Spam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several email variables for this problem: to multiple, cc, attach, dollar, winner, inherit, password, format, re subj, exclaim subj, and sent email. We won't describe what each variable means here for the sake of brevity, but .each is either a numerical or indicator variable.

(a) For variable selection, we fit the full model, which includes all variables, and then we also fit each model where we've dropped exactly one of the variables. In each of these reduced models, the AIC value for the model is reported below. Based on these results, which variable, if any, should we drop as part of model selection? Explain.

(b) Consider the following model selection stage. Here again we've computed the AIC for each leave-one- variable-out model. Based on the results, which variable, if any, should we drop as part of model selection? Explain.

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Variable Dropped None Dropped to_multiple CC attach dollar winner inherit password format re_subj exclaim_subj sent_email AIC 1863.50 2023.50 1863.18 1871.89 1879.70 1885.03 1865.55 1879.31 2008.85 1904.60 1862.76 1958.18