Posted: December 12th, 2022
In Hawaii, condemnation proceedings are under way to enable private citizens to own the property that their homes are built on. Until recently, only estates were permitted to own land, and homeowners leased the land from the estate. In order to comply with the new law, a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land. Each of the following three models were fit to data collected for n = 20 properties, 10 of which are located near a cove.
Model 1: Y = Bo + B1x1 + B2x2 + B3x1x2 + B4x1 + B5x1x2 + e
Where Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square feet
X2 = 1 if property located near cove, 0 if not
Using the data collected for the 20 properties, the following partial output
obtained from Microsoft Excel is shown:
Multiple R 0.985
R Square 0.970
Standard Error 9.5
df SS MS F Signif F
Regression 5 28324 5664 62.2 0.0001
Residual 14 1279 91
Total 19 29063
Coeff StdError t Stat P-value
Intercept -32.1 35.7 -0.90 0.3834
Size 12.2 5.9 2.05 0.0594
Cove -104.3 53.5 -1.95 0.0715
Size*Cove 17.0 8.5 1.99 0.0661
SizeSq -0.3 0.2 -1.28 0.2204
SizeSq*Cove -0.3 0.3 -1.13 0.2749
16. Referring to Table 12-14, given a quadratic relationship between sale price (Y) and property size (X1), what test should be used to test whether the curves differ from cove and non-cove properties?
a. F test for the entire regression model.
b. t test on each of the coefficients in the entire regression model.
c. Partial F test on the subset of the appropriate coefficients.
d. t test on each of the subsets of the appropriate coefficients.
An automotive engineer would like to be able to predict automobile mileages. She believes that the two most important characteristics that affect mileage are horsepower and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is
Y = 40 – 0.05×1 + 20×2 – 0.1x1x2 where X1 = horsepower
X2 = 1 if 4 cylinders, 0 if 6 cylinders
Y = mileage.
18. Referring to Table 12-19, the fitted model for predicting mileages for 4-cylinder cars is ________.
a. 40 – 0.05X1
b. 40 – 0.10X1
c. 60 – 0.10X1
d. 60 – 0.15X1
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