Cellulon, a manufacturer of home insulation, wants to develop guidelines for bui

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: On the basis of the sample results, the regression equation is: Y = 112.48 -2.07X_1 - 1.5X_2 (a) How much natural gas can homeowners expect to use per month if they install 5 inches of insulation and the outdoor temperature is 48 degrees F? (Round your answer to 2 decimal places.) (b) What effect would installing 8 inches of insulation instead of 5 have on the monthly natural gas consumption (assuming the outdoor temperature remains at 48 degrees F)? (Round your answers to 2 decimal places.) (c) Why are the regression coefficients b_1 and b_2 negative? Is this logical?

Explanation / Answer

Given:

Y=112.48-2.07X1-1.5X2

(a)

For 5 inches insulation and the outdoor temperature of 48 degreed F the expected use of natural gas per month is given as

Y = 112.48 - (2.07 * 5) - (1.5 * 48)

Y = 112.48 - 10.35 - 72

Y = 30.13

Expect to use per month 30.13 cubic feet.

(b)

For the given temperature of 48 degree F, the expected expected use of natural gas per month for 8 inch insulation is given as

Y = 112.48 - (2.07 * 8) - (1.5 * 48)

Y = 112.48 - 16.56 - 72

Y = 23.92

Hence, the difference between 5 inch and 8 inch is 30.31 - 23.92 = 6.21.

A decrease of 6.21 cubic feet of monthly natural gas consumption, down to 23.92 cubic feet.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.