Posted: December 12th, 2022

TABLE 12-14

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:

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SUMMARY OUTPUT

Regression Statistics

Multiple R 0.985

R Square 0.970

Standard Error 9.5

Observations 20

ANOVA

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

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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.

TABLE 12-19

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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