You decide to estimate the following three regressions using the same sample of data (assume that sample size is 10,000):
wagei = b0 + b1 femalei + ui (1)
wagei = c0 + c2 malei + vi (2)
wagei = d1 femalei + d2 malei + ei (3)
where wage refers to average hourly earnings, u, v, and e are the regressions’ error terms, and
femalei = 1 if observation i refers to a female, and = 0 if observation i refers to a male
malei = 1 if observation i refers to a male, and = 0 if observation i refers to a female
(a) How much is the expected wage of a female according to each regression?
(b) How much is the expected wage of a male according to each regression?
(c) Interpret the vertical intercept and the slope in regression (1).
(d) Interpret the vertical intercept and the slope in regression (2).
(e) Interpret the coe#cients d1 and d2 in regression (3).

(a) What fraction of the sample variance of ahe is explained by yrseduc?
(b) How much is the standard error of the regression (SER)?
(c) What is the sample size? [Hint: Check the degrees of freedom of the SER and note that we have lost 2 degrees of freedom when
estimating the two coe#cients of the regression.]
(d) What is the OLS estimate of the slope?
(e) What is the standard error of the OLS estimator of the slope?
(f) What is the t-statistic corresponding to the two-sided test with null hypothesis that the slope equals 0.
(g) Will you reject the null hypothesis that the slope equals 0 in favor of the two-sided alternative at 5% signi”cance level?
(h) Find the lower and the upper limit of the 95% con”dence interval for the slope of the regression (use the normal approximation,
which is justi”ed since the sample size is large enough).
(i) Calculate the predicted wage (i.e., average hourly earnings) of a person with 16 years of education.
(j) What would be the predicted increase in the wage of a high-school graduate if he/she obtains a college degree? In answering this
question assume that college takes 4 years.
(k) Give an example of a variable that can directly increase a person’s wage and can be positive correlated with years of education.
(l) In view of (k), do you expect the OLS estimator of the slope to be unbiased? In particular, do you think that the expected value of the
OLS estimator of the slope is greater, smaller, or equal to the true slope?

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