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 GasConsumption (cubicfeet),Thickness ofOutdoorInsulation (inches), Temperature (°F),X1X230.36.4026.9124022.149On the basis of the sample results, the regression equation is:ŷ = 62.65 – 1.86x1 – 0.52x2a. How much natural gas can homeowners expect to use per month if they install 6 inches of insulation and the outdoor temperature is40 degrees F? (Round your answer to 2 decimal places.)Natural gas30.69 cubic feetb. What effect would installing 7 inches of insulation instead of 6 have on the monthly natural gas consumption (assuming the outdoortemperature remains at 40 degrees F)? (Round your answers to 2 decimal places.)A decreaseofcubic feet of monthly natural gas consumption, down to28.83 cubic feet.

Name: Cellulon, a manufacturer of home insulation, wants to develop guidelin
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Description: 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

Suppose y=a0+a1 x1+ a2 x2 is the fitted regression line, then expected value of the dependent…

Answered: On the basis of the sample results, the…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 6PPS

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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
Outdoor
Insulation (inches), Temperature (°F),
X1
X2
30.3
6.
40
26.9
12
40
22.1
49
On the basis of the sample results, the regression equation is:
ŷ = 62.65 – 1.86x1 – 0.52x2
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? (Round your answer to 2 decimal places.)
Natural gas
30.69 cubic feet
b. 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.)
A decrease
of
cubic feet of monthly natural gas consumption, down to
28.83 cubic feet.

Expert Solution

Step 1

Suppose y=a₀+a₁ x1+ a₂ x₂ is the fitted regression line, then expected value of the dependent variable y for given values of x₁ and x₂ is obtained by plugging in the values of x₁ and x₂in the fitted regression line.

(a). At x₁ = 6, x₂ = 40, the expected value of gas consumption is:

y^{^} = 62.65-1.86 $\times$ 6 -0.52 $\times$ 40

= 30.69

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