week3ans - Week 3 Answers 1 Run a regression of wage on...

Week 3 Answers
1. Run a regression of wage on education (educ).
reg wage educ
Source | SS df MS Number of obs = 935
-------------+------------------------------ F( 1, 933) = 111.79
Model | 16340644.5 1 16340644.5 Prob > F = 0.0000
Residual | 136375524 933 146168.836 R-squared = 0.1070
-------------+------------------------------ Adj R-squared = 0.1060
Total | 152716168 934 163507.675 Root MSE = 382.32
------------------------------------------------------------------------------
wage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ | 60.21428 5.694982 10.57 0.000 49.03783 71.39074
_cons | 146.9524 77.71496 1.89 0.059 -5.56393 299.4688
------------------------------------------------------------------------------
2. Interpret the slope and the intercept of the estimated regression line.
Slope: A 1 unit increase in education increases the predicted wage by 60.21.
Intercept: If education is zero, then the average wage is 146.95.
3. Is the slope coefficient statistically significant?
Statistically significant implies that you need to test the following:
H
0
: β
1
= 0
H
A
: β
1
6 = 0
Stata gives the relevant t
stat
which is 10.57 in this case. At the 5% level of significance, the
critical value is 1.96. Thus, | t
stat
| > 1 . 96, which implies that the null can be rejected.
Alternatively, the p-value is 0.000 (also given in the Stata table) which is less than 0.05,
therefore, the null can be rejected.