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Ch16

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Chapter 16

7. In 2011, home prices and mortgage rates fell so far that in a number of cities the monthly cost of owning a home was less expensive than renting. The following data show the average asking rent and the monthly mortgage on the median-priced home (including taxes and insurance) for 10 cities where the average monthly mortgage payment was less than the average asking rent (The Wall Street Journal, November 26-27, 2011).

a. Develop a scatter diagram for these data, treating the average asking rent as the independent variable. Does a simple linear regression model appear to be appropriate?
The below scatter diagram shows a possible curvilinear relationship between the average asking rent and the monthly mortgage on the median-priced home. Therefore, a simple linear regression model does not appear to be appropriate.

b. Use a simple linear regression model to develop an estimated regression equation to predict the monthly mortgage on the median-priced home given the average asking rent. Construct a standardized residual plot. Based upon the standardized residual plot, does a simple linear regression model appear to be appropriate?

The regression equation is
Mortgage ($) = - 198 + 1.07 Rent ($)

Predictor Coef SE Coef T P
Constant -198.0 187.7 -1.05 0.322
Rent ($) 1.0699 0.2148 4.98 0.001

S = 78.7819 R-Sq = 75.6% R-Sq(adj) = 72.6%

Analysis of Variance
Source DF SS MS F P
Regression 1 153962 153962 24.81 0.001
Residual Error 8 49653 6207
Total 9 203614

Unusual Observations Rent Mortgage
Obs ($) ($) Fit SE Fit Residual St Resid 1 840 539.0 700.8 25.5 -161.8 -2.17R
R denotes an observation with a large standardized residual.

Based on the standardized residual plot, the assumed

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