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Home Insulation Manufaturer: Regression Coefficients

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

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?

Solution Preview

a. Y' = 62.65 – 1.86(6) – 0.52(40) = 30.69 cubic feet

b. Installing 7 inches of insulation instead of 6 inches will bring down the monthly ...

Solution Summary

In about 80 words, this solution provides a complete, neat and step-by-step response which determines how natural gas consumption and insulation inquiries can be solved using the given regression equation.