HW2A - demand for co/ee is estimated to be 4.216 When the...

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Econ 444 Elementary Econometrics (Fall 2007) ANSWERS TO HOMEWORK EXERCISE: 2 1. (a) ° X = (80 + 160 + 240) = 3 = 160 , and ° Y = (70 + 110 + 155) = 3 = 111 : 67 . (b) P 3 i =1 ( X i ° ° X ) 2 = (80 ° 160) 2 + (160 ° 160) 2 + (240 ° 160) 2 = 12 ; 800 (c) P 3 i =1 ( X i ° ° X )( Y i ° ° Y ) = (80 ° 160)(70 ° 111 : 67) + (160 ° 160)(110 ° 111 : 67) + (240 ° 160)(155 ° 111 : 67) = 6800 (d) ^ ° 1 = 6800 = 12800 = 0 : 53 . ^ ° 0 = 111 : 67 ° 0 : 53 ± 160 . ^ Y i = 26 : 87 + 0 : 53 X 1 (1) (e) When income is zero, the expected consumption is estimated to be $ 26.87. When income increases by one dollar, the expected consumtion is estimated to increase by $ 0.53. (f) ^ Y 1 = 26 : 87 + 0 : 53 ² 80 = 69 : 27 , ^ Y 2 = 26 : 87 + 0 : 53 ² 160 = 111 : 67 , and ^ Y 3 = 26 : 87 + 0 : 53 ² 240 = 154 : 07 . So e 1 = Y 1 ° ^ Y 1 = 70 ° 69 : 27 = 0 : 73 , e 2 = Y 2 ° ^ Y 2 = 110 ° 111 : 67 = ° 1 : 67 , and e 3 = Y 3 ° ^ Y 2 = 155 ° 154 : 07 = 0 : 93 . (g) RSS = 0 : 73 2 + ( ° 1 : 67) 2 + 0 : 93 2 = 4 : 187 . TSS = (70 ° 111 : 67) 2 + (1110 ° 111 : 67) 2 + (155 ° 111 : 67) 2 = 3616 : 667 , R 2 = 1 ° (4 : 187 = 3616 : 667) = 0 : 999 . 2. (a) When the price of co/ee and the price of tea are zero, the expected
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Unformatted text preview: demand for co/ee is estimated to be 4.216. When the price of co/ee increases by one unit holding the price of tea constant, the expected demand for co/ee is estiamted to decrease by 0.95 units. When the price of tea increases by one unit holding the price of co/ee constant, the expected demand for tea is estimated to increase by 0.877 units. (b) N = 1995 & 1971 + 1 = 25 . For Regression (12), & R 2 = 1 & (1 & : 875)(25 & 1) = (25 & 1 & 1) = 0 : 8696 . For Regression (13), & R 2 = 1 & (1 & : 877)(25 & 1) = (25 & 2 & 1) = 0 : 8656 . Besed on & R 2 , we prefer teh regression with a higher & R 2 . So we prefer regression (12). 1...
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