E7.1 Use the Birthweight_Smoking data set introduced in Empirical Exercise E5.3 to answer the following questions. To begin, run three regressions:

(1) Birthweight on Smoker

(2) Birthweight on Smoker, Alcohol, and Nprevist

(3) Birthweight on Smoker, Alcohol, Nprevist, and Unmarried

a. What is the value of the estimated effect of smoking on birth weight in each of the regressions?

b. Construct a 95% confidence interval for the effect of smoking on birth weight, using each of the regressions.

c. Does the coefficient on Smoker in regression (1) suffer from omitted variable bias? Explain.

d. Does the coefficient on Smoker in regression (2) suffer from omitted variable bias? Explain.

e. Consider the coefficient on Unmarried in regression (3).

i. Construct a 95% confidence interval for the coefficient.

ii. Is the coefficient statistically significant? Explain.

iii. Is the magnitude of the coefficient large? Explain.

iv. A family advocacy group notes that the large coefficient suggests that public policies that encourage marriage will lead, on average, to healthier babies. Do you agree? (Hint: Review the discussion of control variables in Section 7.5. Discuss some of the various factors that Unmarried may be controlling for and how this affects the interpretation of its coefficient.)

f. Consider the various other control variables in the data set. Which do you think should be included in the regression? Using a table like Table 7.1, examine the robustness of the confidence interval you constructed in (b). What is a reasonable 95% confidence interval for the effect of smoking on birth weight?