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Linear Regression for Cellulon, a Manufacturer of a New Type of Home Insulation

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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 the home and (2)of the outdoor temperature. In the laboratory they varied the insulation thickness and temperature. A few of the findings were:

Monthly Natural Thickness of Outdoor
Gas Consumption Insulation Temperature
(cubic feet) (inches) (degrees F)
Y X1 X2
30.3 6 40
26.9 12 40
22.1 8 49

Based on the results, the regression equation is
Y1 = 62.65- 1.86X1 - .52X2

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?
b) What effect would installing 7 inches of insulation have on the monthly natural gas consumption (assuming the outdoor temperature remains at 40 degrees F?
c) Why are the regression coefficients b1 and b2 negative...is this logical?

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Solution Summary

This solution provides calculation and interpretation for the regression analysis in the attached Excel file.

Solution provided by:
Gaurav Agarwal, MS
Education
  • BE, Bangalore University, India
  • MS, University of Wisconsin-Madison
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