7.10 ONLY 7.10. Refer to Commercial properties Problem 6.18. Test whether Bi = -.I and B2 = 4; use a =.01. State the alternatives, full and reduced models, decision rule, and conclusion. 7.11. Refer to the work crew productivity example in Table 7.6. Calculate D2 12 12 12 D2 and R2 Funlain what each coefficient manaus 6.18. Commercial properties. A commercial real estate company evaluates vacancy rates, square footage, rental rates, and operating expenses for commercial properties in a large metropolitan area in order to provide clients with quantitative information upon which to make rental deci- sions. The data below are taken from 81 suburban commercial properties that are the newest, best located, most attractive, and expensive for five specific geographic areas. Shown here are the age (X,), operating expenses and taxes (X2), vacancy rates (X3), total square footage (X4), and rental rates (Y) i: 2 3 . . . 79 80 81 Xn: 1 14 16 . .. 15 11 14 X12: 5.02 8.19 3.00 . . . 11.97 11.27 12.68 X13: 0.14 0.27 . . . 0.14 0.03 0.03 X14: 123,000 104,079 39,998 . . . 254,700 434,746 201,930 13.50 12.00 10.50 15.00 15.25 14.50 a. Prepare a stem-and-leaf plot for each predictor variable. What information do these plots provide? b. Obtain the scatter plot matrix and the correlation matrix. Interpret these and state your principal findings. c. Fit regression model (6.5) for four predictor-variables to the data. State the estimated regression function. d. Obtain the residuals and prepare a box plot of the residuals. Does the distribution appear to be fairly symmetrical? e. Plot the residuals against Y, each predictor variable, and each two-factor interaction term on separate graphs. Also prepare a normal probability plot. Analyze your plots and summarize your findings. f. Can you conduct a formal test for lack of fit here? g. Divide the 81 cases into two groups. placing the 40 cases with the smallest fitted values Y; into group 1 and the remaining cases into group 2. Conduct the Brown-Forsythe test for constancy of the error variance, using o = .05. State the decision rule and conclusion