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# Regression Coefficients and Heating Effects

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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 Natural Gas Consumption (cubic feet), Y Thickness of Insulation (inches), X1 Outdoor Temperature (°F), X2
30.3 6 40
26.9 12 40
22.1 8 49
On the basis of the sample results, the regression equation is:

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