HW Solutions Stat 22

HW Solutions Stat 22 - SSE ( F ) = 4 , 248 . 84, df F = 42,...

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Chapter 7 MULTIPLE REGRESSION – II 7.4. a. SSR ( X 1 ) = 136 , 366, SSR ( X 3 | X 1 )=2 , 033 , 566, SSR ( X 2 | X 1 ,X 3 )=6 , 674, SSE ( X 1 ,X 2 ,X 3 ) = 985 , 530, df : 1, 1, 1,48. b. H 0 : β 2 =0 , H a : β 2 6 =0 . SSR ( X 2 | X 1 ,X 3 )=6 , 674, SSE ( X 1 ,X 2 ,X 3 ) = 985 , 530, F =( 6 , 674 / 1) ÷ (985 , 530 / 4 8 )=0 . 32491, F ( . 95; 1 , 1 7 )=4 . 04265 . If F 4 . 04265 conclude H 0 , otherwise H a . Conclude H 0 . P -value = 0 . 5713. c. Yes, SSR ( X 1 )+ SSR ( X 2 | X 1 ) = 136 , 366+5 , 726 = 142 , 092, SSR ( X 2 )+ SSR ( X 1 | X 2 )= 11 , 394 . 9 + 130 , 697 . 1 = 142 , 092. Yes. 7.5. a. SSR ( X 2 )=4 , 860 . 26, SSR ( X 1 | X 2 )=3 , 896 . 04, SSR ( X 3 | X 2 ,X 1 ) = 364 . 16, SSE ( X 1 ,X 2 ,X 3 )=4 , 248 . 84, df :1 ,1 ,1 ,42 b. H 0 : β 3 =0 , H a : β 3 6 =0 . SSR ( X 3 | X 1 ,X 2 ) = 364 . 16, SSE ( X 1 ,X 2 ,X 3 )=4 , 248 . 84, F = (364 . 16 / 1) ÷ (4 , 248 . 84 / 42)=3 . 5997, F ( . 975; 1 , 42) = 5 . 4039. If F 5 . 4039 conclude H 0 , otherwise H a . Conclude H 0 .P -value = 0 . 065. 7.6. H 0 : β 2 = β 3 =0 , H a : not both β 2 and β 3 =0 . SSR ( X 2 ,X 3 | X 1 ) = 845 . 07 , SSE ( X 1 ,X 2 ,X 3 )=4 , 248 . 84, F = (845 . 07 / 2) ÷ (4 , 248 . 84 / 42)=4 . 1768 ,F ( . 975; 2 , 42) = 4 . 0327. If F 4 . 0327 conclude H 0 , otherwise H a . Conclude H a . P -value = 0 . 022. 7.9. H 0 : β 1 = 1 . 0, β 2 =0 ; H a : not both equalities hold. Full model: Y i = β 0 + β 1 X i 1 + β 2 X i 2 + β 3 X i 3 + ε i , reduced model: Y i + X
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Unformatted text preview: SSE ( F ) = 4 , 248 . 84, df F = 42, SSE ( R ) = 4 , 427 . 7 , df R = 44, F = [(4427 . 7 4248 . 84) / 2] (4 , 248 . 84 / 42) = . 8840, F ( . 975; 2 , 42) = 4 . 0327. If F 4 . 0327 conclude H , otherwise H a . Conclude H . 7.13. R 2 Y 1 = . 0431, R 2 Y 2 = . 0036, R 2 12 = . 0072, R 2 Y 1 | 2 = 0 . 0415, R 2 Y 2 | 1 = 0 . 0019, R 2 Y 2 | 13 = . 0067 R 2 = . 6883 7.14. a. R 2 Y 1 = . 6190, R 2 Y 1 | 2 = . 4579, R 2 Y 1 | 23 = . 4021 b. R 2 Y 2 = . 3635, R 2 Y 2 | 1 = . 0944, R 2 Y 2 | 13 = . 0189 7.17. a. Y = . 17472 X 1 . 04639 X 2 + . 80786 X 3 b. R 2 12 = . 0072, R 2 13 = . 0021, R 2 23 = . 0129 7-1...
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