THE FUEL CONSUMPTION CASE

On the next page we give the average hourly outdoor temperature \((x)\) in a city during a week and the city's natural gas consumption \((y)\) during the week for each of eight weeks (the temperature readings are expressed in degrees Fahrenheit and the natural gas consumptions are expressed in millions of cubic feet of natural gas - denoted MMcf). The output to the right of the data is obtained when MINITAB is used to fit a least squares line to the natural gas (fuel) consumption data.

a Find the least squares point estimates \(b_{0}\) and \(b_{1}\) on the computer output and report their values. interpret \(b_{0}\) and \(b_{1}\). Is an average hourly temperature of \(0^{\circ} \mathrm{F}\) in the experimental region? What does this say about the interpretation of $b_{0}$ ?

b Use the facts that \(S S_{n}=-179.6475, S S_{\mathrm{u}}=1,404.35 S_{;} \bar{y}=10.2125\); and \(\bar{x}=43.98\) to hand calculate (within rounding) \(b_{0}\) and \(b_{1}\).

c Use the least squares tine to compute a point estimate of the mean fuel consumption for all weeks having an average hourly temperature of \(40^{\circ} \mathrm{F}\) and a point prediction of the fuel consumption for an individual week having an average hourly temperature of \(40^{\circ} \mathrm{F}\).

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Solution: The downloadable solution consists of 13 pages, 1237 words and 17 charts.
Deliverable: Word Document