Refer to the example and program on all-subsets regression from Section 5.1.3 with the placekicking data set. Run the genetic algorithm using AICc and include pairwise interactions in the model with marginality = TRUE (no pairwise interactions between variables are considered unless both variables are in the model as well). Use set.seed(837719911) prior to using glmulti(). Note that the function will take a few minutes to run.

(a) Report the best model and its AICc. Compare this to the AICc from the best model found without interactions. Do the interactions improve the model?

(b) How many models are within 2 AICc units of the best model? What does this imply about our confidence in having found the best model?

(c) How many generations did the algorithm produce?

(d) Rerun the algorithm, but do not rerun the set.seed() code. This will cause the algorithm to use different random numbers. Re-examine the same items as requested in (a) - (c) and compare to what you obtained initially.

(e) Rerun the algorithm and the original set.seed() code, increasing the mutation probability to 0.01 (add the argument value mutrate = 0.01; the default is 0.001). Report the results as requested in parts (a) - (c). Are the results any different from those in (a) - (c)? Note that in this context, increasing the mutation probability increases the probability that a variable is randomly added to or removed from a model. In general, increasing the mutation probability can make the algorithm better at finding the top models, but can increase run time.