Review 9 ECON 337 Midterm Fall 2015

Review 9 ECON 337 Midterm Fall 2015 - 1 669 845 and the sum...

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1. Since the residuals must add to 0, the final residual is 669 845 , and the sum of the squares of the residuals is 15794740 714025 22.1207 . 2. SSTOTAL = 2314 110 2 6 = 297.3 ´ 3, so the table is ANOVA df SS MS F p-value Regress’n 3 275.2126 91.73754 8.294267 0.109 Residual 2 22.12071 11.06036 Total 5 297.3333 3. R 2 = 275.2126 297.3 ´ 3 0.9256 . Since the p-value is listed as 0.109 > 0.05, the proportion is not high enough for the model to be considered significant. 4. Use the matrices provided to get s b 1 = 11.06036 × 596 10140 0.806285 . 5. HY = XB = ( 1 1 1 2 1 3 2 3 5 9 6 11 1 4 1 5 1 6 3 5 7 10 2 4 ) × 1 845 ( 2721 2 2054 3046 ) = 1 845 ( 7753 19869 23909 11797 18813 10809 )
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6. ( 1 1 2 3 ) × 1 10140 ( 11872 1526 2262 2038 ) = ( 8756 10140 ) The leverage is 8756 10140 0.863511 7. When x 3 is regressed on x 1 and x 2 , the residuals are, in vector form X 3 ^ X 3 = X 3 H X 3 = X 3 XB = ( 3 9 11 5 10 4 ) ( 1 1 2 1 2 5 1 3 6 1 4 3 1 5 7 1 6 2 ) × 1 2384 ( 2036 178 3666 ) = 1 2384 ( 2038 1446 2726 402 2968 1236 ) The sum of the squares of the residuals is SSE = 24173760 5683436 4.25356 The total sum of squares is SSTOTAL = 352 42 2 6 = 58 The regression sum of squares is SSTOTAL SSE = 53.74664 R 2 = 53.74664 58 0.92666 VIF = 1 1 0.92666 = ¿ 13.63512 Multicollinearity appears to be a problem, since the VIF is greater than 10. 8. When y is regressed on x 1 , R 2 = r 2 = 0 .
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When y is regressed on x 1 x 2 , R 2 = 219.94 297.33 0.7397 . Partial-F test statistic
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