[Solved] STATS202 Homework1

Homework problems are selected from the course textbook: An Introduction to Statistical Learning.

Problem 1

Chapter 2, Exercise 2 (p. 52).

Problem 2

Chapter 2, Exercise 3 (p. 52).

Problem 3

Chapter 2, Exercise 7 (p. 53).

Problem 4

Chapter 10, Exercise 1 (p. 413).

Problem 5

Chapter 10, Exercise 2 (p. 413).

Problem 6

Chapter 10, Exercise 4 (p. 414).

Problem 7

Chapter 10, Exercise 9 (p. 416).

Problem 8

Chapter 3, Exercise 4 (p. 120).

Problem 9

Chapter 3, Exercise 9 (p. 122). In parts (e) and (f), you need only try a few interactions and transformations.

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Problem 10

Chapter 3, Exercise 14 (p. 125).

Problem 11

Let x₁,,x_n be a fixed set of input points and, where with and

. Prove that the MSE of a regression estimate ffit to (x₁,y₁),,(x_n,y_n) for a random test point decomposes into variance, square bias, and irreducible error components.

Hint: You can apply the bias-variance decomposition proved in class.

Problem 12

Consider the regression through the origin model (i.e. with no intercept):

(1)

• (1 point) Find the least squares estimate for .
• (2 points) Assume such that and Var. Find the standard error of the estimate.
• (2 points) Find conditions that guarantee that the estimator is consistent. b. An estimator _n of a parameter is consistent if ^p , i.e. if the estimator converges to the parameter value in probability.

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