Answer Happy

1.43. Refer to the CDI data set in Appendix C.2. The number of active physicians in a CDI (Y) is expected to be related to total population, number of hospital beds, and total personal income. Assume that first-order regression model (1.1) is appropriate for each of the three predictor variables. a. Regress the number of active physicians in turn on each of the three predictor variables. 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. Calculate MSE for each of the three predictor variables. Which predictor variable leads to the smallest variability around the fitted regression line?
Data Set C.2 CDI Variable Number Variable Name 1 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 at 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: Description Identification number 1-440 2 County County name 3 State 4 Land area Two-letter state abbreviation Land area (square miles) Estimated 1990 population 5 Total population 6 Percent of population aged 18-34 Percent of 1990 CDI population aged 18-34 7 Percent of population Percent of 1990 CDI population aged 65 years old or older 65 or older Number of active 8 Number of professionally active nonfederal physicians physicians during 1990 9 Number of hospital beds Total serious crimes 10 Total number of beds, cribs, and bassinets during 1990 Total number of serious crimes in 1990, including murder, rape, robbery, aggravated assault, burglary, larceny-theft, and motor vehicle theft, as reported by law enforcement agencies Percent of adult population (persons 25 years old or older) who completed 12 or more years of school 11 Percent high school graduates 12 Percent bachelor's Percent of adult population (persons 25 years old or older) with bachelor's degree degrees 13 Percent below Percent of 1990 CDI population with income below poverty level poverty level 14 Percent unemployment Percent of 1990 CDI labor force that is unemployed 15 Per capita income Per capita income of 1990 CDI population (dollars) 16 17 Total personal income Geographic region Total personal income of 1990 CDI population (in millions of dollars) Geographic region classification is that used by the U.S. Bureau of the Census, where: 1 = NE, 2= NC, 3 = S, 4 =W Source: Geospatial and Statistical Data Center, University of Virginia. 1350 Appendices 3 4 5 6 7 8 9 10 CA 4060 IL TX 946 1729 8863164 32.1 9.7 23677 27700 688936 5105067 29.2 12.4 15153 21550 436936 2818199 31.3 7.1 7553 12449 253526 *** *** *** *** ww 6537 539 100498 HI 1159 100374 AL 582 100043 26.3 11.7 122 35.7 7.9 87 188 26.2 11.3 192 182 7130 464 4693 11 12 13 14 15 17 16 70.0 22.3 11.6 8.0 20786 184230 4 73.4 22.8 11.1 7.2 21729 110928 2 74.9 25.4 12.5 5.7 19517 55003 3 *** *** *** *** *** 77.9 16.5 10.8 8.0 13169 1323 3 1857 4 77.0 17.8 5.7 3.2 18504 69.4 15.5 9.4 7.1 16458 1647 3 2 1 Los Angeles Cook 2 3 Harris *** *** 438 Montgomery TN 439 Mauil 440 Morgan 1