The National Association of Realtors has reported data on housing affordability for 1990–1999, and values for two of the variables are listed in file XR15093. Representing affordability is y = average monthly mortgage payment as a percentage of median household income. Representing the cost of a mortgage is x = the average mortgage rate, as a percentage.
a. Determine the least-squares regression equation for y as a function of x, then estimate y if the average mortgage rate is x = 8.0%.
b. What percentage of the variation in affordability (y) is explained by the average mortgage rate (x)? At the 0.05 level, does the slope of the equation differ significantly from 0?
c. Given x = 8.0%, construct and interpret the 95% confidence and prediction intervals associated with y.