Question: Cellulon, a manufacturer of a new type of home insulation, wants to develop guidelines for builders and consumers regarding the effects on natural gas consumption (1) of the thickness of the insulation in the attic of a home and (2) of the outdoor temperature. In the laboratory they varied the insulation thickness and temperature. A few of the findings are:
Mo. Nat. Gas Thickness of Outdoor
Consumption Insulation Temperature
(cubic ft) (cm) (Celsius)
Y X1 X2
30.3 12.5 4
26.9 30 4
22.1 20 9
Based on the sample results, the regression equation is:
Y1 (upper) = 38.12 - 0.194X1 - 1.349X2
a. How much natural gas can homeowners expect to use per month if they install 15cm of insulation and the outdoor temperature is 10 degrees Celsius.
b. What effect would installing 18cm of insulation instead of 15 have on the monthly natural gas consumption (assuming the outdoor temperature remains at 10 degrees Celsius)?
c. Why are the regression coefficients, b1 and b2, negative? Is this logical?