Does a mother's smoking affect the birthweight of her child? Using the data file bweight_small we explore this question. The file bweight contains more observations. The variable MSMOKE is the number of cigarettes smoked daily during pregnancy. Nonsmokers \((M B S M O K E=0)\) smoke zero daily. Among smokers \((M B S M O K E=1)\), the variable \(M S M O K E=1\) if 1-5 cigarettes are smoked daily; \(M S M O K E=2\) if 6-10 cigarettes are smoked daily; and \(M S M O K E=3\) if 11 or more cigarettes are smoked daily.

a. Estimate a regression model for BWEIGHT . Include as explanatory variables MMARRIED, MAGE, PRENATAL1, and FBABY, along with MSMOKE. Interpret the estimated coefficient of MSMOKE.

b. From \(M S M O K E\) create three indicator variables, \(S M O K E 2=1\) if a mother smokes 1-5 cigarettes per day, 0 otherwise; \(S M O K E 3=1\) if a mother smokes 6-10 cigarettes per day, 0 otherwise; \(S M O K E 4=1\) if a mother smokes 11 or more cigarettes per day, 0 otherwise. Estimate a regression model for BWEIGHT. Include as explanatory variables MMARRIED, MAGE, PRENATAL1, and \(F B A B Y\), along with SMOKE2, SMOKE3, and SMOKE4. Interpret the estimated coefficients of SMOKE2, SMOKE3, and SMOKE4. Does smoking 1-5 cigarettes per day have a statistically significant negative effect on infant birthweight?

c. Using the results in (b), test the null hypothesis that smoking 11 or more cigarettes per day reduces birthweight by no more than smoking 6-10 cigarettes per day, against the alternative that smoking 11 or more cigarettes per day reduces birthweight by more than smoking 6-10 cigarettes per day.

d. Using the results in (b), test the null hypothesis that smoking 11 or more cigarettes per day reduces birthweight by no more than smoking 1-5 cigarettes per day, against the alternative that smoking 11 or more cigarettes per day reduces birthweight by more than smoking \(1-5\) cigarettes per day.

e. Estimate a regression model for BWEIGHT. Include as explanatory variables MMARRIED, MAGE, PRENATAL1, and FBABY. Estimate the model separately for MSMOKE \(=0,1,2\), and 3. Using each model, estimate the expected birthweight of a child of a married woman who is 25 years old whose first prenatal visit was in the first trimester and who had already given birth to at least one child. What do you observe?

f. Estimate the linear probability model with dependent variable LBWEIGHT as a function of explanatory variables MMARRIED, MAGE, PRENATAL1, and FBABY, along with MSMOKE. Predict the probability of a low-birthweight infant for \(M S M O K E=0,1,2\), and 3 of a married woman who is 25 years old whose first prenatal visit was in the first trimester and who had already given birth to at least one child. What do you observe?