mont4e_sm_ch11_sec05_06

mont4e_sm_ch11_sec05_06 - Sections 11-5 and 11-6 11-37...

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11-23 Sections 11-5 and 11-6 11-37 t α /2,n-2 = t 0.025,12 = 2.179 a) 95% confidence interval on β 1 . . 7423 . 1 . 9173 . 2 ) 2696 . 0 ( 179 . 2 3298 . 2 ) 2696 . 0 ( 3298 . 2 ) ˆ ( ˆ 1 12 , 025 . 1 2 , 2 / 1 ± ± ± β α t se t n b) 95% confidence interval on β 0 . . 3115 . 49 7145 . 46 ) 5959 . 0 ( 179 . 2 0130 . 48 ) ˆ ( ˆ 0 0 12 , 025 . 0 ± ± se t c) 95% confidence interval on μ when x 0 25 = . . 0477 . 43 ˆ 3293 . 41 ) 3943 . 0 ( 179 . 2 1885 . 42 ) ( 844 . 1 ) 179 . 2 ( 1885 . 42 ) ( ˆ ˆ 1885 . 42 ) 5 . 2 ( 3298 . 2 0130 . 48 ˆ 0 2 2 0 0 0 | 3486 . 25 ) 0714 . 3 5 . 2 ( 14 1 ) ( 1 2 12 , 025 . | | ± + ± + ± = = x Y S x x n x Y x Y xx t μ σ d) 95% on prediction interval when x 0 = . . 2513 . 45 1257 . 39 ) 4056 . 1 ( 179 . 2 1885 . 42 ) 1 ( 844 . 1 179 . 2 1885 . 42 ) 1 ( ˆ ˆ 0 348571 . 25 ) 0714 . 3 5 . 2 ( 14 1 ) ( 1 2 12 , 025 . 0 2 2 0 ± + + ± + + ± y t y xx S x x n It is wider because it depends on both the errors associated with the fitted model and the future observation. 11-38 t α /2,n-2 = t 0.005,18 = 2.878 a) () ) ˆ ( ˆ 1 18 , 005 . 0 1 se t ± 0055542 . 0 0027682 . 0 ) 000484 . 0 )( 878 . 2 ( 0041612 . 0 1 ± b) ) ˆ ( ˆ 0 18 , 005 . 0 0 se t ± 447728 . 0 212250 . 0 ) 04095 . 0 )( 878 . 2 ( 3299892 . 0 0 ± c) 99% confidence interval on μ when xF 0 85 = D .
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11-24 7431497 . 0 ˆ 6242283 . 0 0594607 . 0 683689 . 0 ) ( 00796 . 0 ) 878 . 2 ( 683689 . 0 ) ( ˆ ˆ 683689 . 0 ˆ 0 2 2 0 0 0 | 6 . 33991 ) 9 . 73 85 ( 20 1 ) ( 1 2 18 , 005 . | | ± + ± + ± = x Y S x x n x Y x Y xx t μ σ d) 99% prediction interval when F x D 90 0 = . 947256 . 0 420122 . 0 263567 . 0 7044949 . 0 ) 1 ( 00796 . 0 878 . 2 7044949 . 0 ) 1 ( ˆ ˆ 7044949 . 0 ˆ 0 6 . 33991 ) 9 . 73 90 ( 20 1 ) ( 1 2 18 , 005 . 0 0 2 2 0 ± + + ± + + ± = y t y y xx S x x n 11-39 048 . 2 28 , 025 . 0 2 , 2 / = = t t n α a) 95% confidence interval on 1 ˆ β 198 . 15 ˆ 106 . 10 ) 243 . 1 ( 048 . 2 652 . 12 ) 243 . 1 ( 652 . 12 ) ˆ ( ˆ 1 5 , 025 . 0 1 2 , 2 / 1 ± ± ± t se t n b) 95% confidence interval on 0 200 . 13 ˆ 316 . 24 ) 159 . 9 ( 048 . 2 558 . 5 ) 159 . 9 ( 558 . 5 ) ˆ ( ˆ 0 5 , 025 . 0 0
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This note was uploaded on 10/12/2009 for the course IND E 315 taught by Professor Kailashkapur during the Spring '09 term at University of Washington.

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mont4e_sm_ch11_sec05_06 - Sections 11-5 and 11-6 11-37...

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