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Solution_two

# Solution_two - Solutions to Problem Set#2 1 1 1 1 α β β...

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Unformatted text preview: Solutions to Problem Set #2 1. 1 1 1 ) ( ) ( α β β β β β β + + = + + = + + = x u E x y E u x y Let . ) ( ) ( 1 * 1 * * 1 * * 1 * 1 x x u E x y E u x u x y β β α α β β β β β β α β α β + = − + + = + + = + + = − + + + = 2. (i) u x y + + = 1 β β , y = GPA, x = ACT. ∑ ∑ ∑ ∑ − − = − − = 2 2 2 1 ) ( ) ( ˆ x n x y x n y x x x y x x i i i i i i β 5413 , 8 . 670 , 2125 . 3 , 875 . 25 , 8 2 = = = = = ∑ ∑ i i i x y x y x n 573 . ) 875 . 25 )( 102 . ( 2125 . 3 ˆ ˆ 102 . ) 875 . 25 ( 8 5413 ) 2125 . 3 )( 875 . 25 ( 8 8 . 670 ˆ 1 2 1 = − = − = = − − = x y β β β If ACT score increased by 5 points, predicted GPA would increase by .0.51 points. (ii) Obs GPA ACT GPAhat residual 1 2.8 21 2.71429 0.08571 2 3.4 24 3.02088 0.37912 3 3.0 26 3.22527 -0.22527 4 3.5 27 3.32747 0.17253 5 3.6 29 3.53187 0.06813 6 3.0 25 3.12308 -0.12308 7 2.7 25 3.12308 -0.42308 8 3.7 30 3.63407 0.06593 (iii) 6 . 2 ) 30 ( 102 . 573 . 102 . 573 ....
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Solution_two - Solutions to Problem Set#2 1 1 1 1 α β β...

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