1. Consider a simple linear regression of log (fertility) on pctUrban using the UN11 data set in the alr4 package.
a. Write the model you are fitting (in terms of the mean of log (fertility) conditional on knowing the value of pctUrban.
b. What is the equation for the fitted model?
c. Interpret the estimated coefficient for pctUrban.
2. Using the same data set as the previous problem, fit the regression of log (fertility) on log (ppgdp) and lifeExpR.
a. What is the fitted line for this model?
b. If we increase ppgdp by 25%, what is the expected decrease in fertility?
c. State the interpretation of part b. in a straightforward sentence.
3. In a study of faculty salaries in a small Midwest college, a linear regression model was fit, giving the fitted line E^ (Salary|Sex) = 24697 - 3340(Sex), where Sex = 1 if the faculty member was female and 0 if male. The response salary is measured in dollars (the data are from the 1970s).
a. Interpret each of the two estimated coefficients.
b. An alternative mean function fit to these data with an additional term, Years (the number of years employed at this college), gives the estimated mean function E^ (Salary|Sex, Years) = 18065 - 201(Sex) + 759 (Years). Notice that the coefficent for Sex has changed signs. Explain how this could happen. It may help to determine the fitted line for males (Sex = 0) and the fitted line for females (Sex = 1). Draw these two lines. How could observations be placed on these two lines so that males make more, on average, than females, but for females to make more than a male with the same amount of teaching experience at the university?
c. Interpret the coefficients for the fitted line in part b.