6. A developer who specializes in summer cottage properties is considering purch

Question

6. A developer who specializes in summer cottage properties is considering purchasing a large tract of land adjoining a lake, approximately 60 miles from a large urban area. The current owner of the tract hasalready subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The developer wants toforecast the value of each lot. From previous experience, she knowsthat the most important factors a ecting the price of a lot (in $1,000s) are lot size (in square feet), number of mature trees remaining, anddistance to the lake (in feet). From a nearby area, she gathers relevant data about 60 recently sold lots. She has run a regression thatproduced the following output:

The regression equation is

PRICE = 8.242 + 0.102SIZE + 1.348TREES - 2.137DISTANCE

Predictor Coef Stdev t-ratio p-value

Constant   8.242 3.257 2.531 0.0142

SIZE 0.102 0.048 2.125 0.0380

TREES 1.348 0.513 2.628 0.0110

DISTANCE -2.137 0.676 -3.161 0.0026

(b) Do these data provide enough evidence to enable the developerto conclude, at the 1% significance level, that price and distancefrom the lake are negatively linearly related?

Explanation / Answer

a) P-value for lot size is 0.038, which is less than 0.05. There is sufficient evidence to indicate that price and lot size are linearly related.

b) P-value for distance is 0.0026, which is less than 0.01 and slope is negative. These data provide enough evidence to enable the develope rto conclude, at the 1% significance level, that price and distancefrom the lake are negatively linearly related.

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