TABLE 15-4
in Hawaii, Condemnation Proceedings Are Under Way to Enable

Multiple Choice

TABLE 15-4
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. The following model was fit to data collected for n = 20 properties, 10 of which are located near a cove.
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

Model 1: $Y=\beta_{0}+\beta_{1} X_{1}+\beta_{2} X_{2}+\beta_{3} X_{1} X_{2}+\beta_{4} X_{1}^{2}+\beta_{5} X_{1}^{2} X_{2}+\varepsilon$


Using the data collected for the 20 properties, the following partial output obtained from Microsoft Excel is shown: SUMMARY OUTPUT

$\begin{array}{lr}\hline\text { Regression Statistics}\\\hline\text { Multiple R } & 0.985 \\\text { R Square } & 0.970 \\\text { Standard Error } & 9.5 \\\text { Observations } & 20 \\\hline\end{array}$
$$\begin{array}{l}A N O V A\\\begin{array} { l r r r r l } \hline & d f & \text { SS } & M S & F & \text { Significance } F \\\hline \text { Regression } & 5 & 28324 & 5664 & 622 & 0.0001 \\\text { Residual } & 14 & 1279 & 91 & & \\\text { Total } & 19 & 29063 & & & \\\hline\end{array}\end{array}$$ $$\begin{array} { l c r r r } \hline & \text { Coeff } & \text { STd Error } & t \text { Stut } & p \text {-value } \\\hline \text { Intercept } & - 32.1 & 35.7 & - 0.90 & 0.3834 \\\text { Size } & 122 & 5.9 & 2.05 & 0.0594 \\\text { Cove } & - 104.3 & 53.5 & - 1.95 & 0.0715 \\\text { Size } { } ^ { * } \text { Cove } & 17.0 & 8.5 & 1.99 & 0.0661 \\\text { SizeSq } & - 0.3 & 0.2 & - 1.28 & 0.2204 \\\text { SizeSq } { } ^ { * } \text { Cove } & - 0.3 & 0.3 & - 1.13 & 0.2749\end{array}$$
-Referring to Table 15-4, 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?

A) $H_{0}: \beta_{2}=\beta_{3}=\beta_{5}=0$
B) $H_{0}: \beta_{3}=\beta_{5}=0$
C) $H_{0}: \beta_{4}=\beta_{5}=0$
D) $H_{0}: \beta_{2}=0$