6. House price y is estimated as a function of the square footage of a house, x,
ID: 3336561 • Letter: 6
Question
6. 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 thousands of US dollars is given by: y = 118.9 +·12x + 52.6d Compute the predicted price of two houses with ocean views and square footage of 2,000 and 3,000 respectively Compute the predicted price of two houses without ocean views and square footage of 2,000 and 3,000 respectively Discuss the impact of ocean views on the house price Suppose all of the houses in the sample are located in 5 states. Due to differences in the capitalization of property taxes in these states the researcher would like to include a series of dummy variables to account for the state in which the sale was made. If the sample contains houses from 5 states how many dummy variables must the researcher include to capture the sale price differences due to the state of sale (only include the number of new dummy variables, do not count, d, as a dummy variable in this answer) a. b. c. d.Explanation / Answer
a) y = 118.9 + 0.12x + 52.6d
when x = 2000
y = 118.9 + 0.12 * 2000 + 52.6 * 1
y = 411.5 thosand dollars.
when x = 2000
y = 118.9 + 0.12 * 3000 + 52.6 * 1
y = 531.5 thosand dollars.
b) y = 118.9 + 0.12x + 52.6d
when x = 2000
y = 118.9 + 0.12 * 2000 + 52.6 * 0
y = 358.9 thosand dollars.
when x = 2000
y = 118.9 + 0.12 * 3000 + 52.6 * 1
y = 478.9 thosand dollars.
c) if ocean views are there, the price of house increases by 52.6 thousand dollars.
d) This is easy; it's simply k-1, where k is the number of levels of the original variable. You could also create dummy variables for all levels in the original variable, and simply drop one from each analysis. In this instance, we would need to create 5-1 = 4 dummy variables.
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