Question

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		46.0
24.0		12		40
32.3		8		49

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

yˆy?^?? = 100.75 ? 1.06x₁ ? 1.39x₂

How much natural gas can homeowners expect to use per month if they install 6 inches of insulation and the outdoor temperature is 46 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 46 degrees F)? (Round your answers to 2 decimal places.)

The regression coefficients b₁ and b₂ are negative? Is this logical?

Answer 1

Answer:-

Given that,

The multiple regression equation is

= 100.75 - 1.06x₁ - 1.39x₂

(a)

Here we have to find the consumption of natural gas for 6 inches of insulation thickness and 46⁰ F of outdoor temperature

= 100.75 - 1.06x₁ - 1.39x₂

     = 100.75 - 1.06(6) - 1.39(46)

= 30.45

Hence, 30.45 units of natural gas can homeowners expect to use per month

(b)

Here, we have to find the consumption of natural gas for 7 inches of insulatin thickness and 46⁰F outdoor temperature

= 100.75 - 1.06x₁ - 1.39x2
       = 100.75 - 1.06(7) - 1.39(46)

= 29.39

Hence, 29.39 units of natural gas can home owners expect to use per month. If we use 7 inches insulation instead of 6 inches insulation on thickness. The consumption of natural gas per month is low. Hence, it is better to use 7 inches insulation and 46⁰F outdoor temperature for new consumption of natural gas.

(c)

The regression coeffecients b₁ and b₂ are negative, due to the consumption of the natural gas is negtively associated with the insulation thickness and outdoor temperature.