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ECON 337 review sheet for midterm Fall 2016.docx

ECON 337 review sheet for midterm Fall 2016.docx - 1 Data...

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1. Data for the multiple-regression of Y on X1, X2, and X3 are given below, together with some sets of residuals. The residuals have headings of the form ABC. The heading ABC indicates that the residuals are for the multiple regression of A on B and C. For example YX2X3 is the heading of the column of residuals obtained when Y is regressed (multiple regression) on X2 and X3. Using your calculator and appropriate sets of residuals find the numerical values of b 1 , b 2 , and b 3 in the multiple regression . ˆ 3 2 2 1 1 0 b x b x b b y X1 X2 X3 Y 12 2 24 100 13 65 21 233 53 4 6 36 22 36 34 112 15 24 64 278 32 7 23 99 Residuals YX1X2 YX1X3 YX2X3 X1X2X3 X2X1X3 X3X1X2 -49.1472 -59.7702 13.01376 -19.7504 -32.933 -16.8831 -6.03127 83.01178 31.55656 -4.04851 30.34491 -12.1449 5.586047 14.57259 1.816092 14.29179 1.525165 -2.18715 -57.5795 -50.0338 -73.3801 3.001983 11.87063 4.786449 105.3318 24.97317 21.66229 5.404685 -0.26893 27.9188 1.840138 -12.7535 5.331382 1.100466 -10.5388 -1.49013 2. For the same data set consider the following matrices. Some numbers have been deleted. Let the capital letter X stand for the design matrix. 0 2158461494 ?? 1916262 13766544 879586066 - ? 9551684 8402988 480494782 - ? ? 33199016 1401285544 - ? ? ? 6 7419511219 1 6834 4358 3323 172 ? 6166 2457 138 ? ? 4855 147 ? ? ? ??
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