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Regression Coefficients and Heating Effects

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Cellulon, a manufacturer of a home insulation, wants to develop guidelines for builders and consumers regarding the effects (1) of the thickness of the insulation in the attic of a home and (2) of the outdoor temperature on natural gas consumption. In the laboratory they varied the insulation thickness and temperature. A few of the findings are:
Monthly Natural Gas Consumption (cubic feet), Y Thickness of Insulation (inches), X1 Outdoor Temperature (°F), X2
30.3 6 40
26.9 12 40
22.1 8 49
On the basis of the sample results, the regression equation is:

1. 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?
2. 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)?
3. Why are the regression coefficients b1 and b2 negative? Is this logical?

Solution Summary

Solution attaches an Excel spreadsheet of data handling and Word document report to answer this problem of home insulation.

Solution provided by:
Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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