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Intro to Statistical Learning (2nd Ed), Solution to Problem 6.8A | Model-Selection Methods

6.8A In this exercise, we will generate simulated data, and will then use this data to perform best subset selection. (a) Use the rnorm() function to generate a predictor X of length n = 100, as well as a noise vector ϵ of length n = 100. (b) Generate a response vector Y of length n = 100 according to the model Y=β0+β1X+β2X2+β3X3+ϵ , where β0 , β1 , β2 , and β3 are constants of your choice. (c) Use the regsubsets() function to perform best subset selection in order to choose the best model containing the predictors X,X2,...,X10 . What is the best model obtained according to Cp , BIC , and adjusted R2 ? Show some plots to provide evidence for your answer, and report the coefficients of the best model obtained. Note you will need to use the data.frame() function to create a single data set containing both X and Y . (d) Repeat (c), using forward stepwise selection and also using backwards stepwise selection. How does your answer compare to the results in (c)? (e) Now fit a lasso model to the simulated data, again using X,X2,...,X10 as predictors. Use cross-validation to select the optimal value of λ. Create plots of the cross-validation error as a function of λ. Report the resulting coefficient estimates, and discuss the results obtained. (f) Now generate a response vector Y according to the model Y=β0+β7X7+ϵ , and perform best subset selection and the lasso. Discuss the results obtained. Colab (R): https://colab.research.google.com/dri... My GitHub (R): https://github.com/nicklausmillican/I... My GitHub (Python): https://github.com/nicklausmillican/I... Download Book: https://www.statlearning.com/ Authors' Lectures (R):    • Statistical Learning with R   Authors' Lectures (Python):    • Statistical Learning with Python