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Solution to Tutorial 8

# Solution to Tutorial 8 - Solution to Tutorial 8 1(a Hard...

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Solution to Tutorial 8 1. (a) Hard hat: E ( Y ) = β 0 + β 2 + β 1 X 1 Bump hat: E ( Y ) = β 0 + β 3 + β 1 X 1 None: E ( Y ) = β 0 + β 1 X 1 (b) (1) H 0 : β 3 = 0; H a : β 3 = 0; (1) H 0 : β 3 = β 2 ; H a : β 3 = β 2 ; 2. (1) β 3 means the difference in the intercepts between M2 and M4 (2) β 4 β 3 is the difference in the intercepts between M2 and M3 (3) when all the other factors are fixed, the expected increment of Y as X 1 increase by one unit. (4) β 7 = 0 means there is no difference on the effect of X 1 on the response for M3 and M4. (5) β 5 β 6 is difference on the effect of X 1 on the response for M1 and M2. 3. See R-code 4. See R-code 5. a. X = 1 1 1 1 . . . 1 1 1 0 1 0 . . . 1 0 thus X X = n n 1 n 1 n 1 We have ( X X ) 1 = 1 n n 1 1 n n 1 1 n n 1 n ( n n 1 ) n 1

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