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 (XI), operating expenses and taxes (Xl), vacancy rates (X3), total square footage (X4 ),
Data as follows-
Y1 Xi1 Xi2 Xi3 Xi4
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
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?
