House price y is estimated as a function of the square footage of a house x and a dummy variable d that equals 1 if the house has ocean views. The estimated house price, measured in $1,000s, is given by yˆ = 118.90 + 0.12x + 52.60d. a-1. Compute the predicted price (in $1,000s) of a house with ocean views and square footage of 2,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.) a-2. Compute the predicted price (in $1,000s) of a house with ocean views and square footage of 3,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.) b-1. Compute the predicted price (in $1,000s) of a house without ocean views and square footage of 2,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.) b-2. Compute the predicted price (in $1,000s) of a house without ocean views and square footage of 3,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.) c. Discuss the impact of ocean views on the house price. multiple choice An ocean view increases the value of a house by approximately $52,600. An ocean view decreases the value of a house by approximately 10%. An ocean view decreases the value of a house by approximately $52.600. An ocean view increases the value of a house by approximately 10%.

Question

23-04-2021
Mathematics

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House price y is estimated as a function of the square footage of a house x and a dummy variable d that equals 1 if the house has ocean views. The estimated house price, measured in $1,000s, is given by yˆ = 118.90 + 0.12x + 52.60d. a-1. Compute the predicted price (in $1,000s) of a house with ocean views and square footage of 2,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.) a-2. Compute the predicted price (in $1,000s) of a house with ocean views and square footage of 3,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.) b-1. Compute the predicted price (in $1,000s) of a house without ocean views and square footage of 2,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.) b-2. Compute the predicted price (in $1,000s) of a house without ocean views and square footage of 3,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.) c. Discuss the impact of ocean views on the house price. multiple choice An ocean view increases the value of a house by approximately $52,600. An ocean view decreases the value of a house by approximately 10%. An ocean view decreases the value of a house by approximately $52.600. An ocean view increases the value of a house by approximately 10%.

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Answer:

a-1. The predicted price of a house with ocean views and square footage of 2,000 is $411,500.00.

a-2. The predicted price of a house with ocean views and square footage of 3,000 is $531,500.00.

b-1. The predicted price (in $1,000s) of a house without ocean views and square footage of 2,000 is $358,900.

b-2. The predicted price of a house without ocean views and square footage of 3,000 is $478,900.00.

c. The correct option is An ocean view increases the value of a house by approximately $52,600.

Step-by-step explanation:

Given:

yˆ = 118.90 + 0.12x + 52.60d ………………. (1)

a-1. Compute the predicted price (in $1,000s) of a house with ocean views and square footage of 2,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)

This implies that we have:

x = 2,000

d = 1

Substituting the values into equation (1), we have:

yˆ = 118.90 + (0.12 * 2000) + (52.60 * 1) = 411.50

Since the predicted price is in $1,000s, we have:

yˆ = 411.50 * $1000

yˆ = $411,500.00

Therefore, the predicted price of a house with ocean views and square footage of 2,000 is $411,500.00.

a-2. Compute the predicted price (in $1,000s) of a house with ocean views and square footage of 3,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)

This implies that we have:

x = 3,000

d = 1

Substituting the values into equation (1), we have:

yˆ = 118.90 + (0.12 * 3,000) + (52.60 * 1) = 531.50

Since the predicted price is in $1,000s, we have:

yˆ = 531.50 * $1000

yˆ = $531,500.00

Therefore, the predicted price of a house with ocean views and square footage of 3,000 is $531,500.00.

b-1. Compute the predicted price (in $1,000s) of a house without ocean views and square footage of 2,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)

This implies that we have:

x = 2,000

d = 0

Substituting the values into equation (1), we have:

yˆ = 118.90 + (0.12 * 2000) + (52.60 * 0) = 358.90

Since the predicted price is in $1,000s, we have:

yˆ = 358.90 * $1000

yˆ = $358,900.00

Therefore, the predicted price of a house without ocean views and square footage of 2,000 is $358,900.00.

b-2. Compute the predicted price (in $1,000s) of a house without ocean views and square footage of 3,000. (Round intermediate calculations to at least 4 decimal places. Round your answer to 2 decimal places.)

This implies that we have:

x = 3,000

d = 0

Substituting the values into equation (1), we have:

yˆ = 118.90 + (0.12 * 3,000) + (52.60 * 0) = 478.90

Since the predicted price is in $1,000s, we have:

yˆ = 478.90 * $1000

yˆ = $478,900.00

Therefore, the predicted price of a house without ocean views and square footage of 3,000 is $478,900.00.

c. Discuss the impact of ocean views on the house price.

Since the coefficient of d in equation (1) is 52.60 and positive, and the predicted price is in $1,000s; the correct option is An ocean view increases the value of a house by approximately $52,600.