Spam filtering, Part II. In Exercise 9.21, we encountered a data set where we applied logistic regression to aid in spam classification for individual emails. In this exercise, we’ve taken a small set of these variables and fit a formal model with the following output:
| Estimate | Std. Error | z value | Pr(z) | |
| (Intercept) | -0.8124 | 0.0870 | -9.34 | 0.0000 |
| to_ multiple | -2.6351 | 0.3036 | -8.68 | 0.0000 |
| winner | 1.6272 | 0.3185 | 5.11 | 0.0000 |
| format | -1.5881 | 0.1196 | -13.28 | 0.0000 |
| re_ subj | -3.0467 | 0.3625 | -8.40 | 0.0000 |
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Write down the model using the coefficients from the model fit.
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Suppose we have an observation where , , , and . What is the predicted probability that this message is spam?
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Put yourself in the shoes of a data scientist working on a spam filter. For a given message, how high must the probability a message is spam be before you think it would be reasonable to put it in a spambox (which the user is unlikely to check)? What tradeoffs might you consider? Any ideas about how you might make your spam-filtering system even better from the perspective of someone using your email service?