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Refer to the CDI data set in Appendix C.2.
a. For each geographic region, regress the number of serious crimes in a CDI (Y) against population density (X1 total population divided by land area), per capita personal income (X2), and percent high school graduates (X3). Use first-order regression model (6.5) with three predictor variables. State the estimated regression functions.
b. Are the estimated regression functions similar for the four regions? Discuss.
c. Calculate MSE and R2 for each region. Are these measures similar for the four regions? Discuss.
d. Obtain the residuals for each fitted model and prepare a box plot of the residuals for each fitted model Interpret your plots and state your findings.
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: