# XR19-11 A developer who specialises in holiday cottage properties is considering purchasing a large.

XR19-11 A developer who specialises in
holiday 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
the lot are size, number of mature trees and distance to the lake. From a
nearby area, she gathers the relevant data for 60 recently sold lots. These
data are recorded (
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XR19-11 A developer who specialises in
holiday 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
the lot are size, number of mature trees and distance to the lake. From a
nearby area, she gathers the relevant data for 60 recently sold lots. These
data are recorded (Column 1 = price in thousands of dollars, column 2 = lot
size in hundreds of square metres, column 3 = number of mature trees, and
column 4 = distance to the lake in metres). A multiple regression analysis was
performed. The Excel printout is shown below.

a What is the standard error of estimate?
Interpret its value.

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

c 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?

d Test the overall utility of the model.
What does the p-value of the test statistic tell you?

e Interpret each of the coefficients.

f Test to determine whether each of the
independent variables is linearly related to the price of the lot.

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