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

Monthly Natural Gas Consumption Thickness of Insulation Outdoor Temps(F)
(Y) X_1 x_2

30.3 6 40
26.9 12 40
22.1 8 49

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

Yhat = 62.65 - 1.86X_1 - 0.52X_2

How much natural gas can homeowners expect to use per month if they install 6 inches of insulation and the outdoor temperature is 40^o F?

What effect would installing 7 inches of insulation instead of 6 have on the monthly natural gas consumption (assuming the outdoor temp remains at 40^o F?)

Why are the regression coefficients b_1 and b_2 negative? Is this logical?