House price y is estimated as a function of the square footage of a house x, a d
ID: 3227004 • Letter: H
Question
House price y is estimated as a function of the square footage of a house x, a dummy variable d (hat 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 cap y = 78 + 017x + 35d + 0.04xd. a. Compute the predicted price of a house with ocean views and square footage of 2, 000 and 3, 000, 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 2, 000 and 3, 000, 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
Solution:
Here, It is given that,
y-hat = 78 + 0.17x + 35d + 0.04xd
a1) the predicted price (in $1,000s) of a house with ocean views and square footage of 2000 =
78 + 0.17 × 2000 + 35 ×1 + 0.04 × 2000 × 1 = 533
a2) the predicted price (in $1,000s) of a house with ocean views and square footage of 3000 =
78 + 0.17 × 3000 + 35 ×1 + 0.04 × 3000 × 1 = 743
b1) The predicted price (in $1,000s) of a house without ocean views and square footage of 2000 = 78 + 0.17 × 2000 = 418
b2) the predicted price (in $1,000s) of a house without ocean views and square footage of 3000 = 78 + 0.17 × 3000 = 588
c)
For both the option with and without ocean view the price difference is calculated as :
3000 sqft has price difference of 743 - 588 = 155
2000 sqft has price difference of 533 - 418 = 115
Hence as square footage increases, the price difference between houses with and without ocean views becomes larger as well and it is 155.
and as square footage decreases, the price difference between houses with and without ocean views becomes smaller and it is 115.
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