$($a$)$ Perform the following four model selection methods and compare their best models. Comment on how are they different or similar in terms of sele ted variables in the final model. No need to interpret outputs.

Stepwise selection with $0\mathrm{.}01$ p$-$value criteria for both entry and stay

Forward selection with $0\mathrm{.}01$ p$-$value criteria for entry

Backward selection with $0\mathrm{.}01$ p$-$value criteria for a stay

Adjusted R$-$squared criteria

NOTE: R output from Backward selection displays variables "removed" from each step.

Answer the following questions from the best model determined by Stepwise selection with $0\mathrm{.}01$ p $-$value criteria.