Solution Found!
Urban population estimation using satellite images. Can
Chapter 12, Problem 149SE(choose chapter or problem)
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 \(\left(x_1\right)\), and proportion of block with high-density residential areas \(\left(x_2\right)\). A first-order model for y was fit to the data with the following results:
\(\hat{y}=-.0304+2.006 x_1+5.006 x_2, R^2=.686\)
a. Give a practical interpretation of each \(\beta\) estimate in the model.
b. Give a practical interpretation of the coefficient of determination, \(R^2\).
c. State \(H_0\) and \(H_{\mathrm{a}}\) 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 \(\alpha=.01\).
Questions & Answers
QUESTION:
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 \(\left(x_1\right)\), and proportion of block with high-density residential areas \(\left(x_2\right)\). A first-order model for y was fit to the data with the following results:
\(\hat{y}=-.0304+2.006 x_1+5.006 x_2, R^2=.686\)
a. Give a practical interpretation of each \(\beta\) estimate in the model.
b. Give a practical interpretation of the coefficient of determination, \(R^2\).
c. State \(H_0\) and \(H_{\mathrm{a}}\) 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 \(\alpha=.01\).
ANSWER:Step 1 of 7
(a)
Interpretation:
The estimated value of 
The estimated value of 
In the given model, 