homework.2

# homework.2 - α 1 = 0. Compare your results. Comment on the...

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Homework 2 1. Assume you have a CRD with a treatments and 1 control so that n . = a +1 i =1 n i . Assume you are interested in the contrasts α i - α a +1 ,i = 1 ,...,a and hence interested in minimizing a i =1 V ( ¯ Y i. - ¯ Y a +1 . ). Simplify the expression as a function of σ 2 ; which values of n i minimize this expression? 2. (Estimability) Consider the following data set: Factor level 1 2 3 12 15 17 14 13 21 9 12 18 8 11 18 Write the normal equations for the unconstrained model (see slide 3 from the notes); simplify the equations by entering the actual values for n (the number of replications at each factor level), y .. (the grand sum), y 1 . (the sum of observations at factor level 1), etc. Find estimates for μ , μ + α 1 + α 2 , α 1 - 2 α 2 + α 3 under the constraint α i = 0. Estimate the same eﬀects under the constraint
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Unformatted text preview: α 1 = 0. Compare your results. Comment on the estimability of these eﬀects. 3. Problem 8.2. Analyze the data in SAS using a saturated full factorial model for the three factors, speed, stride, mass ; the response is vo2 (the SAS code on Yandell’s homepage is not necessarily relevant). Find an appropriate model by deleting unim-portant terms (but make sure your recommended model is hierarchical). Compute the contrast sum of squares for the stride main eﬀect by hand–conﬁrm that this equals the stride sum of squares from your output. Generate and interpret any relevant interaction plots. 1...
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## This note was uploaded on 10/01/2009 for the course STAT stat706 taught by Professor Johnm.grego during the Spring '08 term at South Carolina.

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