Question: Refer to the situation in Exercise. Use a model-based analysis to estimate the total number of physicians in the United States. Which model did you choose, and why? What are the assumptions for the model? Do you think they are met? Be sure to examine the residual plots for evidence of the inadequacy of the model. How do your results differ from those you obtained in Exercise 5?
Exercise: The data set counties.dat contains information on land area, population, number of physicians, unemployment, and a number of other quantities for an SRS of 100 of the 3141 counties in the United States (U.S. Bureau of the Census 1994). The total land area for the United States is 3,536,278 square miles; the 1993 population was estimated to be 255,077,536.
a Draw a histogram of the number of physicians for the 100 counties.
b Estimate the total number of physicians in the United States, along with its standard error, using Ny.
c Plot the number of physicians versus population for each county. Which method do you think is more appropriate for these data: ratio estimation or regression estimation? Why?
d Using the method you chose in part (c), use the auxiliary variable population to estimate the total number of physicians in the United States, along with the standard error.
e The "true" value for total number of physicians in the population is 532,638. Which method of estimation came closer?