Urban population estimation using satellite images. Can the population of an urban area be estimated without taking a census? In Geographical Analysis (January 2007) geography professors at the University of Wisconsin-Milwaukee and Ohio State University demonstrated the use of satellite image maps for 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 fit to the data with the following results:

yˆ = -.0304 + 2.006x₁ + 5.006x₂, R² = .686

(a) Give a practical interpretation of each β-estimate in the model.

(b) Give a practical interpretation of the coefficient of determination, R^2.

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

(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.