1. 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. First column is rental rates(Y ), second column is the age of properties(X1), third column is the operating expenses and taxes(X2), fourth column is the vacancy rates(X3) and last column is the total square footage(X4). Data can be downloaded at: https://netfiles.umn.edu/users/nacht001/www/nachtsheim/Kutner/ Chapter%20%206%20Data%20Sets/CH06PR18.txt

(a) What is response variable? What are the independent variables?

(b) For each variable, calculate 5 number summary, mean and variance. Use your own word to describe the data.

(c) Draw boxplot for X1, X2, X3 and X4, what are your findings based on the boxplot?

(d) What are the difference between scatter plot, quantile plot and q-q plot?

(e) Draw histogram, q-q plot for X1, X2, X3 and X4.

(f) Draw scatter plot for each pair of X1, X2, X3 and X4, what are your findings? Calculate correlation coefficient to confirm your findings.

(g) Calculate the covariance of X1, X2, X3 and X4.

(h) Is it necessary that data transformation techniques applied? If yes, why and propose one data transformation technique.

(i) Find a regression model to the data and state your model.

(j) Based on the output of fit, summarise your findings and conclusion.

dataset:

 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