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HW #5 solution

HW #5 solution - STAT 420 Spring 2007 Homework#5 From the...

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Unformatted text preview: STAT 420 Spring 2007 Homework #5 From the textbook: 5.6 a) x y x x- y y- ( ) 2 x x- ( ) ( ) y y x x-- ( ) 2 y y- 2 20 –2 –12.2 4 24.4 148.84 3 27 –1 –5.2 1 5.2 27.04 4 33 0 0.8 0 0 0.64 5 38 1 5.8 1 5.8 33.64 6 43 2 10.8 4 21.6 116.64 20 161 0 0 10 57 326.8 SXX SXY SYY 5 20 = x = 4, 5 161 = y = 32.2. 10 57 SXX SXY ˆ = = β = 5.7 . x y ˆ ˆ β α- = = 32.2 – 5.7 ⋅ 4 = 9.4 . b) In class we showed that since ( ) ( ) x x y x x y x y i i i i- + = +- = + = ˆ ˆ ˆ ˆ ˆ ˆ β β β β α , SSR = ( ) ( ) ( ) 2 2 2 2 2 2 ˆ ˆ ˆ ˆ β β β =- =- =- & & & x x x x y y i i i SXX = 324.9. OR x y y ˆ e e 2 2 20 20.8 -0.8 0.64 3 27 26.5 0.5 0.25 4 33 32.2 0.8 0.64 5 38 37.9 0.1 0.01 6 43 43.6 -0.6 0.36 20 161 161 0 1.9 SSE Source SS df MS F Regression 324.9 1 324.9 513 Residual (Error) 1.9 3 0.63333 Total 326.8 4 F 0.05 ( 1, 3 ) = 10.13. Reject H : β = 0. ( p-value ≈ 0.000188 ) 5.7 a) x y x x- ( ) y y- ( ) 2 x x- ( ) ( ) y y x x-- ( ) 2 y y- 10 15 0 3 0 0 9 5 9 –5 –3 25 15 9 7 3 –3 –9 9 27 81 19 25 9 13 81 117 169 11 7 1 –5 1 -5 25 8 13 –2 1 4 -2 1 60 72 0 0 120 152 294 6 60 = = & n x x = 10 6 72 = = & n y y = 12 ( ) ( ) ( ) 15 19 120 152 2 & ˆ = = &- &-- = x x y y x x ≈ 1.266667 ....
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HW #5 solution - STAT 420 Spring 2007 Homework#5 From the...

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