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

question 52

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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.

Model 1: Y=β0+β1X1+β2X2+β3X1X2+β4X12+β5X12X2+ε 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

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: SUMMARY OUTPUT
Regression
Statistics
 Multiple R 0.985 R Square 0.970 Standard Error 9.5 Observations 20\begin{array}{lr}\text { Multiple R } & 0.985 \\\text { R Square } & 0.970 \\\text { Standard Error } & 9.5 \\\text { Observations } & 20 \\\hline\end{array}
ANOVAdf SS MSF Significance F Regression 528324566462.20.0001 Residual 14127991 Total 1929063\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 & 62.2 & 0.0001 \\\text { Residual } & 14 & 1279 & 91 & & \\\text { Total } & 19 & 29063 & & & \\\hline\end{array}\end{array}  Coeff  STd Error t Stut p-value  Intercept 32.135.70.900.3834 Size 1225.92.050.0594 Cove 104.353.51.950.0715 Size  Cove 17.08.51.990.0661 SizeSq 0.30.21.280.2204 SizeSq  Cove 0.30.31.130.2749\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, is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y) ?

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