Question

A real estate study was conducted in the Washington, DC, area to determine if certain variables are related to the sales price of a townhouse. As part of his investigation, he ran the following multiple regression model: Sales Price = β0 + β1(Square Feet) + β2(Distance) + εi where the deviations εi were assumed to be independent and normally distributed with mean 0 and standard deviation σ. The two explanatory variables are the square footage of the townhouse and the distance each townhouse is to a Metro stop. The data were obtained by selecting a random sample of 50 townhouses from the population of townhouses in the Washington, DC, area. This model was fit to the data using the method of least squares. The following results were obtained from statistical software: Source df Sum of Squares Model 2 86,528 Error 47 2,722 Variable Parameter Estimate Standard Error of Parameter Estimate Constant –16.11 90.06 Square Feet 0.55935 0.07127 Distance –41.065 8.730 Reference: Ref 11-3 The proportion of the variation in the variable Sales Price that is explained by the explanatory variables Square Feet and Distance is: 0.9583. 0.5000. 0.9846. 0.9695.

Answer 1

Answer:

The proportion of the variation in the variable Sales Price that is explained by the explanatory variables Square Feet and Distance = 0.9695

Explanation:

The proportion of the variation in the variable Sales Price that is explained by the explanatory variables Square Feet and Distance (or the R Square value) is obtained using the following formula,

where

SSE = Sum of Square of Error, and

SST = Sum of Square of Error

SST = Sum of Square of Model + Sum of Square of Error

SST = SSM + SSE = 86528 + 2722 = 89250

Now,