# 8.11 - 8.11(a Case No Obs S'mt Cal S'mt Yi Xi Yi2 Xi2 XiYi...

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Unformatted text preview: 8.11 (a) Case No. Obs. S'mt. Cal. S'mt. Yi Xi Yi 2 Xi 2 XiYi Xi'=a+bYi (Xi-Xi') 2 Total: On the basis of calculations in the above table we obtain the respective sample means of X and Y as, Y = 600.4/25 = 24, X = 491.8/25 = 19.7 and corresponding sample variances, 91 . 1401 ) 24 25 16 . 48063 ( 24 1 2 2 = × − = Y S , 98 . 1185 ) 7 . 19 25 51 . 38138 ( 24 1 2 2 = × − = X S From Eq. 8.4 & 8.3, we also obtain, 884 . 24 25 16 . 48063 7 . 19 24 25 51 . 41546 2 = × − × × − = β ¡ , α ¡ = 19.7 – 0.884 × 24 = -1.551 Hence, E(X | y) = α + β y = -1.551 + 0.884y From Eq. 8.6a, the conditional variance is, ∑ = − − = n i i i Y X x x n S 1 2 ' 2 | ) ( 2 1 = 2182.967 / (25 – 2) = 94.912 and the corresponding conditional standard deviation is = 9.742 Y X S | (b) From Eq. 8.9, the correlation coefficient is, 96 . 91 . 1401 98 . 1185 24 7 . 19 25 51 . 41546 24 1 1 1 ˆ 1 = ⋅ × × − = − − = ∑ = y x n i i i s s y x n y x n ρ (c) To determine the 95% confidence interval, let us use the following selected values of Y...
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• Fall '08
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