Evaluate the predictive optimism of the final model you obtained in Problem 6.4 using h-fold cross-validation, leave-one-out crossvalidation, bootstrapping, or a similar technique. List the predictors...

Evaluate the predictive optimism of the final model you obtained in Problem 6.4 using h-fold cross-validation, leave-one-out crossvalidation, bootstrapping, or a similar technique. List the predictors you obtained in the final model in Problem 6.4, name the technique you used to evaluate predictive optimism, and describe the results of the predictive optimism evaluation.

Problem 6.4

Data analysts are often confronted with a set of few measured independent variables and are to choose the “best” predictive equation. Not infrequently, such an analysis consists of taking the measured variables, their pairwise cross-products, and their squares; throwing the whole lot into a computer; and using a variable selection method (usually stepwise regression) to select the best model. Using the data for the urinary calcium study in Problems 2.6, 3.8, 5.5, and 6.4 (data in Table D-5, Appendix D), do such an analysis using several variable selection methods. Do the methods agree? Is there a problem with multicollinearity, and, if so, to what extent can it explain problems with variable selection? Does centering help? Is this “throw a whole bunch of things in the computer and stir” approach useful?