(2) Recalling the birthweight data set from chapter 5 [link]. It contains data for a random sample of babies born in Pennsylvania in 1989. The data include the baby's birth weight

together with various characteristics of the mother, including whether she smoked during the pregnancy. A detailed description is given in Birthweight_Smoking. We 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? How does it change? 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. Discuss some of the various factors that Unmarried may be controlling for and how this affects the interpretation of its coefficient.) f. Do you think Age and Educ should be included in the regression? Examine the robustness of the confidence interval you constructed in (b) (how is it changed?)