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HW Solutions Stat 83

# HW Solutions Stat 83 - c 7 Xij 7 8 Xij 8 9 Xij 9 ij Full...

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+ ρ 7 X ij 7 + ρ 8 X ij 8 + ρ 9 X ij 9 + ij c. Full model : ˆ Y = 77 . 15556 + 4 . 84444 X 1 + 4 . 40000 X 2 + 2 . 17778 X 3 +3 . 17778 X 4 + 1 . 17778 X 5 + . 84444 X 6 1 . 15556 X 7 3 . 82222 X 8 4 . 15556 X 9 6 . 55556 X 10 2 . 55556 X 11 SSE ( F ) = 110 . 6667 Reduced model : ˆ Y = 76 . 70000 + 5 . 30000 X 1 + . 30000 X 2 + 2 . 63333 X 3 +3 . 63333 X 4 + 1 . 63333 X 5 + 1 . 30000 X 6 . 70000 X 7 3 . 36667 X 8 3 . 70000 X 9 SSE ( R ) = 1 , 311 . 3333 H 0 : τ 1 = τ 2 = 0, H a : not both τ 1 and τ 2 equal zero. F = (1 , 200 . 6666 / 2) ÷ (110 . 6667 / 17) = 92 . 22 , F ( . 95; 2 , 17) = 3 . 59. If F 3 . 59 conclude H 0 , otherwise H a . Conclude H a . d. ˆ L = ˆ τ 2 ˆ τ 3 = 2ˆ τ 2 + ˆ τ 1 = 11 . 66667, s 2 { ˆ τ i } = . 44604 ( i = 1 , 2), s { ˆ τ 1 , ˆ τ 2 } = . 20494, s { ˆ L } = 1 . 1876, t ( . 975; 17) = 2 . 11 , 11 . 66667 ± 2 . 11(1 . 1876), 14 . 17 L ≤ − 9 . 16 23.20. See Problem 19.10a. L 1 = . 3 µ 11 + . 6 µ 21 + . 1 µ 31 , L 2 = . 3 µ 12 + . 6 µ 22 + . 1 µ 32 . H 0 : L 1 = L 2 , H a : L 1 = L 2 . ˆ L 1 ˆ L 2 = 25 . 43332 25 . 05001 = . 38331 , MSE = 2 . 3889, s { ˆ L 1 ˆ L 2 } = . 6052, t = . 38331 /. 6052 = . 63 , t ( . 975; 30) = 2 . 042. If |
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