ECON-337-Assignment-1answers-Fall-2012.doc

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1. For this question use the data below. Some matrix computations are given. x 1 x 2 y 2 5 7 3 8 12 5 9 12 5 11 16 6 12 17 435 206 45 206 99 21 45 21 5 X X t 9 40 68 48 29 15 50 120 95 10 109 115 143 2 254 1 54 85 129 85 150 135 129 135 629 1 t X a) Regress y on the two variables x 1 and x 2 . Answer: First find the determinant. 175 1 0 0 0 1 0 0 0 1 175 0 0 0 175 0 0 0 175 1 435 206 45 206 99 21 45 21 5 54 85 129 85 150 135 129 135 629 1 Next find B. 2 1 2 1 0 2 1 ˆ 2 1 1 17 16 12 12 7 9 40 68 48 29 15 50 120 95 10 109 115 143 2 254 175 1 x x y b b b b) Determine whether the first line of data is an outlier according to the leverage criterion. A point is an outlier if its leverage exceeds 2p/n, where p is the number of explanatory variables counting the constant, and n is the number of data points. Answer: Find the hat matrix.
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509 . 0 * * * * * 429 . 0 * * * * * 749 . 0 * * * * * 577 . 0 * * * * * 737 . 0 89 65 47 8 34 65 75 5 55 15 47 5 131 41 43 8 55 41 101 52 34 15 43 52 129 175 1 9 40 68 48 29 15 50 120 95 10 109 115 143 2 254 175 1 12 6 1 11 5 1 9 5 1 8 3 1 5 2 1 ) ( 1 t t X X X X H N.B. Really all that is needed is * * * * * * * * * * * * * * * * * * * * * * * * 737 . 0 * * * * 29 * * * * 10 * * * * 254 175 1 * * * * * * * * * * * * 5 2 1 ) ( 1 t t X X X X H 2p/n = 6/5 = 1.2. Since 0.737 is not greater than 1.2, the first line of data is not an outlier by the leverage criterion. c) Calculate SSE. Y-HY gives the set of residuals:
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