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Unformatted text preview: Stat 511 Homework 4 Spring 2011 Due: 11am, Monday Feb 7 The week after this we will use the eigen decomposition of a variancecovariance matrix, specifically the concept of an inverse square root matrix. Please look at pages 78  107 Ken Koehler’s notes. p 89 discusses inverse square root matrices. 1. Last HW had the β vector and X matrix for a very messed up experiment. They were: μ α 1 α 2 α 3 α 4 α 5 α 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1) The X matrix and data, y , are in the file ’messedup.txt’ on the class web site. (a) Estimate a 90% confidence interval for α 4 ( α 2 + α 5 + α 6 ). (NB. α 4 ( α 2 + α 5 + α 6 ) is estimable). (b) Test Ho: α 1 = 0. (N.B. α 1 is estimable). Report your test statistic and pvalue. (c) Test Ho: α 1 = 0 , α 2 = 0 , α 4 = 0 , and α 5 + α 6 = 0. (N.B. This hypothesis is testable) Report your test statistic and pvalue. 2. This problem is based on a research proposal I read last week. A researcher on campus is studying whether monkeys are selective in what they eat. One of the major items in the dietstudying whether monkeys are selective in what they eat....
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 Spring '08
 Staff
 Covariance, Normal Distribution, Variance, researcher, class web site, measurement variance, soup Old Red.

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