Refer to Exercise 13.12. The realtors suspect that the impact on selling price of increasing age of home is itself increasing. That is, there is little difference in the selling prices of homes with age = 1 year to 10 years, but a larger decrease for homes from 11 years to 20 years old, a very large decrease for homes from 21 to 30 years old, and so on.
a. What terms would be needed in the regression model to evaluate whether the realtors’ suspicion is valid?
b. If the realtors’ suspicion is true, what type of pattern would you expect to see in a plot of the residuals versus age of home from a regression model having just a first order term in age of home?
In exercise
A business analyst at a major real estate firm wants to build a regression model that will predict the price of a single- family home based on a number of explanatory variables. The real estate firm’s data base has an enormous amount of information on selling prices of homes and potential variables that are related to that price. After a number of discussions with experienced realtors, you decide to model price of a home as a function of the following variables: size of home in terms of floor space, lot size, number of bathrooms, number of bedrooms, age of home, garage size, number of months home has been on the market, distance to nearest elementary school, type of neighborhood, traffic volume on street, and racial mixture of neighborhood.