MidtermIans - Stat 511 Midterm I solutions 24 February 2011...

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Unformatted text preview: Stat 511 Midterm I solutions 24 February 2011 1. (a) X = 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 0 If you only wrote out three rows, you’re describing a study with 3 subjects, not this study with 6 subjects. (b) In terms of model parameters, the four cell means and the column marginal means are: Study time Absent Present 1 min μ + α 1 + β 1 μ + α 1 + β 2 5 min μ + α 2 + β 1 μ + α 1 + β 2 ave. μ + ( α 1 + α 2 ) / 2 + β 1 μ + ( α 1 + α 2 ) / 2 + β 2 Hence the main effect of refresher is the column mean for absent - column mean for present = β 1- β 2 . Yes, this is estimable. One possible linear combination of rows is obs. 2 - obs. 3, which has the desired expected value. Note: A few of you used a different definition of the average difference between present and absent. I accepted that. But, please realize that is not the customary definition of main effect. (c) Yes, this is estimable. One possible linear combination of rows is obs. 5 - obs. 2 + obs. 3., i.e. μ 5 A- ( β 1- β 2 ). 2. (a) 15 × 15. You can work this out in at least two ways: P X = X ( X X )- X , X is 15 × 8, and work out the dimension of the product. P X maps a vector of 15 observations into a vector of 15 expected values. Hence it has to have 15 columns for the matrix multiplication to be conformable. And it has to have 15have 15 columns for the matrix multiplication to be conformable....
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This note was uploaded on 02/11/2012 for the course STAT 511 taught by Professor Staff during the Spring '08 term at Iowa State.

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MidtermIans - Stat 511 Midterm I solutions 24 February 2011...

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