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HW Solutions Stat 10

HW Solutions Stat 10 - 2.28 a Yh = 84.9468 scfw_Yh =...

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2.28. a. ˆ Y h = 84 . 9468, s { ˆ Y h } = 1 . 05515, t ( . 975; 58) = 2 . 00172, 84 . 9468 ± 2 . 00172(1 . 05515), 82 . 835 E { Y h } ≤ 87 . 059 b. s { Y h (new) } = 8 . 24101, 84 . 9468 ± 2 . 00172(8 . 24101), 68 . 451 Y h (new) 101 . 443 c. W 2 = 2 F ( . 95; 2 , 58) = 2(3 . 15593) = 6 . 31186, W = 2 . 512342, 84 . 9468 ± 2 . 512342(1 . 05515), 82 . 296 β 0 + β 1 X h 87 . 598, yes, yes 2.29. a. i : 1 2 . . . 59 60 Y i ˆ Y i : 0.823243 -1.55675 . . . -0.666887 8.09309 ˆ Y i ¯ Y : 20.2101 22.5901 . . . -14.2998 -19.0598 b. Source SS df MS Regression 11,627.5 1 11,627.5 Error 3,874.45 58 66.8008 Total 15,501.95 59 c. H 0 : β 1 = 0, H a : β 1 = 0. F = 11 , 627 . 5 / 66 . 8008 = 174 . 0623, F ( . 90; 1 , 58) = 2 . 79409. If F 2 . 79409 conclude H 0 , otherwise H a . Conclude H a . d. 24.993% or .24993 e. R 2 = 0 . 750067, r = 0 . 866064 2.42. b. .95285, ρ 12 c. H 0 : ρ 12 = 0, H a : ρ 12 = 0. t = ( . 95285 13) / 1 ( . 95285) 2 = 11 . 32194, t ( . 995; 13) = 3 . 012. If | t | ≤ 3 . 012 conclude H 0 , otherwise H a . Conclude H a . d. No 2.44. a. H 0 : ρ 12 = 0, H a : ρ 12 = 0. t = ( . 87 101) / 1 ( . 87) 2 = 17 . 73321, t ( . 95; 101) = 1 . 663. If | t | ≤ 1 . 663 conclude H 0 , otherwise H a . Conclude H a . b. z = 1 . 33308, σ { z } = . 1, z ( . 95) = 1 . 645, 1 .
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