In Hawaii, condemnation proceedings are under way to enable private citizens to

Question

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

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

SUMMARY OUTPUT

Regression Statistics
Multiple R             0.890
R Square              0.7921
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

What is the percent of variation explained on the dependent variable by using this model?

Explanation / Answer

percent of variation on the dependent variable is said by Rsquare

In this model ,[Y] the dependent variable is sale price of property and the independent variables are :

[X1 ]Size of property and [X2 ]= 1 : if property located near cove, 0 if not ( categorical variable)

Therefore  sale price of property is predicted by [X1 ]Size of property and [X2 ]= 1 ( if property located near cove)

by using Rsquare

In this model, it is given that Rsquare is 0.79 i.e 79%

Therefore sale price is predicted that 79% that the independent variables X1( size of property) and X2 (  property located near cove ) is effecting the saleprice

size and property location is effecting 79% i.e more for saleprice of property

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