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Foundations of Linear and Generalized Linear Models by Alan Agresti

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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 θi = μi, bi) = θ2i/2, ϕ = σ2, a(ϕ) = ϕ, and c(yi, ϕ) = −y2i/2ϕ − log (2πϕ). Use the identity link function.

    1. 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?
  1. The predicted number of standard deviation change in y for a standard deviation change in xi, adjusting for the other explanatory variables.

  1. Taking ,

    numbered Display Equation
    1. Let . Then .
    1. For the model E(yij) = β0 + βi + γxij, let , , and
    2. (i) γ, because for each group it is a difference ...

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