Linear regression analysis y x1 x2 x3 x4
13.5 1 5.02 0.14 123000
12 14 8.19 0.27 104079
10.5 16 3 0 39998
15 4 10.7 0.05 57112
14 11 8.97 0.07 60000
10.5 15 9.45 0.24 101385
14 2 8 0.19 31300
16.5 1 6.62 0.6 248172
17.5 1 6.2 0 215000
16.5 8 11.78 0.03 251015
17 12 14.62 0.08 291264
16.5 2 11.55 0.03 207549
16 2 9.63 0 82000
16.5 13 12.99 0.04 359665
17.225 2 12.01 0.03 265500
17 1 12.01 0 299000
16 1 7.99 0.14 189258
14.625 12 10.33 0.12 366013
14.5 16 10.67 0 349930
14.5 3 9.45 0.03 85335
16.5 6 12.65 0.13 235932
16.5 3 12.08 0 130000
15 3 10.52 0.05 40500
15 3 9.47 0 40500
13 14 11.62 0 45959
12.5 1 5 0.33 120000
14 15 9.89 0.05 81243
13.75 16 11.13 0.06 153947
14 2 7.96 0.22 97321
1. A commercial real estate company evaluates vacancy rates, square footage, rental rates, and operating expense for commercial properties in a large metropolitan area in order to provide clients with quantitative information upon which to make rental decisions. The data were taken from 81 suburban commercial properties that the newest, best located, most attractive, and expensive for five specific geographic areas. The variables are age (X1), operating expense and taxes (X2), vacancy rates (X3), total square footage (X4), and rental rates (Y). Data is in commercial. xlsx.
a) Use R to generate appropriate models, and then based on the summary of the model, calculate R33, R 3|1, RÝ3|1,2, and R3|1,2,4
b) Perform a hypothesis test to see whether X3 can be dropped from a model that already contains X1, X2 and X4, at a = 0.05. X1-X1.
c) Use R to draw a scatter plot between X1 and Y, does it exhibit some curvature pattern? Transform X1 by scaling it (i. e,, newX1 = *1714). Fit a polynomial regression model with newX1, the square of newX1, X2, and X4. Explain whether you consider this model is a good fit (hint, you can evaluate the model on the adjusted R2, Goodness-of-fit test, and the residual plot). S(X1)
d) Use the polynomial model to estimate the mean rental rate for a commercial property that is 8 years old, operation cost is 16 (Thousands per year) and 250,000 square feet, at a 95% confidence level.