Data set link:

http://users.stat.ufl.edu/~rrandles/sta4210/Rclassnotes/data/textdatasets/KutnerData/Appendix%20C%20Data%20Sets/APPENC02.txt

This data set provides selected county demographic information (CDI)for 440 of the most populous counties in the United States. Each line of the data set has an identification number with a county name and state abbreviation and provides information on 14 variables for a single county. Counties with missing data were deleted from the data set. The information generally pertains to the years 1990 and 1992. The 17 variables are:

Identification Number

County

State

Land Area

Total Population

Percent of Population aged 18-34

Percent of population 65 or older

Number of active physicians(Y)

Number of hospital beds

Total serious crimes

Percent high school graduates

Percent bachelor's degrees

Percent below poverty level

Percent unemployment

Per capita income

Total personal income

Geographic region(1 = Northeast, 2 = Midwest, 3 = South, 4 = West

The goal is to model the number of physicians per 1000 inhabitants, using the other demographic variables.

(1) Plot Number of active physiciansagainst each of Total Population, Total personal income, per capita income , Total serious crimes and pop65plus.

(2) Plot ln(Number of active physicians) against the others (Total Population, Total personal income, per capita income , Total serious crimes and pop65plus). Does is seem reasonable to take the log?

(3)

a. Regress the ln(number of active physicians) in turn on (SLR)each of the three predictor variables (total population, number of hospital beds, and total personal income). State the estimated regression functions.

b. Plot the three estimated regression functions and data on separate graphs. Does a linear regression relation appear to provide a good fit for each of the three predictor variables?

c. Calculates(sqrt(MSE)) for each of the three predictor variables. Which predictor variable leads to the smallest variability around the fitted regression line?

d. Obtain Bonferroni joint confidence intervals for 0 and 1 using a 95 percent family confidence coefficient and interpret the interval for all the models.

e. An investigator has suggested that for model with total population 0 should be -100 and 1 should be .0028. Do the joint confidence intervals in part (d) support this view? Discuss.

f. Estimate the expected number of active physicians for counties with total population of X = 500, 1000, 5000 thousand with Bonferroni family confidence coefficient 0.90.