Estimate the linear regression

ln(wage_i) = ₁ + ₂educ_i + e_i:

where e_i is the error and ₁ and ₂ are the unknown population coe cients.

a. Report the estimation results in a common form as introduced in the lecture note 3. For example, see page 9 of the note 3, where the estimates are presented in an equation form, along with standard errors and some measures for model t.

b. Construct a scatter diagram of educ and ln(wage) and plot the estimated re-gression equation in (a) on the scatter diagram. Give informative title and labels for the variables, e.g., do not use the default title and labels.

c.  Assuming that E[ejeduc] = 0, interpret the estimated coe cient on educ (2 points) and test whether or not the population coe cient is zero at the 1 % signi cance level (2 points).

d. You suspect that the hourly wage could depend on working hours per week. Discuss under what condition(s) the estimated coe cients in (a) would be biased due to the omission of the weekly working hours (2 points). Give a reasonable and intuitive story on why omission of the weekly working hours would cause omitted variable bias in the regression in (a) (2 points). Under your story, explain whether the estimated coe cient on educ in (a) would be overestimated or underestimated (2 points). See pages 4 and 5 of Lecture note 4.

e. The variable hrswk is the average weekly working hours for each individual in the data. Regress ln(wage) on educ and hrswk. Discuss the estimation results. In particular, how would you revise your answer in (c)? Are the estimates are statistically signi cant?

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