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Unformatted text preview: PSTAT 120C: Assignment # 8 Final Exam, June 13 8:00AM This questions are to help you study for the final exam, and it will not be collected. The solutions will be published on the June 8. 1. To see how problems arise when the numbers of observations are not the same in each group, consider the problem of estimating τ i . Assume that the observations y ijm are from b blocks of k treatments and r ij observations in the j th block and i th treatment. Consider an additive model without an interaction y ijm = μ + τ i + β j + σ ijm where ∑ i τ i = ∑ j β j = 0 and the errors ijm are iid N (0 , 1). ¯ y i ·· = 1 ∑ b j =1 r ij b X j =1 r ij X m =1 y ijm and ¯ y ··· = 1 ∑ k i =1 ∑ b j =1 r ij b X j =1 k X i =1 r ij X m =1 y ijm (a) First, assume that all the r i,j = r are the same. Show that ˆ τ i = ¯ y i ··- ¯ y ··· is an unbiased estimate of τ i . (b) Show that ˆ τ i is not necessarily an unbiased estimate if the r ij are different....
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- Spring '07
- #, 1 k, df SS MS, Total DF SS