Urban/rural ratings of counties. Professional Geographer (February 2000) published a study of urban and rural counties in the western United States. University of Nevada (Reno) researchers asked a sample of 256 county commissioners to rate their ‘‘home'' county on a scale of 1 (most rural) to 10 (most urban).
The urban/rural rating (y) was used as the dependent variable in a first-order multiple regression model with 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). Some of the regression results are shown in the next table.
(a) Write the least squares prediction equation for y.
(b) Give the null hypothesis for testing overall model adequacy.
(c) Conduct the test, part b, at α = .01 and give the appropriate conclusion.
(d) Interpret the values of R2 and R2a.
(e) Give the null hypothesis for testing the contribution of population growth (x4) to the model.
(f) Conduct the test, part e, at α = .01 and give the appropriate conclusion.
