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), Thickness of Insulation (inches), Outdoor Temperature (ºF), y x1 x2 30.3   6.0   40.0   24.2   12   40   27.9   8   49       On the basis of the sample results, the regression equation is:     yˆy⁢^⁢  = 56.26 − 0.66x1 − 0.59x2     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.)         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.)         Why are the regression coefficients b1 and b2 negative? Is this logical?

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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), Thickness of Insulation (inches), Outdoor Temperature (ºF),
y x1 x2
30.3   6.0   40.0  
24.2   12   40  
27.9   8   49  
 

 

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

 

 

yˆy⁢^⁢ 

= 56.26 − 0.66x1 − 0.59x2

 

 

  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.)

 

 

 

 

  1. 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.)

 

 

 

 

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

 

 

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