The National Association of Realtors Existing-Home Sales Series provides a measurement of the residential real estate market. One of the measurements it produces is the Housing Affordability Index (HAI). It is a measure of the financial ability of U.S. families to buy a house. A value of 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.
a. Construct a second order of the polynomial relating the HAI to the median family income.
b. Conduct a test of hypothesis to determine if this polynomial is useful in predicting the HAI. Use a p -value approach and a significance level of 0.01.
c. Determine if monthly principal and interest interact with the relationship between the HAI and the median family income indicated in part b. Use a significance level of 0.01.