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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…show more content…
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
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