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Housing prices The following regression model was found for the houses in upstate New York considered in the chapter:
- a) Find the predicted price of a 2 bedroom, 1000-sq-ft house from this model.
- b) The house just sold for $135,000. Find the residual corresponding to this house.
- c) What does that residual say about this transaction?
a.
Find the predicted price of a 2 bedroom, 1,000 sq-ft house.
Answer to Problem 1E
The predicted price of a 2 bedroom, 1,000 sq-ft house in upstate New York is likely to be $99,859.89.
Explanation of Solution
Given info:
The regression model for the price of houses in upstate New York with respect to number of bedrooms and living area is given as:
Calculation:
The given regression equation is:
Substitute
Thus, the predicted price of a 2 bedroom, 1,000 sq-ft house in upstate New York is likely to be $99,859.89.
b.
Find the residual corresponding to a house that sold for $135,000.
Answer to Problem 1E
The residual corresponding to a house that sold for $135,000 is $35,140.11.
Explanation of Solution
Calculation:
Residual:
The residual corresponding to a predictor variable is given as the difference between actual value of the response variable and the predicted value. That is,
Put the actual value of ‘price’ as
Then,
Thus, the residual corresponding to a house that sold for $135,000 is $35,140.11.
c.
Explain what the residual says about the transaction.
Explanation of Solution
Justification:
The real price, at which the house is sold, is $135,000. The regression model predicted that the price of the house would be sold at $99,859.89.
The residual $35,140.11 means that the house is sold at a price of $35,140.11 more than what was predicted.
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