Why do both regressions give the same coefficient on wages (-21.6789) as the reg

Question

Why do both regressions give the same coefficient on wages (-21.6789) as the regression of hours on wages and kidslt6?

Explan wheter the kidslt6 variable is significant at the 5% significance level? Write out the bull and alternative hypothesis used for the test, explain how the test statistic is derived, and how the conclustion about the test is reached.

Explain whether the regression variables are jointly significant at 5% significance using the F-test reported in your regression. Explain what your null hypothesis is for this test and how this F-statistic is derived and how the conclusion about the test is reached?

Do husbands' wages and hours worked have a significant impact on lnhours? To answer, state your null hypothesis.

regress hours wage kidslt6 Number of obs F( 2,425) Prob > F R-squared Adj R-squared = 0.0323 Root MSE 428 8.12 - 0.0003 - 0.0368 Source df MS Model Residual 9475185.38 2 4737592.69 247835835 425 583143.14 Total 257311020 427602601.92 - 763.64 hours Coef. Std . Err. [95% Conf. Interval] wage kidslt6 cons 21.6760911.16923 327.380194.33814 1439.3860.62916 1.940.053 -3.470.001 23.74 0.000 43.62989 512.8075 1320.21 2777113 141.9527 1558.55

Explanation / Answer

Ans:

Both regression give the same coefficients on wages of -21.6789 because the first case shows the regression of the variable hours on the explanatory variables wage and kidslt6. On the other hand, when wages are regressed on kidslt6 and the resultant predicted wage level regressed on hours, it is the same as case 1 when we directly regress hours on wages and kidslt6.

As the p value for the coefficient of kidslt6 is 0, thus, we reject the null hypothesis that this variable does not have impact on the dependent variable. Thus, the variable kidslt6 is significant at 5% level of significance.

H0: B=0

H1: B not= 0

The test statistic is foung by regressing the dependent variable on the explanatory variables. from the coefficients of the regression, we see their p value and the t value. If the p value comes out to be less than 0.05, we state that we can reject the null hypothesis and the variable is significant. The contrary holds when the the p value is more than 0.05. The similar conclusions can be reached from t value. Thus, the test of significance leads to the rejection or acceptance of the null hypotheses.

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