Property valuation

The government plans to build a new subway and rail terminal, and is oering compensation to the land property owner where the terminal is to be developed. The government claims that the oered compensation amount is based on market prices. The property owner believes that the new development would add substantial value to the properties around it, and that she should be compensated for that as well. She obtained results of two simple regressions; both regression outputs are in the worksheetPropertyValuationof the Excel workbookFinalExam Outputs.

Regression 1 has the current market value of properties (variable nameValue, in hundreds of thousands of dollars, i.e., measured in units of$100,000) as the dependent variable, and the size of the property (variable nameSize, measured in acres; 1 acre4,047 square meters) as the independent variable. Regression 2 uses the same independent variableSize, but it uses percentage increase in the property value based on the size of the property after similar government developments occurred (variable nameIncrValue, in percentage points, i.e., a decrease in value of 12% would correspond toIncrValue= -12).

The government oered$1 million compensation to the owner of a three acre property where the terminal will be built. The owner is considering an appeal based on the argument that she also needs to be compensated for the increase in property values. However, government ocials only consider counter-oers that are NOT extreme in the context of the argument of the appeal, so the counter-oer must be within the 95% range of valuations of comparable properties within each model used to support the argumentation provided with the appeal. What is the largest potential counter-oer amount supported by the two regression models (Regression 1 and Regression 2) that will be considered by the government ocials?

Regression 1: Dependent Variable: Value Independent Variables: Size Regression Statistics R Square Adj.RSqr Std.Err.Reg. # Cases # Missing t(2.5%,285) 0.175 0.149 0.695 287 0 1.968 Summary Table Variable Coeff Std.Err. t-Stat. P-value Intercept 1.784 0.382 4.670 0.000 Size 2. 103 0.112 18.777 0.000 Forecasted : Value Size Forecast StErrFst Fest#1 3.887 1.033 Fest#2 2 5.990 1.000 Fest#3 3 8.093 0.953Regression 2: Dependent Variable: IncrValue Independent Variables: Size Regression Statistics R Square Adj.RSqr Std.Err.Reg. # Cases # Missing t(2.5%,490) 0.273 0.252 2.210 492 0 1.965 Summary Table Variable Coeff Std.Err. t-Stat. P-value Intercept 14.601 0.412 35.439 0.000 Size -2.101 0.301 -6.980 0.000 Forecasted : IncrValue Size Forecast StErrFst Fest#1 3 8.298 3.022 Fest#2 2 10.399 2.873 Fest#3 12.500 2.788