6) Use the following formula and the regression results below to test the joint null hypothesis that neither mother's nor father's education has an effect on wages (10 points) : F =_ (SSRr - SS Rur) /9 ~ Fan-k-1 SSRur/ (n - k - 1) What is the F-statistic, and what is the 18 critical value for that F-stat? What do you conclude? How can your conclusion be correct, given that neither of the relevant coefficients is significant at even 5% by itself? Regression 1) Source SS df MS Number of obs = 722 F( 8, 713) = 24

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6) Use the following formula and the regression results below to test the joint null hypothesis that neither mother's nor father's education has an effect on wages (10 points) : F =_ (SSRr - SS Rur) /9 ~ Fan-k-1 SSRur/ (n - k - 1) What is the F-statistic, and what is the 18 critical value for that F-stat? What do you conclude? How can your conclusion be correct, given that neither of the relevant coefficients is significant at even 5% by itself? Regression 1) Source SS df MS Number of obs = 722 F( 8, 713) = 24.84 Model | 27 . 6422885 8 3. 45528607 Prob > F = 0 . 0000 Residual | 99.1696272 713 . 139087836 R-squared = 0. 2180 -+ Adj R-squared = 0. 2092 Total | 126. 811916 721 . 175883378 Root MSE . 37294 1wage Coef. Std. Err. t P>It| [95% Conf. Interval] educ . 0562629 007967 7. 06 0 . 000 0406214 0719045 exper . 014224 . 0044905 3. 17 0 . 002 . 0054077 . 0230402 tenure . 009331 . 0029518 3.16 0 . 002 . 0035356 . 0151264 age . 0096873 . 0055133 1 . 76 0. 079 - . 001137 . 0205117 south - . 0807515 . 0305296 -2. 65 0 . 008 -. 1406902 - . 0208128 urban 1672097 . 0313994 5.33 0 . 000 . 1055634 . 228856 meduc . 0108041 . 0061195 1 . 77 0 . 078 - . 0012103 . 0228185 feduc . 0086483 . 0054328 1. 59 0. 112 - . 0020179 . 0193145 cons 5. 184015 . 1749834 29. 63 0. 000 4. 84047 5. 527559

Regression 2) Source | SS df MS Number of obs 722 -+- F ( 6, 715) = 30.89 Model 1 26.1070112 6 4 . 35116853 Prob > F = 0 . 0000 Residual 1 100 . 704905 715 . 14084602 R-squared = 0 . 2059 -+ Adj R-squared = 0 . 1992 Total | 126.811916 721 . 175883378 Root MSE = . 37529 Iwage | Coef. Std. Err. t P>It| [95% Conf. Interval] educ . 066289 . 007407 8. 95 0. 000 . 0517469 0808312 exper . 0139483 0045166 3 . 09 0 . 002 . 0050809 . 0228158 tenure . 0092854 . 0029681 3. 13 0 . 002 . 0034582 . 0151126 age . 008745 . 0055379 1 . 58 0 . 115 - . 0021275 . 0196175 south -. 0968346 . 0303248 -3. 19 0 . 001 -. 156371 - . 0372982 urban 17171 . 0314958 5 . 45 0 . 000 . 1098747 . 2335453 cons 5. 288836 . 1730791 30 .56 0 . 000 4. 949032 5 . 62864