$4.[12$ marks total$]$ Comparing Model Selection Methods $($a$)[6$ marks$]$ Explain the theoretical underpinnings of the forward selection, backward elimination, and stepwise selection methods. Discuss how these methods balance the trade$-$off between model complexity and goodness$-$of$-$fit. $($b$)[6$ marks$]$ Consider a scenario where you have a dataset with a large number of predictors. Discuss the potential pitfalls of using forward selection and backward elimination in this context. What are the advantages and disadvantages of using the stepwise selection method instead?