Exercise 21

Spam filtering, Part I. 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.

1. 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.

   Variable Dropped	AIC
   None Dropped	1863.50
   to_ multiple	2023.50
   cc	1863.18
   attach	1871.89
   dollar	1879.70
   winner	1885.03
   inherit	1865.55
   password	1879.31
   format	2008.85
   re_ subj	1904.60
   exclaim_ subj	1862.76
   sent_ email	1958.18

   See the next page for part (b).

2. 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.

   Variable Dropped	AIC
   None Dropped	1862.41
   to_ multiple	2019.55
   attach	1871.17
   dollar	1877.73
   winner	1884.95
   inherit	1864.52
   password	1878.19
   format	2007.45
   re_ subj	1902.94
   sent_ email	1957.56