The Professional Geographer (Feb. 2000) published a study of urban and rural counties in the western United States. Six independent variables total county population (x1), population density (x2), population concentration (x3), population growth (x4), proportion of county land in farms (x5), and 5-year change in agricultural land base (x6)-were used to model the urban/rural rating (y) of a county, where rating was recorded 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. Below is a correlation matrix for data collected on n = 256 counties.

a. Based on the correlation matrix, is there any evidence of extreme multicollinearity?
b. The first-order model with all six independent variables was fit, and the results are shown in the next table. Based on the reported tests, is there any evidence of extreme multicollinearity?

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Independent Variable t: Total population x2: Population density ぶPopulation .20 45 43 concentration : Population growth -0514 01 1s: Farm land 16-15 07 20 Agricultural change 12 12 22-06 06 Independent Variable x: Total population B Estimate p-value 0.110 0.065 0.045 0.230 : Population density r: Population 0.540 0,009 -0,150 -0.027 0.000 0.860 0.003 0.580 concentration Population growth t: Farm land Agricultural change Overall model: R,..43 F. 32.47 p-value < .001