Factors identifying urban counties. The Professional Geographer (Feb. 2000) published a study of urban and rural counties in the western United States. The researchers used six independent variables—total county population 1x12, population density 1x22, population concentration 1x32, population growth 1x42, proportion of county land in farms 1x52, and five-year change in agricultural land base 1x62—to model the urban/

rural rating (y) of a county on a scale of 1 (most rural) to 10 (most urban). Prior to running the multiple-regression analysis, the researchers were concerned about possible multicollinearity in the data. Following is a MINITAB printout of correlations between all pairs of the independent variables:

a. On the basis of the correlation printout, is there any evidence of extreme multicollinearity?

b. The first-order model with all six independent variables was fit to the data. The multiple-regression results are shown in the accompanying MINITAB printout. On the basis of the reported tests, is there any evidence of extreme multicollinearity?

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Correlations: X1, X2, X3, X4, X5, X6 X1 X2 X3 X4 X5 X2 0.20 X3 0.45 0.43 X4 -0.05 -0.14 -0.01 X5 X6 -0.16 -0.15 -0.12 -0.12 -0.07 -0.20 -0.22 -0.06 -0.06 Cell Contents: Pearson correlation