# 8.4 - i = 600 5400 and 10300 and with t 0.975,6 = 2.447 from Table A.3 we obtain At X i = 600 997 1835 263 62 4725 8 252520000 4725 600 8 1 113 608

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8.4 (a) (b) Country # Per Capita GNP Per Capita Energy Consumption Xi Yi Xi 2 Yi 2 XiYi Yi'=a+bXi (Yi-Yi') 2

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Total: On the basis of calculations in the above table we obtain the respective sample means of X and Y as, X = 37800/8 = 4725, Y = 16800/8 = 2100 and corresponding sample variances, 71 . 10559285 ) 4725 8 252520000 ( 7 1 2 2 = × = x S , 86 . 1137142 ) 2100 8 43240000 ( 7 1 2 2 = × = y S From Eq. 8.4 & 8.3, we also obtain, 279 . 0 4725 8 252520000 2100 4725 8 99980000 2 = × × × = β ± , α ± = 2100 – 0.279 × 4725 = 781.725 (c) From Eq. 8.9, the correlation coefficient is, 85 . 0 86 . 1137142 71 . 10559285 2100 4725 8 99980000 7 1 1 1 ˆ 1 = × × = = = y x n i i i s s y x n y x n ρ (d) From Eq. 8.6a, the conditional variance is, = = n i i i X Y y y n S 1 2 ' 2 | ) ( 2 1 = 2218817.515 / 6 = 369801.799 and the corresponding conditional standard deviation is = 608.113 X Y S | (e) To determine the 95% confidence interval, let us use the following selected values of X
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Unformatted text preview: i = 600, 5400 and 10300, and with t 0.975,6 = 2.447 from Table A.3, we obtain, At X i = 600; ) 997 . 1835 263 . 62 ( ) 4725 8 252520000 ( ) 4725 600 ( 8 1 113 . 608 447 . 2 37 . 950 2 2 95 . → = × − − + × ± = > < X Y µ At X i = 5400; ) 253 . 2827 407 . 1749 ( ) 4725 8 252520000 ( ) 4725 5400 ( 8 1 113 . 608 447 . 2 12 . 2288 2 2 95 . → = × − − + × ± = > < X Y At X i = 10300; ) 469 . 4754 391 . 2556 ( ) 4725 8 252520000 ( ) 4725 10300 ( 8 1 113 . 608 447 . 2 74 . 3653 2 2 95 . → = × − − + × ± = > < X Y (f) Similarly, 588 . 2 = β ± , α ± = -709.673 and = 1853.080 for predicting the per capita GNP on the basis of the per capita energy consumption. Y X S |...
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## This note was uploaded on 04/07/2008 for the course CVEN 3227 taught by Professor Strzepek during the Spring '08 term at Colorado.

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8.4 - i = 600 5400 and 10300 and with t 0.975,6 = 2.447 from Table A.3 we obtain At X i = 600 997 1835 263 62 4725 8 252520000 4725 600 8 1 113 608

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