House price y is estimated as a function of the square footage of a house x; a d

Question

House price y is estimated as a function of the square footage of a house x; a dummy variable d that equals 1 if the house has ocean views and 0 otherwise; and a product of this dummy and the square footage xd. The estimated house price, measured in $1,000s, is given by y = 86 + 0.11x + 42d + 0.04xd. a. Compute the predicted price of a house with ocean views and square footage of 1, 900 and 2, 900, respectively. (Round your final answers to the nearest whole number.) b. Compute the predicted price of a house without ocean views and square footage of 1, 900 and 2, 900, respectively. (Round your final answers to the nearest whole number.) c. Discuss the impact of ocean views on the house price. As square footage increases, the price difference between houses with and without ocean views becomes larger as well. As square footage decreases, the price difference between houses with and without ocean views becomes smaller.

Explanation / Answer

predicted price of house is given by
y = 86 + 0.11x + 42d + 0.04xd

(A)
For x = 1900 and d = 1, y = 86 + 0.11*1900 + 42*1 + 0.04*1900*1 = 413

For x = 2900 and d = 1, y = 86 + 0.11*2900 + 42*1 + 0.04*2900*1 = 563

(B)
For x = 1900 and d = 0, y = 86 + 0.11*1900 + 42*0 + 0.04*1900*0 = 295

For x = 2900 and d = 0, y = 86 + 0.11*2900 + 42*0 + 0.04*2900*0 = 405

(C)

As square footage increases difference in prices also increases for with and without oceanic view houses.

Square Footage Price ($ 000) 1900 413 2900 563

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