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: = 56.26 - 0.4 X_1 - 0.59X_2 (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? (Round your answer to 2 decimal places.) Expect to use per month ______________ cubic feet (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)? (Round your answers to 2 decimal places.) A of _________ cubic feet of monthly natural gas consumption, down to _____________ cubic feet (c) Why are the regression coefficients b_1 and b_2 negative? Is this logical? logically, as the amount of insulation and outdoor temperature the consumption of natural gas decreases.

Explanation / Answer

a) Equation is:

y = 56.26 - 0.4x1 - 0.59x2

If x1 = 6 and x2 = 40

y = 56.26 - 0.4 * 6 - 0.59 * 40

y = 30.26 cubic feet

b) Now x1 = 7 instead of 6

y = 56.26 - 0.4 * 7 - 0.59 * 40

y = 29.86

Thus, a decrease of 0.4 cubic feet down to 29.86 cubic feet.

c) Yes, they should be negative.

As if more insulation is used, consumption will decrease.

And also, if outdoor temp is high, people will not cook hot stuff in the house. They would like to have cold stuff.

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