The following partial MINITAB regression output for the fuel consumption data relates to predicting the city's fuel

Question:

The following partial MINITAB regression output for the fuel consumption data relates to predicting the city's fuel consumption (in MMcf of natural gas) in a week that has an average hourly temperature of 40°F.

a. Report (as shown on the computer output) a point estimate of and a 95 percent confidence interval for the mean fuel consumption for all weeks having an average hourly temperature of 40°F.
b. Report (as shown on the computer output) a point prediction of and a 95 percent prediction interval for the fuel consumption in a single week that has an average hourly temperature of 40°F.
c. Remembering that s = .6542; SSXY = 1.404.355; = 43.98; and n = 8. hand calculate the distance value when x0 = 40 Remembering that the distance value equals (S/s). use s and S from the computer output to calculate (within rounding) the distance value using this for¬mula. Note that, because MINITAB rounds s, the first hand calculation is the more accurate calculation of the distance value.
d. Remembering that for the fuel consumption data b0 = 15.84 and b1 = -.1279, calculate (within rounding) the confidence interval of part (a) and the prediction interval of part (b).
e. Suppose that next week the city's average hourly temperature will be 40°F. Also, suppose that the city's natural gas company will use the point prediction = 10.721 and order 10.721 MMcf of natural gas to be shipped to the city by a pipeline transmission system. The city will have to pay a fine to the transmission system if the city's actual gas useage y differs from the order of 10.721 MMcf by more than 10.5 percent-that is, is outside of the range [10.721 ± .105(10.721)] = [9.595, 11.847]. Discuss why the 95 percent prediction interval for y- [9.015, 12.427]-says that y might be outside of the allowable range and thus does not make the city 95 percent confident that it will avoid paying a fine.
In the exercises of Chapter 14 we will use multiple regression analysis to predict y accurately enough that the city is likely to avoid paying a fine.