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 decisions. 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 (X1), operating expenses and taxes (X2), vacancy rates (X3), total square footage (X4 ),and rental rates (Y)

Data as follows-

Y X1 X2 X3 X4

13.500 1 5.02 0.14 123000 12.000 14 8.19 0.27 104079 10.500 16 3.00 0.00 39998 15.000 4 10.70 0.05 57112 14.000 11 8.97 0.07 60000 10.500 15 9.45 0.24 101385 14.000 2 8.00 0.19 31300 16.500 1 6.62 0.60 248172 17.500 1 6.20 0.00 215000 16.500 8 11.78 0.03 251015 17.000 12 14.62 0.08 291264 16.500 2 11.55 0.03 207549 16.000 2 9.63 0.00 82000 16.500 13 12.99 0.04 359665 17.225 2 12.01 0.03 265500 17.000 1 12.01 0.00 299000 16.000 1 7.99 0.14 189258 14.625 12 10.33 0.12 366013 14.500 16 10.67 0.00 349930 14.500 3 9.45 0.03 85335 16.500 6 12.65 0.13 235932 16.500 3 12.08 0.00 130000 15.000 3 10.52 0.05 40500 15.000 3 9.47 0.00 40500 13.000 14 11.62 0.00 45959 12.500 1 5.00 0.33 120000 14.000 15 9.89 0.05 81243 13.750 16 11.13 0.06 153947 14.000 2 7.96 0.22 97321 15.000 16 10.73 0.09 276099 13.750 2 7.95 0.00 90000 15.625 3 9.10 0.00 184000 15.625 3 12.05 0.03 184718 13.000 16 8.43 0.04 96000 14.000 16 10.60 0.04 106350 15.250 13 10.55 0.10 135512 16.250 1 5.50 0.21 180000 13.000 14 8.53 0.03 315000 14.500 3 9.04 0.04 42500 11.500 15 8.20 0.00 30005 14.250 1 6.13 0.00 60000 15.500 15 8.32 0.00 73521 12.000 1 4.00 0.00 50000 14.250 15 10.10 0.00 50724 14.000 3 5.25 0.16 31750 16.500 3 11.62 0.00 168000 14.500 4 5.31 0.00 70000 15.500 1 5.75 0.00 27000 16.750 4 12.46 0.03 129614 16.750 4 12.75 0.00 129614 16.750 2 12.75 0.00 130000 16.750 2 11.38 0.00 209000 17.000 1 5.99 0.57 220000 16.000 2 11.37 0.27 60000 14.500 3 10.38 0.00 110000 15.000 15 10.77 0.05 101206 15.000 17 11.30 0.00 288847 16.000 1 7.06 0.14 105000 15.500 14 12.10 0.05 276425 15.250 2 10.04 0.06 33000 16.500 1 4.99 0.73 210000 19.250 0 7.33 0.22 240000 17.750 18 12.11 0.00 281552 18.750 16 12.86 0.00 421000 19.250 13 12.70 0.04 484290 14.000 20 11.58 0.00 234493 14.000 18 11.58 0.03 230675 18.000 16 12.97 0.08 296966 13.750 1 4.82 0.00 32000 15.000 2 9.75 0.03 38533 15.500 16 10.36 0.02 109912 15.900 1 8.13 0.23 236000 15.250 15 13.23 0.05 243338 15.500 4 10.57 0.04 122183 14.750 20 11.22 0.00 128268 15.000 3 10.34 0.00 72000 14.500 3 10.67 0.00 43404 13.500 18 8.60 0.08 59443 15.000 15 11.97 0.14 254700 15.250 11 11.27 0.03 434746 14.500 14 12.68 0.03 201930

(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 on separate graphs. Also prepare a normal probability plot. Analyze the 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 Yi into the group 1and the remaining cases into group 2. Conduct the Brown-Forsythe test for constancy of the error variance, using alpha= 0.05. State the decision rule and conclusion. Please give the solution of all the above questions in R.

Please give all the answers in R.