A Few Comments About Ch. 5 of Text

1. The last sentence of the 2nd paragraph on p. 198 isn't good! We don't apply the statistical learning method to the held out observations. Rather, the method is applied to the rest of the data (those observations not held out), and the fitted model that results is used to produce predicted response values for the held out observations (and by comparing these predicted values to the actual response values of the held out observations we can estimate the test error).
2. The model given by (5.5) on p. 206 is referred to as a quadratic model, but some would think a quadratic model would also include the interaction/product term as well. (Certainly a full 2nd-order model includes the interaction/product term, and to be more clear one could call the model given by (5.5) an additive 2nd-order model. (When there is more than one predictor, it may be best to avoid the phrase quadratic model, since it's a bit vague.))
3. In the investment example that starts on p. 209, I don't like that the variance is referred to as the risk. If we associate risk with the likelihood of losing money, a low-variance investment with a negative mean would be a very risky thing ... there may be little chance of making money with it. On the other hand, if an investment with a large variance also had a large mean then there may be little chance of losing money (even though the variance is high, provided that the mean is large enough).