Homework 6

Chapter 6

Complete the following 6 problems:

1. Problem 6.1
   • For this and the next problem, you can submit a hand-written solution if you do not want to figure out how to typeset matrices / vectors using LaTeX.
2. Problem 6.2
3. Problem 6.5a-d
   • For part b, interpret both \(b_{1}\) and \(b_{2}\) in the context of the problem.
   • For part c, also plot a density plot with a rug plot.
   • For part d, also include the four-panel residual plot we used for simple linear regression.
4. Problem 6.10a-d
   • For part b, also plot a density plot with a rug plot.
   • For part c, also include the four-panel residual plot we used for simple linear regression.
   • For part d, a "time plot" is just a plot of residuals against the time index.
5. Problem 6.22
   • Hint: Consider whether you can transform either the predictors or the response to put the equation in the form \[W_{i} = \beta_{0} + \sum_{j = 1}^{p} \beta_{j} Z_{i, j} + \epsilon_{i}\] where \(W_{i} = g(Y_{i})\) and \(Z_{i, j} = h_{i}(X_{i, j})\).
6. Problem 6.25
   • Hint: Can you create a transformed response variable that already accounts for the contribution of \(X_{i, 2}\) in the regression equation?