Problem 1 Consider the prostate cancer surgery data from the faraway library in R. The variable 1psa is a measurement of prostate specific antigen on the log scale. Treat 1psa as the response and all the other variables in the data frame as potential predictors. a) Using backward elimination testing and an alpha cutoff of 0.10, find the best model according to this procedure. Be sure to include the steps and the final model. Answer: b) Use backward selection in a stepwise algorithm to find the best model according to the AIC criterion. Be sure to include the steps and the final model. Answer: c) Use stepwise selection with the "both" option to find the best model according to the BIC criterion. Include the steps and the final model. Answer: d) Use the leaps and bounds algorithm to determine the model with smallest residual sums of squares for each model size from 2 to the maximum possible based on the number of columns in the data frame. Display the results by showing "which" variables were selected for model sizes 2, 3, etc. Answer:e) Using the results from d) and further calculations, graph BIC versus model size for the models selected in part d). Which model is the overall best model according to BIC