## Description

**1**. For each of parts (a) through (d), indicate whether we would generally expect the performance of a ﬂexible statistical learning method to be better or worse than an inﬂexible method. Justify your answer.

- The sample size
*n*is extremely large, and the number of predictors*p*is small. - The number of predictors
*p*is extremely large, and the number of observations*n*is small. - The relationship between the predictors and response is highly non-linear.
- The variance of the error terms, i.e. σ
^{2}= Var(), is extremely high.

**2**. We now revisit the bias-variance decomposition.

- Provide a sketch of typical (squared) bias, variance, training error, test error, and Bayes (or irreducible) error curves, on a single plot, as we go from less ﬂexible statistical learning methods towards more ﬂexible approaches. The x-axis should represent the amount of ﬂexibility in the method, and the y-axis should represent the values for each curve. There should be ﬁve curves. Make sure to label each one.
- Explain why each of the ﬁve curves has the shape displayed in part (a).

**3**. What are the advantages and disadvantages of a very ﬂexible (versus a less ﬂexible) approach for regression or classiﬁcation? Under what circumstances might a more ﬂexible approach be preferred to a less ﬂexible approach? When might a less ﬂexible approach be preferred?**4**. Describe the diﬀerences between a parametric and a non-parametric statistical learning approach. What are the advantages of a parametric approach to regression or classiﬁcation (as opposed to a nonparametric approach)? What are its disadvantages?