Can the population of an urban area be estimated without taking a census? In Geographical Analysis (Jan. 2007) geography professors at the University of Wisconsin at Milwaukee and Ohio State University demonstrated the use of satellite image maps in estimating urban population. A portion of Columbus, Ohio, was partitioned into n = 125 census block groups, and satellite imagery was obtained. For each census block, the following variables were measured: population density (y), proportion of block with low-density residential areas (x1), and proportion of block with high-density residential areas (x2). A first-order model for y was fitted to the data and produced the following results:

y = – .0304 + 2.006x1 + 5.006x2, R2 = .686

a. Give a practical interpretation of each b -estimate in the model.

b. Give a practical interpretation of the coefficient of determination, R2.

c. State H0 and Ha for a test of the overall adequacy of the model.

d. Refer to part c. Compute the value of the test statistic.

e. Refer to parts c and d. Make the appropriate conclusion at α = .01.