Question: 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 for ten markets and the monthly mortgage on the median priced home (including taxes and insurance) for ten cites 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 chart for these data, treating the average asking rent as the independent variable. Does a simple linear regression model 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 plot of the residuals against the independent variable rent. Based on this residual plot, does a simple linear regression model appear to be appropriate?
c. Using a quadratic regression model, develop an estimated regression equation to predict the monthly mortgage on the median-priced home, given the average asking rent.
d. Do you prefer the estimated regression equation developed in part a or part c? Create a plot of the linear and quadratic regression lines overlaid on the scatter chart of the monthly mortgage on the median-priced home and the average asking rent to help you assess the two regression equations. Explain your conclusions.