The article “Selling Prices/Sq. Ft. of Office Buildings in Downtown Chicago – How Much Is It Worth to Be an Old but Class-A Building?” (J. Real Estate Res. 2010: 1–22) considered a regression model to relate y = ln($/ft²) to 16 predictors, including age, age squared, number of stories, occupancy rate, and indicator variables for whether it is a class-A building, whether a building has a restaurant and whether it has conference rooms. The model was fit to data resulting from 203 sales.

a. The coefficient of multiple determination was .711. What is the value of the adjusted coefficient of multiple determination? Does it suggest that the relatively high R² value was the result of including too many predictors in the model relative to the amount of data available?

b. Using the R² value from (a), carry out a test of hypotheses to see whether there is a useful linear relationship between the response variable and at least one of the predictors.
c. The estimated coefficient of the indicator variable for whether or not a building was class-A was .364. Interpret this estimated coefficient, first in terms of y and then in terms of $/ft².
d. The t ratio for the estimated coefficient of (c) was 5.49. What does this tell you?