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)"

Q1)Do summary statistics on the data. What percent are white?

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"] .

Q3)Second, you decide to run a regression with children's birth weight in ounces as the dependent variable and average daily number of cigarettes consumed by the mother during pregnancy, family income, sex of child, race, and the parity of the child as the explanatory variables. What is F-statistics for this regression model (two decimals)?

Q4)Based on the F-statistics your conclusion is that the model is [ Select ] ["valid", "invalid"] because the p-value for the F-statistics is [ Select ] ["is close to zero", "larger than 0.05", "larger than 0.10"] .

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."]

Q7)Is there enough evidence to conclude that the effect of cigarette consumption during pregnancy is linearly related to birth weight at the 5% significance level?

Group of answer choices

Yes - there is enough evidence

No - there is not enough evidence

Q8)Is there enough evidence to conclude that the effect of family income during pregnancy is linearly related to birth weight at the 5% significance level?

Group of answer choices

Yes - there is enough evidence

No - there is not enough evidence

Q9)Is there enough evidence to conclude that the effect of being a boy is linearly related to birth weight at the 5% significance level?

Group of answer choices

Yes - there is enough evidence

No - there is not enough evidence

Q10)Is there enough evidence to conclude that the effect of being white is linearly related to birth weight at the 5% significance level?

Group of answer choices

Yes - there is enough evidence

No - there is not enough evidence

Q11)The model shows that for every [ Select ] ["one extra cigarette per day", "one extra pack of cigarettes per day", "one extra pack of cigarettes per week", "one extra cigarette per week"] birth weight [ Select ] ["increases", "decreases"] by [ Select ] ["0.49", "4.9", "49.0", "0.049"]

Q12)The coefficient for male indicates that:

Group of answer choices

a)boys weigh, on average, 3.2 oz

b)boys weigh, on average, 3.2 oz more than girls, holding everything else equal.

c)boys weigh, on average, 3.2 lbs

d)boys weigh, on average, 3.2 oz more than girls

e)boys weigh, on average, 3.2 lbs more than girls.

Q13)White children weigh, on average,

Group of answer choices

a)5.6 lbs

b)5.6 oz more than non-white babies, holding everything else constant

c)5.6 oz

d)5.6 oz more than non-white babies because white families on average have a higher income.

e)5.6 oz more than non-white babies

Q14)What percentage of the variation in birth weight is explained by the model? ( e.g. for 4.6%, write 4.6 not 0.046)

Q15)What percentage of the variation in birth weight is explained by the model once you take into account the number of observations and number of explanatory variables?

Source

https://docs.google.com/spreadsheets/d/1uDYjP6zfxWNk7dm2jNepCk0lDNspPvsV/edit?usp=sharing&ouid=112256274931170174923&rtpof=true&sd=true