Cellulon, a manufacturer of home insulation, wants to develop guidelines for bui

Question

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:

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

yˆy^ = 62.65 – 1.86x1 – 0.52x2

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? (Round your answer to 2 decimal places.)

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)? (Round your answers to 2 decimal places.)

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

Monthly Natural Gas Consumption (cubic feet), Thickness of Insulation (inches), Outdoor Temperature (ºF), y x1 x2 30.3 6 40 26.9 12 40 22.1 8 49

Explanation / Answer

a.Y= 62.65-1.86(6)-.52(40)
62.65- 11.16-20.8= 30.69 cubic feet

b. Y= 62.65-1.86(7)-.52(40)
62.65- 13.02-20.8= 28.83

c. Yes, because in the relationship there is an increase/ decrees relationship. When you add more insulation, or higher temperature it is logical to assume you would use less energy to heat a house.

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