A reporter calls to interview you for an article she is writing on wages in the United States. Use the following command in Stata to load the WAGE1 dataset:

use http://fmwww.bc.edu/ec-p/data/wooldridge/wage1.dta, clear

Using this dataset, answer this reporter's questions using a regression of the hourly wage in dollars (wage) on years of education (educ), number of dependents (numdep), and years of experience (exper). Assume that MLR.1 through MLR.6 hold.

a) Provide the reporter with a 99% confidence interval for the returns to education. Calculate this confidence interval by hand and then verify your calculation using Stata.

b) The reporter wants to know whether having more dependents is associated with higher or lower wages and, if so, by how much. Provide a point estimate of the impact of number of dependents on wages. In addition, using a 1% significance level, test whether number of dependents has an impact on wages. Calculate your test statistic by hand and then verify that it's correct using Stata.

c) What is the smallest significance level at which you can reject the null hypothesis from part (b)? Calculate your answer and then verify that it's correct using Stata.

d) Now you wish to test whether number of dependents has a positive impact on wages. Exactly how would this change the answer you gave for parts (b) and (c)?

e) The reporter believes the impact of a year of education on wages is ten times the impact of a year of experience. Perform a statistical test of her null hypothesis using a 1% size of test. (Calculate this test statistic by hand rather than using the test command.) Are you able to draw a definitive conclusion, or is the test inconclusive?

f) Another researcher interviewed by the reporter claims that neither education nor experience impact wages. Without using the Stata test command, perform this (joint) hypothesis test using a 1% significance level. (Calculate this test statistic by hand rather than using the test command.) Are you able to draw a definitive conclusion, or is the test inconclusive?

g) As a final sanity check, you decide to check whether all of the regressors in your model are jointly significant. (Once again, calculate this test statistic by hand and use a 1% significance level.)

h) Use Stata to verify the test statistics that you calculated in parts (e), (f) and (g).