Question: Material and labor costs. 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 estimates for new homes on the total area of the house and whether cen­tral air conditioning is to be installed.

a. Write a main effects model relating the mean cost of material and labor, E(y), to the area and central air-conditioning variables.

b. Write a complete second-order model for the mean cost as a function of the same two variables.

c. What hypothesis would you test to determine whether the second-order terms are useful for predicting mean cost?

d. Refer to part c. The contractor samples 25 recent jobs and fits both the complete second-order model (part b) and the reduced main effects model (part d), so that a test can be conducted to determine whether the addi­tional complexity of the second-order model is neces­sary. The resulting SSE and R² values are shown in the table. Is there sufficient evidence to conclude that the second-order terms are important for predicting the mean cost? Use = .05.