DSC330_hw2_sol

# DSC330_hw2_sol - DSC 330 HW2 SOLUTIONS 1 Solutions(a ˆ...

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Unformatted text preview: DSC 330 HW2 SOLUTIONS 1. Solutions: (a) ˆ u1D70C = u1D446u1D446 u1D465u1D44C √ u1D446u1D446 u1D465u1D465 u1D446u1D446 u1D44C u1D44C = 20 25 = 0 . 8 u1D445 2 = (ˆ u1D70C ) 2 = 0 . 64 (b) ˆ u1D6FD 1 = u1D446u1D446 u1D465u1D44C u1D446u1D446 u1D465u1D465 = 20 25 = 0 . 8 ˆ u1D6FD = ¯ u1D44C − ˆ u1D6FD 1 ¯ u1D465 = 5 The regression line is ˆ u1D44C = 5 + 0 . 8 u1D465 (c) u1D446u1D446u1D438 = u1D446u1D446u1D447 (1 − u1D445 2 ) = 25 ∗ (1 − . 64) = 9 The estimate of u1D70E 2 is MSE=SSE/(n-2)=9/4 The estimate of u1D70E is u1D460 = √ u1D440u1D446u1D438 = 3 / 2 = 1 . 5 (d) u1D460 = 1 . 5. u1D460u1D452 ( ˆ u1D6FD 1 ) = u1D460 √ u1D446u1D446 u1D465u1D465 = 1 . 5 √ 25 = 0 . 3 ˆ u1D6FD 1 ± u1D461 4 , . 025 1 . 5 5 . 8 + 2 . 776 ∗ . 3 (-0.0328,1.6328) (e) u1D43B : u1D6FD 1 = 0 u1D43B u1D44E : u1D6FD 1 ∕ = 0 u1D461 = . 8 1 . 5 / 5 = 2 . 67 (Note: u1D460u1D452 ( ˆ u1D6FD 1 ) = 0 . 3) Rejection region: u1D461 4 , . 05 = 2 . 132, u1D461 < − 2 . 132 or u1D461 > 2 . 132 Reject u1D43B (f) u1D43B : u1D6FD 1 = 0 . 9...
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DSC330_hw2_sol - DSC 330 HW2 SOLUTIONS 1 Solutions(a ˆ...

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