{Exercise 17.1}

The following exercise requires the use of a computer and statistical software. Use a 5% significance level.

Dataset: [Xr17-01]

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 to the lake. From a nearby area, she gathers the relevant data for 60 recently sold lots.

a. Find the regression equation (to 3 decimals).

= + x1 + x2 - x3

b. What is the standard error of estimate (to 2 decimals)?

sz =

c. What is the coefficient of determination to (to 4 decimals)?

R2 =

What does this statistic tell you?
% of the variation in prices is explained by the model.

d. What is the coefficient of determination, adjusted for degrees of freedom (to 4 decimals)?

It differs from R2 because it includes an adjustment for the number of SelectdependentindependentItem 9 variables.

e. Test the validity of the model (to 4 decimals).
p-value =

What does the p-value of the test statistic tell you?

There is Selectenoughnot enoughItem 11 evidence to conclude that the model is valid.

f. Interpret each of the coefficients (to 3 decimals).

b1 = ; for each addition thousand square feet the price on average SelectincreasesdecreasesItem 13 by thousand dollars provided that the other variables remain constant.

b2 = ; for each addition tree the price on average SelectincreasesdecreasesItem 16 by thousand dollars provided that the other variables remain constant.

b3 = ; for each addition foot from the lake the price on average SelectincreasesdecreasesItem 19 by thousand dollars provided that the other variables remain constant.

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

Lot size:	Selectlinearnot linearItem 21
Trees:	Selectlinearnot linearItem 22
Distance:	Selectlinearnot linearItem 23

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.
We predict that the lot in question will sell for between $ and $ .

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.
Estimated average price lies between $ and $ .

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