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). i: 1 2 81 Xil: 1 14 14 X12: 5.02 8.19 12.68 X13: 0.14 0.27 0.03 : Xi4 123,000 104,079 Y₁: 13.50 12.00 201,930 14.50 (i) Fit the model Y₁ = ẞ0+ẞ1Xi1+ẞ2X12+ẞ3Xi3+ẞ4Xi4+; to the data. State the estimated regression function. (ii) The researcher want to estimate the mean rental rates for the property with X₁ = 5, X2 = 8.25, X3 = 0, x4 = 250,000. What is the estimate based on the regression function in (i)? (iii) Find a 99% confidence interval for the coefficient of age. (iv) Can you conclude that ẞ₁> 1? Perform the appropriate hypothesis test.
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). i: 1 2 81 Xil: 1 14 14 X12: 5.02 8.19 12.68 X13: 0.14 0.27 0.03 : Xi4 123,000 104,079 Y₁: 13.50 12.00 201,930 14.50 (i) Fit the model Y₁ = ẞ0+ẞ1Xi1+ẞ2X12+ẞ3Xi3+ẞ4Xi4+; to the data. State the estimated regression function. (ii) The researcher want to estimate the mean rental rates for the property with X₁ = 5, X2 = 8.25, X3 = 0, x4 = 250,000. What is the estimate based on the regression function in (i)? (iii) Find a 99% confidence interval for the coefficient of age. (iv) Can you conclude that ẞ₁> 1? Perform the appropriate hypothesis test.
Chapter5: Working With Excel Tables, Pivottables, And Pivotcharts
Section5.3: Pivottable And Pivotchart
Problem 6QC
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Using R language. Here is the information link. http://www.cnachtsheim-text.csom.umn.edu/Kutner/Chapter%20%206%20Data%20Sets/CH06PR18.txt
Transcribed Image Text: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).
i:
1
2
81
Xil:
1
14
14
X12:
5.02
8.19
12.68
X13:
0.14
0.27
0.03
:
Xi4 123,000 104,079
Y₁: 13.50 12.00
201,930
14.50
(i) Fit the model Y₁ = ẞ0+ẞ1Xi1+ẞ2X12+ẞ3Xi3+ẞ4Xi4+; to the data. State the estimated regression
function.
(ii) The researcher want to estimate the mean rental rates for the property with X₁ = 5, X2 = 8.25,
X3 = 0, x4 = 250,000. What is the estimate based on the regression function in (i)?
(iii) Find a 99% confidence interval for the coefficient of age.
(iv) Can you conclude that ẞ₁> 1? Perform the appropriate hypothesis test.
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