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)"

You can download the R data set here Links to an external site., and use "load" to get it into RStudio. The easiest method is, however, to load the data straight into RStudio by including the following line in your R script (requires an internet connection when you run the script):

load(url("https://www.dropbox.com/s/cnwtcr096szm8im/omsba_5112_birthweight.rdata?raw=1"))

This will load a data frame called "birthweight". You can rename it if you want.

Question 1: The models we worked with last week were good starting points, but it is possible that we can learn more about what determines birth weight by trying other specifications.

First, you want to figure out if income follows a polynomial. Expand the model above with the square of family income. What is your interpretation of the effect of income now, and do you think we should keep the square variable in the model?

As an alternative version, run the original equation, but with the log of birth weight as the dependent outcome.

Question 2: What is the interpretation of the coefficient on parity when you use log of birth weight as the outcome?

Question 3: For the same model, what is the interpretation of the male dummy?

Question 4: Yet another version is to use the log of birth weight as the outcome and log of family income instead of family income (there already is a variable, "lfaminc", so no need to create anything new).

What is the interpretation of the coefficient on the log of family income?

Question 5: Say we want to know whether the effect of smoking varies by race. Run a model based on the original model, and interpret your results.

Question 6: Finally, we want to know if the effect of income varies by race. Run this model-again based on the original model-and interpret the results.

Question 7: Based on your analysis of the data so far what would be your recommendation to the DoH in terms of what they should focus on to improve child health as measured by birth weight?