# STA314 Homework 1 solution

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1. 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. σ2 = Var(), is extremely high.
1. 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).
1. 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?
2. 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?