sta108_handout7

sta108_handout7 - Handout 7 Simultaneous inference...

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Unformatted text preview: Handout 7 Simultaneous inference Simultaneous confidence intervals for β and β 1 : Simultaneous (1- α )100% confidence intervals for β and β 1 are given by β : b ± Bs ( b ) , β 1 : b 1 ± Bs ( b 1 ) , where B = t (1- α/ 4; n- 2). For the Housing data, we want to obtain simultaneous confidence intervals for β and β 1 . Recall that b = 28 . 981 ,s ( b ) = 8 . 5438 ,b 1 = 2 . 941 ,s ( b 1 ) = 0 . 5412 . Since α = 0 . 05, we have B = t (1- α/ 4; n- 2) = t (1- . 05 / 4;17) = t ( . 9875;17) = 2 . 4581 . Simultaneous 95% confidence intervals for β and β 1 are β : 28 . 941 ± (2 . 4581)(8 . 5438) ,i.e., 28 . 981 ± 21 . 002 , β 1 : 2 . 941 ± (2 . 4581)(0 . 5412) ,i.e., 2 . 941 ± 1 . 330 . Simultaneous confidence intervals for the mean response Two methods for constructing simultaneous (1- α )100% confidence intervals for the mean responses at g different X-values are ˆ Y h ± Bs ( ˆ Y h ) , where B = t (1- α 2 g ; n- 2) , [Bonferroni method] , ˆ Y h ± Ws ( ˆ Y h ) , where...
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sta108_handout7 - Handout 7 Simultaneous inference...

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