Chapter 14, Problem 4E

Cellulon, a manufacturer of home insulation, wants to develop guidelines for builders and consumers on how the thickness of the insulation in the attic of a home and the outdoor temperature affect natural gas consumption. In the laboratory, it varied the insulation thickness and temperature. A few of the findings are:

On the basis of the sample results, the regression equation is:

$\hat{y}=62.65-1.86x_1-0.52x_2$

1. a. How much natural gas can homeowners expect to use per month if they install 6 inches of insulation and the outdoor temperature is 40 degrees F?
2. b. What effect would installing 7 inches of insulation instead of 6 have on the monthly natural gas consumption (assuming the outdoor temperature remains at 40 degrees F)?
3. c. Why are the regression coefficients b₁ and b₂ negative? Is this logical?