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HW Solutions Stat 24

# HW Solutions Stat 24 - Chapter 8 MODELS FOR QUANTITATIVE...

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Chapter 8 MODELS FOR QUANTITATIVE AND QUALITATIVE PREDICTORS 8.4. a. ˆ Y =82 . 9357 1 . 18396 x + . 0148405 x 2 , R 2 = . 76317 b. H 0 : β 1 = β 11 =0 , H a : not both β 1 and β 11 =0 . MSR = 5915 . 31, MSE =64 . 409, F = 5915 . 31 / 64 . 409=91 . 8398, F ( . 95; 2 , 57)=3 . 15884 . If F 3 . 15884 conclude H 0 , otherwise H a . Conclude H a . c. ˆ Y h =99 . 2546, s { ˆ Y h } =1 . 4833, t ( . 975; 57) = 2 . 00247, 99 . 2546 ± 2 . 00247(1 . 4833), 96 . 2843 E { Y h }≤ 102 . 2249 d. s { pred } =8 . 16144, 99 . 2546 ± 2 . 00247(8 . 16144), 82 . 91156 Y h (new) 115 . 5976 e. H 0 : β 11 =0 , H a : β 11 6 =0 . s { b 11 } = . 00836, t = . 0148405 /. 00836 = 1 . 7759, t ( . 975; 57) = 2 . 00247. If | t |≤ 2 . 00247 conclude H 0 , otherwise H a . Conclude H 0 . Alternatively, SSR ( x 2 | x ) = 203 . 1, SSE ( x, x 2 ) = 3671 . 31, F = (203 . 1 / 1) ÷ (3671 . 31 / 57 )=3 . 15329, F ( . 95; 1 , 57 )=4 . 00987. If F 4 . 00987 conclude H 0 , otherwise H a . Conclude H 0 . f. ˆ Y = 207 . 350 2 . 96432 X + . 0148405 X 2 g. r X,X 2 = . 9961, r x,x 2 = . 0384 8.5. a. i : 1 2 3 . . . 58 59 60 e i : -1.3238 -4.7592 -3.8091 . . . -11.7798 -.8515 6.22023 b. H 0 : E { Y } = β 0 + β 1 x + β 11 x 2 , H a : E { Y } 6 = β 0 + β 1 x + β 11 x 2 .MSLF =62 . 8154, MSPE =66 . 0595, F =62 . 8154 / 66 . 0595 = 0 . 95 ,F ( .
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