Cottage Practices

     A developer who specializes in summer cottage properties is considering purchasing a large tract of land adjoining a lake. The current owner of the tract has already subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The developer wants to forecast the value of each lot. From previous experience, she knows that the most important factors affecting the price of a lot are size, number of mature trees, and distance from the lake. From a nearby area, she gathers relevant data for 60 recently sold lots.

  R-square = .2425, R-square (adjusted) =  .2019   

Sε = 40.24,

F = 5.97,

p-value = .0013   Intercept: coefficient = 51.39,

Standard   Error = 23.52

t-stat = 2.19

p-value = .0331

  Lot Size: coefficient = .700

Standard   Error = .559

t-stat = 1.25

p-value = .2156   

Trees: coefficient = .679, Standard Error   = .229

t-stat = 2.96

p-value = .0045   

Distance: Coefficient = -.378

Standard   Error = .195

t-stat = -1.94

p-value = .0577   (Use a 5% significance level)

  a. Find the regression equation   

b. What is the standard error of   estimate? Interpret it’s value   

c. What is the coefficient of   determination? What does this statistic tell you?   

d. What is the coefficient of determination, adjusted for degrees of freedom? Why does this value differ from the coefficient of determination? What does this tell you about the model?   

e. Test the validity of the model. What   does the p-value of the test statistic tell you?   

f. Interpret each of the coefficients   

g. Test to determine whether each of the independent variables is linearly related to the price of the lot in this   model   

h. Predict with 90% confidence the selling price of a 40,000-square-foot lot that has 50 mature trees and is 25 feet from the lake   

i. Estimate with 90% confidence the average selling price of 50,000-square-foot lots that have 10 mature trees and are 75 feet from the lake