A sociologist investigating the recent increase in the incidence of homicide throughout the United States studied the extent to which the homicide rate per 100,000 population (Y) is associated with the city's population size (X1), the percentage of families with yearly income less than $5,000 (X2), and the rate of unemployment (X3). Data are provided in the following table for a hypothetical sample of 20 cities.

a. Using the regression results presented next, determine the , R2-values for each two-variable model, and comment on which appears to be the best.

b. When Y is regressed on X1, X2, and X3, we get SSE = 337.0571. Determine and comment on the increase in R2 in going from a model with just X2 and X3 to a model that includes all three independent variables.
c. Consider the model with independent variables X2, X3, and X4, where X4 = X2X3. The ANOVA table for this model, from SAS's GLM procedure, is given next. Does the addition of X4 lead to a large improvement in fit over the model with X2 and X3 as the only independent variables? Explain.
SAS Output (PROC GLM)
Regression of Y on X2, X3, X4