11.77 Many companies must accurately estimate their costs before a job is begun in order to acquire a contract and make a profit. For example, a heating and plumbing contractor may base cost estimate for new homes on the total area of the house, the number of baths in the plans, and whether central air conditioning is to be installed.

a Write a first-order model relating the mean cost of material and labor E(Y ) to the area, number of baths, and central air conditioning variables.

b Write a complete second-order model for the mean cost as a function of the same three variables as in (a).

c How could you test the research hypothesis that the second-order terms are useful for predicting mean cost?