Midterm.06 - Midterm 1 Consider a CRD on the quantitative factor X with 80 90 and 100 We are interested in the linear contrast L = c 1 E Y | X = 60

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Unformatted text preview: Midterm 1. Consider a CRD on the quantitative factor X with levels 60, 70, 80, 90 and 100. We are interested in the linear contrast L = c 1 E ( Y | X = 60)+ .. . + c 5 E ( Y | X = 100) with contrast coefficients c = (- 4 ,- 2 , , 2 , 4 ). (a) Under the linear model E ( Y | X ) = β + β 1 X , show that a test of L = 0 is equivalent to a test of β 1 = 0. (b) Analyze the data in the pilot study below. Is the linear contrast L significant? Report on lack of fit as well. (c) Write the non-centrality parameter for the contrast L as a function of β 1 . As- suming σ = 10, construct a power curve (as a function of n ) for β 1 = . 5. How many replications would we need to detect β 1 = . 5 with 80% power? X Y 60 27.2, 23.9, 18.5 70 32.3, 29.7, 1.3 80 40.2, 37.8, 19.6 90 19.4, 37.1, 32.7 100 36.0, 29.0, 37.1 2. Consider the following 2 4 unreplicated factorial design: Run Response Run Response (1) 7. 2 d 12.9 a 6.5 ad 19.4 b 6.2 bd 12.4 ab 4.6 abd 17.5 c 9.5 cd 16.2 ac 4.1 acd 18.9 bc 5.8 bcd...
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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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Midterm.06 - Midterm 1 Consider a CRD on the quantitative factor X with 80 90 and 100 We are interested in the linear contrast L = c 1 E Y | X = 60

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