You have been hired by the Department of Health (DoH) after graduating. The main reason you were picked over the competition was your excellent applied statistics skills, demonstrated through your answers to the R questions posed by the Hiring Committee during your interview. As a result, you have been thrown in the deep end during your first week at work. DoH's aim to better understand the relationship between smoking and infant health, possibly mediated by the effect of family income. They are especially interested in one specific measure of child health which is birth weight. Higher birth weight has been shown by prior research to be positively correlated with better future health and schooling outcomes. A dataset was collected recently, but the senior people at DoH have all gotten a bit rusty in their skills, so the dataset has been collecting dust since it was collected and it falls to you to do the analyses.

Load the data set as described below.Some of the variables are described below:

faminc = family income ($1,000s) cigtax = "Cigarette tax in home state, 1988" cigprice = "Cigarette price in home state, 1988" bwght = birth weight (ounces) fatheduc = "Father's education (years)" motheduc = "Mother's education (years)" parity = birth order of baby (1 is first-born) male = 1 if male baby, 0 if female white = 1 if white baby, 0 else cigs = average daily cigarette consumption of the mother during pregnancy lbwght = "Natural log of birth weight" bwghtlbs = "Birth weight, pounds" packs = "Packs smoked per day while pregnant" lfaminc = "log(faminc)"

Q2)First, run two regressions with birth weight in ounces as the dependent variable.

In the first regression usefamily income in $1,000, sex of child, and race as the explanatory variables. The coefficient on family income is [ Select ] ["0.0055", "0.030", "0.088", "0.0007", "0.0499"] .

In the second regression add mother's education as an additional regressor. The coefficient on family income is [ Select ] ["0.074", "0.216", "0.064"] . The effect of family income changes because [ Select ] ["because the degrees of freedom changes", "women with more education live, on average, in households with higher income.", "there is no relation between the two"] .

Q5)Before you present your results you want to check the assumptions about the error term. You decide to begin by looking at the normality assumption (you should create the relevant graph). It appears that the errors are [ Select ] ["normally distributed", "not normally distributed"] . This is important because it means that [ Select ] ["the model produces unbiased estimates.", "our inferences might not hold", "at least one of the assumptions needed for inferences are fulfilled.", "model produces biased estimates"] .

Q6) After looking at whether the errors are normal, you move on to the constant variance assumption.You should create the relevant graph using R for this problem set to support your discussion. Based on your graph you conclude that there [ Select ] ["is non-constant variance", "is constant variance"] . This is important because it means that [ Select ] ["at least one of the assumptions needed for inferences are fulfilled.", "our inferences might not hold", "model produces biased estimates", "the model produces unbiased estimates."]