mont4e_sm_ch12_sec02 - Sections 12-2 12-19. a) n = 10, k =...

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Sections 12-2 12-19. a) n = 10, k = 2, p = 3, α = 0.05 0 ... : 2 1 0 = = = = k H β 0 : 1 j H for at least one j = = = = 8 . 104736 8 . 43550 1916 ' 4490 10 ) 1916 ( 6 . 371595 2 1 2 i i i i i yy y x y x y y X S [] 7 . 83 3 . 4406 4490 3 . 4406 10 1916 9 . 371511 9 . 371511 8 . 104736 8 . 43550 1916 126 . 1 713 . 3 055 . 171 ' ' ˆ 2 = = = = = = = R yy E R SS S SS SS y X 7 , 2 , 05 . 0 0 7 , 2 , 05 . 0 0 74 . 4 25 . 184 7 / 7 . 83 2 / 3 . 4406 f f f f p n SS k SS E R > = = = = 12-9
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Reject H 0 and conclude that the regression model is significant at α = 0.05. P-value = 0.000 b) 957 . 11 ˆ 2 = = = p n SS MS E E σ 229 . 0 ) 00439 . 0 ( 957 . 11 ˆ ) ˆ ( 11 2 1 = = = c se σβ 10199 . 0 ) 00087 . 0 ( 957 . 11 ˆ ) ˆ ( 22 2 2 = = = c se 0 : 1 0 = β H 0 2 = 0 : 1 1 H 0 2 21 . 16 229 . 0 713 . 3 ) ˆ ( ˆ 1 1 0 = = = se t 04 . 11 10199 . 0 126 . 1 ) ˆ ( ˆ 2 2 0 = = = se t 365 . 2 7 , 025 . 0 7 , 2 / = = t t α Reject H 0 , P-value < 0.001 Reject H 0 , P-value < 0.001 Both regression coefficients significant 12-20. 00 . 742 = yy S a) 0 : 2 1 0 = = H 0 : 1 j H for at least one j α = 0.01 () 45 . 56 55 . 685 742 55 . 685 4840 5548 . 5525 10 220 9965 36768 220 2532 . 0 0931 . 0 9122 . 1 ) ( ' ' ˆ 2 1 2 = = = = = = = = R yy E n i i R SS S SS n y y X SS 7 , 2 , 01 . 0 0 7 , 2 , 01 . 0 0 55 . 9 51 . 42 7 / 45 . 56 2 / 55 . 685 f f f f p n SS k SS E R > = = = = Reject H 0 and conclude that the regression model is significant at α = 0.01. P-value = 0.000121 0643 . 8 7 45 . 56 ˆ 2 = = = = p n SS MS E E 0254 . 0 ) 5 9799 . 7 ( 0643 . 8 ) ˆ ( 1 = = E se 12-10
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b) 0 : 1 0 = β H 0 : 1 1 H 67 . 3 0254 . 0 0931 . 0 ) ˆ ( ˆ 1 1 0 = = = se t 7 , 005 . 0 0 7 , 005 . 0 | | 499 . 3 t t t > = Reject H 0 and conclude that 1 is significant in the model at α = 0.01 P-value = 21 0 (( −< P ) ) t t = 2(1 - 0.996018) = 0.007964 c) 1 x is useful as a regressor in the model. 12-21. a) 82 . 4 : 0 1 = t P-value = 2(4.08 E-5) = 8.16 E-5 21 . 8 : 0 2 = t P-value = 291.91 E-8) = 3.82 E-8 98 . 0 : 0 3 = t P-value = 2 (0.1689) = 0.3378 b) 0 : 3 0 = H 0 : 3 1 H α = 0.05 98 . 0 0 = t 23 , 025 . 0 0 22 , 025 . 0 | | 074 . 2 t t t > / = Do not reject H . Here 0 3 x does not contribute significantly to the model. 12-22. a) 0 : 4 3 2 1 0 = = = = H H 1 at least one 0 j α = 0.05 7 , 4 , 05 . 0 0 7 , 4 , 05 . 0 0 12 . 4 08 . 10 f f f f > = = Reject H P-value = 0.005 0 b) α = 0.05 0 : 1 0 = H 0 2 = 0 3 = 0 4 = 0 : 1 1 H 0 2 0 3 0 4 71 . 2 0 = t 87 . 1 0 = t 37 . 1 0 = t 87 . 0 0 = t 365 . 2 7 , 025 . 0 , 2 / = = t t p n α 0257 . 0 0 | | t t > / for 2 , 3 and 4 Reject H 0 for 1 . 12-11
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12-23. a) 0 : 6 5 4 3 2 1 0 = = = = = = β H H 1 : at least one 0 14 , 6 , 05 . 0 0 14 , 6 , 05 . 0 14 , 6 , 0 848 . 2 53 . 19 f f f f f > = = = α Reject H 0 and conclude regression model is significant at α = 0.05 b) The t-test statistics for β 1 through β 6 are -0.45, -0.07, -3.42, 0.17, -2.90, 0.69. Because t 0.025,14 =-2.14, the regressors that contribute to the model at α =0.05 are etw and axle . 12-24. a) 0 : 0 = j H for all j 0 : 1 j H for at least one j 14 , 4 , 05 . 0 0 14 , 4 , 05 . 0 11 . 3 16 . 7 f f f f > = = Reject H 0 and conclude regression is significant at α = 0.05. P-value = 0.0023 b) 7792 . 0 ˆ = σ α = 0.05 t t np α /, . , . 2 025 14 2 145 = = H 02 0 : β= β 3 0 = β 4 0 = β 5 0 = H 12 0 : β≠ β 3 0 β 4 0 β 5 0 t 0 0 113 =− . t 0 383 = . t 0 191 = − . t 0 09 = − . || tt /> α 1 4 1 4 1 4 > α α 1 4 α Do not reject H 0 Reject H 0 Do not reject H 0 Do not reject H 0 All variables do not contribute to the model. 12-25. a) 0 : 3 2 1 0 = = = H H j 1 0 : for at least one j 16 , 3 , 05 . 0 0 16 , 3 , 05 . 0 34 . 3 828.31 f f f f > = = Reject H 0 and conclude regression is significant at α = 0.05 b) 2856 . 12 ˆ 2 = α = 0.05 α . 2 025 16 212 = = H 01 0 : β 2 0 = β 3 0 = H 11 0 : β 2 0 β 3 0 58 . 2 0 = t 84 . 1 0 = t 82 . 13 0 = t 16 , 025 . 0 0
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mont4e_sm_ch12_sec02 - Sections 12-2 12-19. a) n = 10, k =...

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