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?^? = 112.48 ? 2.07x1 ? 1.50x2

How much natural gas can homeowners expect to use per month if they install 5 inches of insulation and the outdoor temperature is 48 degrees F? (Round your answer to 2 decimal places.)

What effect would installing 8 inches of insulation instead of 5 have on the monthly natural gas consumption (assuming the outdoor temperature remains at 48 degrees F)? (Round your answers to 2 decimal places.)

The regression coefficients b1 and b2 are negative? Is this logical?

Monthly Natural Gas Consumption (cubic feet), Thickness of Insulation (inches), Outdoor Temperature (ºF), y x1 x2 30.3 5.0 48.0 22.6 12 40 27.8 8 49

Explanation / Answer

Solution:

1. When x1 = 5, x2 = 48, the predicted natural gas would be

y^ = 112.48 - 2.07 (5) - 1.50 (48)

y^ = 30.13

2.

When x1 = 7, x2 = 48, the predicted natural gas would be

y^ = 112.48 - 2.07 (7) - 1.50 (48)

y^ = 25.99

3. Yes, because there is an increase or decrease relationship. When more insulation is added, or high temperature it is logical to assume you would less energy to heat a house.

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