Intro Stats, Books a la Carte Edition (5th Edition)
Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Chapter 9, Problem 1E

Housing prices The following regression model was found for the houses in upstate New York considered in the chapter:

P r i c e ^ = 20 , 986.09 7483.10 B e d r o o m s + 93.84 L i v i n g A r e a

  1. a) Find the predicted price of a 2 bedroom, 1000-sq-ft house from this model.
  2. b) The house just sold for $135,000. Find the residual corresponding to this house.
  3. c) What does that residual say about this transaction?

a.

Expert Solution
Check Mark
To determine

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:

Price^=20,986.097483.10 Bedrooms+93.84 Living Area.

Calculation:

The given regression equation is:

Price^=20,986.097483.10 Bedrooms+93.84 Living Area

Substitute Bedrooms=2 and Living Area=1,000 in the equation:

Price^=20,986.09(7483.10×2)+(93.84×1,000)=20,986.0914,966.2+93,840=99,859.89.

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.

Expert Solution
Check Mark
To determine

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, e=yy^, where y be the actual value of the response variable and y^ be the predicted value of the response variable for same predictor variable.

Put the actual value of ‘price’ as y=135,000 and the predicted value as y^=99,859.89.

Then,

e=135,00099,859.89=35,140.11.

Thus, the residual corresponding to a house that sold for $135,000 is $35,140.11.

c.

Expert Solution
Check Mark
To determine

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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