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# Home Insulation Manufaturer: Regression Coefficients

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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 Thickness of Outdoor
Gas Consumption Insulation Temperature
(cubic feet), (inches), (degrees F),
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

Questions:
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?

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)?

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