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.

1. Write a main effects model relating the mean cost of material and labor, E(y), to the area and central air-conditioning variables.
2. Write a complete second-order model for the mean cost as a function of the same two variables.
3. 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 a), so that a test can be conducted to determine whether the additional complexity of the second-order model is necessary. The resulting SSE and R ² 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 \(\alpha \) = .05.

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