1. Use the Birthweight_Smoking data set introduced in Empirical ExerciseE5.3 to answer the following questions. a. Regress Birthweight on Smoker. What is the estimated effect of smoking on birth weight? b. Regress Birthweight on Smoker, Alcohol, and Nprevist. i. ii. iii. Using the two conditions in Key Concept 6.1, explain why the exclusion of Alcohol and Nprevist could lead to omitted variable bias in the regression estimated in (a). Is the estimated effect of smoking on birth weight substantially different from the regression that excludes Alcohol and Nprevist? Does the regression in (a) seem to suffer from omitted variable bias? Jane smoked during her pregnancy, did not drink alcohol, and had 8 prenatal care visits. Use the regression to predict the birth weight of Jane's child. iv. Compute R2 and R 2. Why are they so similar? c.Estimate the coefficient on Smoking for the multiple regression model in (b), using the three-step process in Appendix (6.3) (the Frisch-Waugh theorem). Verify that the three-step process yields the same estimated coefficient for Smoking as that obtained in (b). d. An alternative way to control for prenatal visits is to use the binary variables Tripre0 through Tripre3. Regress Birthweight on Smoker, Alcohol, Tripre0, Tripre2, and Tripre3. ii. Why is Triprel excluded from the regression? What would happen if you included it in the regression? The estimated coefficient on Tripre0 is large and negative. What does this coefficient measure? Interpret its value. iii. iv. Interpret the value of the estimated coefficients on Tripre2 and Tripre3. Does the regression in (d) explain a larger fraction of the variance in birth weight than the regression in (b)? -2 345 Variable 1 birthweight smoker age educ Description Birthweight and Smoking birth weight of infant (in grams) indicator equal to one if the mother smoked during pregnancy and zero, otherwise. Mother's Attributes years of educational attainment (more than 16 years coded as 17) indicator 1 if mother is unmarried age unmarried 6 alcohol 7 8 drinks tripre1 9 tripre2 10 tripre3 11 tripre0 12 nprevist This Pregnancy indicator=1 if mother drank alcohol during pregnancy number of drinks per week indicator=1 if 1st prenatal care visit in 1st trimester indicator=1 if 1st prenatal care visit in 2nd trimester indicator=1 if 1st prenatal care visit in 3rd trimester indicator=1 if no prenatal visits total number of prenatal visits