Cellulon, a manufacturer of a home insulation, wants to develop guidelines for builders and consumers regarding the effects (1) of the thickness of the insulation in the attic of a home and (2) of the outdoor temperature on natural gas consumption

Cellulon, a manufacturer of a home insulation, wants to develop guidelines for builders and consumers regarding the effects (1) of the thickness of the insulation in the attic of a home and (2) of the outdoor temperature on natural gas consumption. In the laboratory, they varied the insulation thickness and temperature. A few of the findings are.

Monthly Thickness of Outdoor
Natural Gas Insulation Temperature
Consumption (inches) (F)
(cubic feet)
Y X1 X2
30.3 6 40
26.9 12 40
22.1 8 49

On the basis of the sample results, the regression equation is: Y' = 62.65 - 1.86X1 - 0.52X2

a. How much natural gas can homeowners expect to use per month if they install 6 inches of installation and the outdoor temperature is 40 degrees F?

b. What effect would installing 7 inches of installation instead of 6 have on the monthly natural gas consumption (assuming the outdoor temperature remains at 40 degrees F)?

c. Why are the regression coefficients b1 and b2 negative? Is this logical?