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 (x1), population density (x2), population concentration (x3), population growth (x4), proportion of county land in farms (x5), and five-year change in agricultural land base (x6) €”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:
Correlations: X1, X2, X3, X4, X5, X6

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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X1 0.20 0.45 X2 X3 X4 Xs X2 X3 X4 xs X6 0.43 -0.05 0.14 -0.01 -0.16 -0.15 -0.07-0.20 -0.12 -0.12 -0.22 0.06 -0.06 Cell Contents: Pearson correlation Coet Predictor Constant X1 X2 X3 X4 XS x6 0.210 0.065 0.540 -0.009 -0.150 -0.027 2.01 0.045 1.20 0.230 3.59 0.000 -0.18 0.860 “3.00 0.003 -0.55 0,580 R-Sq 44.0% R-Sq (adj ) -43.0 . Analysis of Variance DE S5 Regression Residual Ezror 249 Total 32.47 0.000 255