Because you are using DIST=NORMAL and LINK=ID, you can actually use PROC GLMSELECT to solve this problem (probably faster and provides more statistics).
At any rate, the answer to your question is that the HPGENSELECT procedure (and GLMSELECT, too) creates a macro variable that contains the names of the variables that are selected in the final model. You can reference the macro variable on the MODEL statement of other procedures (GLM, GENMOD,....) to obtain statistics for the final model.
If your model includes CLASS variables, you can't use PROC REG unless you also generate the design matrix. See the last example in the article.
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