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    Natural Gas Consumption Controls

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

    Monthly Natural Thickness of Outdoor
    gas consumption insulation (inches) Temperature
    (cubic feet) (◦F)
    Y X1 X2
    30.3 6 40
    26.9 12 40
    22.1 8 49

    Based on the sample results, the regression equation is:
    Y1=62.65 - 1.86X1 - 0.52X2

    A). How much natural gas can homeowners expect to use per month if they install 6 inches of installation and the outdoor temperature is 40 degrees F?

    B). What effects would installing 7 inches of installation instead of 6 have on the monthly natural gas consumption (assuming the outdoor temp 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 looks at the data provided for the monthly natural gas consumption and determines the regression equation, how much natural gas homeowners can use, the effects of installing 7 inches of installation, and the regression coefficients. All steps are show with explanations.