Assignment 1

Assignment 1 - -5775836-550250 734159 325030 23039-5775836...

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Eric Kemeny 260191440 Econ 337: Assignment 1 September 27, 2007 1) Design Matrix X: Xt: Y: 1 2 1 1 1 1 1 123 1 5 2 5 5 7 10 150 1 5 164 1 7 205 1 10 214 a) XtX: XtX inverse: 5 29 1.17 -0.17 29 203 -0.17 0.03 b) Delta: 174 adj(XtX): 203 -29 -29 5 c) X(XtX inverse) : X(XtX inverse)Xt = H : 0.83 -0.11 0.61 0.29 0.29 0.07 -0.26 0.33 -0.02 0.29 0.22 0.22 0.17 0.1 0.33 -0.02 0.29 0.22 0.22 0.17 0.1 0 0.03 0.07 0.17 0.17 0.24 0.34 -0.5 0.12 -0.26 0.1 0.1 0.34 0.71 d) (XtX inverse)Xt : 0.83 0.33 0.33 0 -0.5 -0.11 -0.02 -0.02 0.03 0.12 (XtX inverse)XtY : 100.17 12.25 y-h = 100.1667 + 12.24713x e) B=(XtX inverse)XtY where X : 2 5 5 7 10 B = 26.56 y-h = 26.55665x 2) X: Xt:
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Eric Kemeny 260191440 Econ 337: Assignment 1 September 27, 2007 1 2 28 23 1 1 1 1 1 1 5 23 45 2 5 5 7 10 1 5 27 12 28 23 27 18 11 1 7 18 54 23 45 12 54 37 1 10 11 37 a) XtX: XtX inverse : 5 29 107 171 105.67 -5.97 -2.87 -0.27 29 203 542 1079 -5.97 0.37 0.16 0.01 107 542 2487 3382 -2.87 0.16 0.08 0.01 171 1079 3382 6983 -0.27 0.01 0.01 0 b) det(XtX) 2010376 adj(XtX) : ### ###
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Unformatted text preview: -5775836-550250 ### 734159 325030 23039-5775836 325030 159436 13998-550250 23039 13998 3423 c) X(XtX inverse)Xt = H : Leverages: 0.98 0.11-0.02-0.09 0.02 0.98 0.11 0.46 0.08 0.46-0.12 0.46-0.02 0.08 0.99-0.07 0.02 0.99-0.09 0.46-0.07 0.6 0.1 0.6 0.02-0.12 0.02 0.1 0.97 0.97 d) (XtX inverse)XtY : 18.28 y-h = 18.28212 + 16.09874x1 + 2.146673x2 + 0.397847x3 16.1 2.15 0.4 e) B = 17.13 y-h = 17.13161x1 + 2.643744x2 + 0.445202 2.64 0.45 3) a) Y: 123 HY: 119.74 Y-HY = 3.26 150 166.05-16.05 164 161.51 2.49 205 191.1 13.9 214 217.6-3.6 b) SSE = (Y-HY)t(Y-HY) = 480.8 c) S(y)^2 = 1449.7 SSTOTAL = 4*S(y)^2 = 5798.8 R^2 = SSR / SSTOTAL = (SSTOTAL - SSE) / SSTOTAL = 0.92...
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This homework help was uploaded on 04/20/2008 for the course ECON 337 taught by Professor Mackenzie during the Fall '08 term at McGill.

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Assignment 1 - -5775836-550250 734159 325030 23039-5775836...

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