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:
Monthly Natural Gas Consumption (cubic feet), Y |
Thickness of Insulation (inches), X1 |
Outdoor Temperature (ºF), X2 |
|||
30.3 | 6 | 45 | |||
27.9 | 12 | 40 | |||
22.2 | 8 | 49 | |||
On the basis of the sample results, the regression equation is: |
YˆY^ = 97.11 -1.47X1 -1.29X2 |
(a) |
How much natural gas can homeowners expect to use per month if they install 6 inches of insulation and the outdoor temperature is 45 degrees F? (Round your answer to 2 decimal places.) |
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 45 degrees F)? (Round your answers to 2 decimal places.) |
A (Click to select)decrease or increase of cubic feet monthly natural gas consumption, down to cubic feet. |
(c) | Why are the regression coefficients b1 and b2 negative? Is this logical? |
(Click to select)No or Yes , logically, as the amount of
insulation (Click to select)decreases or increases and outdoor
temperature (Click to select) increases or decreases, the consumption of natural gas (Click to select)increasesdecreases. |
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