Pstat 127 HW4.pdf - PSTAT 127 Winter 2018 Homework 4 Due in lecture February 14 No late homework Throughout this homework you may state and use any

Pstat 127 HW4.pdf - PSTAT 127 Winter 2018 Homework 4 Due in...

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PSTAT 127, Winter 2018, Homework 4 - Due in lecture February 14. No late homework. Throughout this homework, you may state and use any results you know from pre-requisite classes (PSTAT 120A, 120B, 126) as well as lectures. Clear working must be shown to receive credit. There are three questions for which solutions must be handed in - in addition to the first item which is a reading assignment. 1. Reading: nothing needs to be handed in for this reading - but you are responsible for the material in it.(a) Review your PSTAT 126 material and R code, including the residual diagnostics you studied in PSTAT 126, the nested F test andthe marginal T tests in the ANOVA table.(b) Read chapter 1 pages 1 through 17 (up to, but not including Robust Regression) of the textbook and run all the R code yourselves.Make sure you understand the results. Ask if questions.(c) In the textbook, read chapter 2 pages 25 through 40 (up to, but not including Goodness of Fit in this week’s reading assignment).Run all the corresponding R code yourselves. Make sure you understand the results. Ask if questions. However, I don’t expect youto be able to derive the explicit displayed formula for D provided on page 33, as long as you understand how to use the deviancevalues in testing nested models at this stage.2. SupposeYihas density in the exponential family form used in class, fori∈ {1, . . . , n}. Assume the formulae I wrote on the board inlecture forE(Yi)andV ar(Yi)for a random variable following such an exponential family distribution, namely thatE(Yi) =b0(θi) =∂ b(θi)∂θiandV ar(Yi)=ai(φ)b00(θi) =ai(φ)2b(θi)∂θ2i.

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