# Ch16

1260 Words Feb 24th, 2014 6 Pages
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
It shows a possible a curvilinear regression model. Thus, a simple linear regression model does not appear to be appropriate.

c. Using a second-order model, develop an estimated regression equation to predict the monthly mortgage on the median-priced home given the average asking rent.

The regression equation is
Mortgage (\$) = 3966 - 8.26 Rent (\$) + 0.00513 RentSq

Predictor Coef SE Coef T P
Constant 3966 1335 2.97 0.021
Rent (\$) -8.261 2.982 -2.77 0.028
RentSq 0.005131 0.001637 3.13 0.017

S = 54.3363 R-Sq = 89.8% R-Sq(adj) = 86.9%

Analysis of Variance
Source DF SS MS F P
Regression 2 182947 91474 30.98 0.000
Residual Error 7 20667 2952
Total 9 203614

Source DF Seq SS
Rent (\$) 1 153962
RentSq 1 28986

Unusual Observations Rent Mortgage
Obs (\$) (\$) Fit SE Fit Residual St Resid 1 840 539.0 646.8 24.6 -107.8 -2.23R
R denotes an observation with a large standardized residual.

d. Do you prefer the estimated regression equation developed in part (a) or part (c)? Explain.
The model in part (c) provides a better result than the model in part (a). The R-Sq(adj) was 86.9% which is also better than part (a). The P value for the new variable RentSq added in the model is less than 0.05. It shows the variable RentSq is significant. The standardized residual plot in