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

Transcribed Image Text:

Xi Xi City Y (thousands)x CityY (thousands) XX 587 643 635 692 1,248 643 1,964 1,531 713 749 7.895 762 2.793 741 625 854 716 921 595 3,353 18.1 60 23.1 74 19.1 58 24.7 8.6 18.6 65 24.9 83 14.5 26.9 15.7 11.2 16.5 6.2 20.5 6.4 26.3 9.3 16.5 5.3 19.2 7.3 12 40.7 5 24.8 12.7 20.9 35.7 8.7 9.6 16.5 5.9 20.2 6.4 21.3 7.6 17.2 4.9 14.3 6.4 16 17 18 19 20 18.1 28.9 14.9 25.8 21.7 25.7 22.4 8.6 20.2 4 16.9 67 10 SSY 1,855.2020, SSE 537.4036 Y regressed on Xi and X:; Y regressed on Xi and X Y regressed on X and X: SSE 431.9700 SSE 367.3426 Source Model Error Corrected Total DF Sum of Squares 1490.571279 364.630721 1855.202000 Mean Square F ValuePr> F 496.857093 21.80 <.0001 16 22.789420 19