By Michael Kutner, Christopher Nachtsheim, John Neter, William Li

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**Additional info for Applied Linear Statistical Models 5th Edition - Instructor's Solutions Manual**

**Sample text**

5857 . . 0407 f. No g. 9905. 9905 conclude error variance constant, otherwise error variance not constant. Conclude error variance constant. 19. a. H0 : β1 = β2 = β3 = β4 = 0, Ha : not all βk = 0 (k = 1, 2, 3, 4). 4920. 4920 conclude H0 , otherwise Ha . Conclude Ha . P -value = 0+ b. 00000138) c. 20. 21. 22. a. Yes b. 2 No, yes, Yi = loge Yi = β0 + β1 Xi1 + β2 Xi2 + εi , where εi = loge εi c. Yes d. No, no e. 23. a. Q = (Yi − β1 Xi1 − β2 Xi2 )2 ∂Q = −2 (Yi − β1 Xi1 − β2 Xi2 )Xi1 ∂β1 ∂Q = −2 (Yi − β1 Xi1 − β2 Xi2 )Xi2 ∂β2 Setting the derivatives equal to zero, simplifying, and substituting the least squares estimators b1 and b2 yields: Yi Xi1 − b1 2 − b2 Xi1 Yi Xi2 − b1 Xi1 Xi2 − b2 Xi1 Xi2 = 0 2 Xi2 =0 and: b1 = 2 Yi Xi2 Xi1 Xi2 − Yi Xi1 Xi2 2 2 ( Xi1 Xi2 )2 − Xi1 Xi2 2 Yi Xi1 Xi1 Xi2 − Yi Xi2 Xi1 2 2 ( Xi1 Xi2 )2 − Xi1 Xi2 n 1 1 √ L= exp − 2 (Yi − β1 Xi1 − β2 Xi2 )2 2σ i=1 2πσ 2 It is more convenient to work with loge L: n 1 loge L = − loge (2πσ 2 ) − 2 (Yi − β1 Xi1 − β2 Xi2 )2 2 2σ ∂ loge L 1 = 2 (Yi − β1 Xi1 − β2 Xi2 )Xi1 ∂β1 σ ∂ loge L 1 = 2 (Yi − β1 Xi1 − β2 Xi2 )Xi2 ∂β2 σ Setting the derivatives equal to zero, simplifying, and substituting the maximum likelihood estimators b1 and b2 yields the same normal equations as in part (a), and hence the same estimators.

18. a. 19 a. x1 , x2 , x3 , x1 x2 b. 20. X3 , X5 , X6 in appendix. 21. 22. a. 871 1 b.

Conclude H0 . 0148405X 2 g. 0384 a. b. c. 8091 ... 22023 H0 : E{Y } = β0 + β1 x + β11 x2 , Ha : E{Y } = β0 + β1 x + β11 x2 . 87519. 87519 conclude H0 , otherwise Ha . Conclude H0 . 000337x3 H0 : β111 = 0, Ha : β111 = 0. 00324. 00324 conclude H0 , otherwise Ha . Conclude H0 . Yes. 01297. 01297 conclude H0 , otherwise Ha . Conclude H0 . Yes. 6. a. 81434 8-1 b. H0 : β1 = β11 = 0, Ha : not all βk = 0 (k = 1, 11). 6136. 6136 conclude H0 , otherwise Ha . Conclude Ha . P -value = 0+ c. 8. 0356 e. H0 : β11 = 0, Ha : β11 = 0.

### Applied Linear Statistical Models 5th Edition - Instructor's Solutions Manual by Michael Kutner, Christopher Nachtsheim, John Neter, William Li

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