The National Association of Realtors Existing-Home Sales Series provides measurements on the residential real estate market. One of the measurements is the Housing Affordability Index (HAI). It is a measure of the financial ability of U.S. families to buy a house:

100 means that families earning the national median income have just the amount of money needed to qualify for a mortgage on a median-priced home, higher than 100 means they have more than enough, and lower than 100 means they have less than enough.

The file titled Index contains the HAI and associated variables for the years 2013–2015 (source: “Housing Affordability Index,” National Association of Realtors, www.realtor.org).

a. Construct a scatter plot relating the HAI to the median family income.

b. Obtain the estimated regression equation for a second-order polynomial model.

c. Discuss the model you developed in part

b. Perform appropriate statistical tests using alpha = 0.05.