hw6soln - STAT 4220 HW6 Solution 1 Problem 1 A H I D G F B...

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STAT 4220 HW6 Solution 1 Problem 1 A B C D E F G H I H D F G C I E B A I G E B H A C F D D C H F A E B I G G E B H I D F A C F I A C B G H D E B H G I D C A E F C A D E F H I G B E F I A G B D C H 9 6 8 4 3 7 1 5 2 5 4 7 1 8 2 3 6 9 2 1 3 6 5 9 8 7 4 4 8 5 7 9 3 6 2 1 1 3 6 5 2 4 7 9 8 7 2 9 8 6 1 5 4 3 6 5 1 2 4 8 9 3 7 8 9 4 3 7 5 2 1 6 3 7 2 9 1 6 4 8 5 1
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2 Problem 2 Consider the following model: y i jk = μ + α i + β j + γ k + ε i jk 1 i I , 1 j J , 1 k K , where ε i jk ’s are i.i.d. Normal ( 0 , σ 2 ) . This is the three-way layout model with no interactions. (a) (2 points) How many degrees of freedom are there for the residual sum of squares? ( IJK - 1 ) - ( I - 1 ) - ( J - 1 ) - ( K - 1 ) = IJK - I - J - K + 2 (b) (2 points) Write down the expression for the estimate of σ 2 . ˆ σ 2 = I i = 1 J j = 1 K k = 1 ( y i jk - ¯ y i .. - ¯ y . j . - ¯ y .. k + y ... ) 2 ( IJK - I - J - K + 2 ) (c) (2 points) If the model above had included two-way interaction terms ( αβ ) i j , ( αγ ) ik , ( βγ ) jk , write down the estimates.
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