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The University of Hong Kong - STAT 3302solution3

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STAT 3302/4602 Suggested Solutions for Assignment 3 Question1. a) We test for total independence; that is, H0 : ρij = 0; for all i 6= j: The test statistic is T = −n log Λ = −n log jRj : T ... he p-value of this test can be approximated by P (T > t) ≈ P χ2 (ν) > t ; where ν = p(p−1)=2. In this problem, n = 24, p = 4. The calculated sample correlation matrix is R = 2664 1:0000 0:8990 0:9139 0:8948 · 1:0000 0:8276 0:7973 · · 1:0000 0:9432 · · · 1:0000 3775 ; and ν = 6. The computed test statistic is T = 137.4522; and the p-value≈ 0. There is no evidence that the cork borings are independent in all four directions. b) We test for equicorrelation; that is, H0 : ρij = ρ; for all i 6= j: The test statistic is Q = n − 1 λ^2 24 X i<j (rij − r¯)2 − µ¯ p X i =1 (¯ rk − r¯)23 5 ; with all notations refered to the lecture notes. The computed test statistic is Q = 16.2926 > CV = χ20:05 (5) = 11:0705. Therefore, there is no evidence that correlation between any two directions are the same. Alternatively, the same conclusion can be drawn since pvalue is 0:0061 < 5%. c) We test for an intraclass correlation model; that is, H0 : Σ = σ2 (1 − ρ) I + ρeeT : [Show More]

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