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insulation thickness and temperature

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Cellon, 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.

Please provide formulae and work in excel format. File is attached.

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Correlate insulation thickness and temperature in the case example.

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Multiple Regression

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 13 40
22.1 8 49

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?

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