneously performs variable selection and coefficient estimation, finding a sparse solution that generalizes well even in high-dimensional settings.
Full explanation below image
Full Explanation
B is correct because when p > n, ordinary least squares (OLS) regression is underdetermined and produces infinitely many solutions with perfect fit and no generalization. PROC HPREG with SELECTION=LASSO applies L1 regularization that simultaneously performs variable selection and coefficient estimation, finding a sparse solution that generalizes well even in high-dimensional settings. A is wrong because OLS with p > n is not uniquely solvable. C (PROC FACTOR) reduces dimensionality but principal components may not correspond to the most predictive features. D is wrong because while random forests handle high-dimensional data, they are not immune to p > n — they require choosing VARS_TO_TRY carefully.