Instruction 16-5
In Hawaii, condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built. 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. The following model was fit to data collected for n = 20 properties, 10 of which are located near a cove. Model 1: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₁X₂ + β₄+ β₅X₂ + ε
where
Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square metres
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:
Note: Std. Error = Standard Error
-Referring to Instruction 16-5,given a quadratic relationship between sale price (Y) and property size (X1) ,what null hypothesis would you test to determine whether the curves differ from cove and non-cove properties?

Question

Instruction 16-5
In Hawaii, condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built. 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. The following model was fit to data collected for n = 20 properties, 10 of which are located near a cove. Model 1: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₁X₂ + β₄+ β₅X₂ + ε
where
Y = Sale price of property in thousands of dollars
X1 = Size of property in thousands of square metres
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:

Note: Std. Error = Standard Error
-Referring to Instruction 16-5,given a quadratic relationship between sale price (Y) and property size (X1) ,what null hypothesis would you test to determine whether the curves differ from cove and non-cove properties?

Quizplus · Accepted Answer

The null hypothesis should test whether the quadratic relationship between sale price and property size differs between cove and non-cove properties, which means we need to test whether the coefficients of X1^2*X2, X1*X2^2, and X1^2*X2^2 are equal to zero. Thus, the null hypothesis should be H₀: β₃ = β₅ = 0.

Instruction 16-5 In Hawaii, Condemnation Proceedings Are Under Way to Enable Private