Foundations of Linear and Generalized Linear Models

Appendix B Solution Outlines for Selected Exercises

Note: This appendix contains brief outlines of solutions and hints of solutions for at least a few exercises from each chapter. Many of these are extracts of solutions that were kindly prepared by Jon Hennessy for Statistics 244 at Harvard University in 2013.

Chapter 1

1. In the random component, set θ_i = μ_i, b(θ_i) = θ²_i/2, ϕ = σ², a(ϕ) = ϕ, and c(y_i, ϕ) = −y²_i/2ϕ − log (2πϕ). Use the identity link function.

2. 2. Hint: What is the range for a linear predictor, and what is the range of the identity link applied to a binomial probability or to a Poisson mean?

5. The predicted number of standard deviation change in y for a standard deviation change in x_i, adjusting for the other explanatory variables.

11. Taking ,

    

18. 2. Let . Then .
19. 1. For the model E(y_ij) = β₀ + β_i + γx_ij, let , , and
    2. (i) γ, because for each group it is a difference ...