# HW7_sol - 4.18 4.18 B1B2=1234*2345=15 So the interaction 15...

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4.18 4.18 B 1 B 2 = 1234 * 2345 = 15 . So the interaction 15 15 is confounded with the block effect B 1 B 2 and the ability to estimate 15 15 is sacrificed. The main effect 5 will not be affected. 4.19. (a) 23457 , 1457 , 2367 , 123456 167 , 456 , 123 : 3 2 1 3 2 3 1 2 1 3 2 1 1 = = = = = = = B B B B B B B B B B B B b ) 0 , 1 , 1 , 2 , 3 , 0 , 0 ( ) ( 1 = b g . Order of estimability=2. (b) From Table 4A.1, ) 0 , 0 , 0 , 7 , 0 , 0 , 0 ( ) ( 2 = b g . Order of estimability=3. (c) In the second scheme all the 3 factor interactions are estimable, whereas in the first scheme the interactions 123, 456, and 167 are confounded with block effects. 4.21. (a) Code the blocking variable as (-1,-1,1,1,-1,1,-1,1). The correlations of the blocking variable with the 7 columns are, 1 2 3 12 12 13 23 23 123 0 0.5 0.5 -0.5 0.5 0 0 Because the correlation coefficients are neither 1 nor –1, the blocking variable is not identical to any of the columns and therefore is not confounded with any of the
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