A heating and plumbing contractor estimates material and lab

A heating and plumbing contractor estimates material and labor costs for new homes (y) based on the total area of the house (x1) and whether central air conditioning is to be installed (x2).

(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 E(y) as a function of the same variables.

(c) What hypothesis would you test in order to determine whether the second-order terms are useful for predicting the 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 R2 values are shown in the following table. Is there sufficient evidence to conclude that the second-order terms are important for predicting the mean cost? Use =0.05.

                    SSE                R2
Main effects:          8.548 0.950

Second-order:      6.133               0.964

Solution