# Question

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

c. Remembering that s = .6542; SSxx = 1,404.355; x-bar = 43.98; and n = 8hand calculate the distance value when x0 = 40. Remembering that the distance value equals (sy/s)2, use s and from the computer output to calculate (within rounding) the distance value using this formula. Note that, because MINITAB rounds sy, the first hand calculation is the more accurate calculation of the distance value.

d. Remembering that for the natural gas consumption data and 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 and order 10.721 MMcf of natural gas to be shipped to the city by a pipeline transmission system. The company will have to pay a fine to the transmission system if the city’s actual gas usage 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 company 95 percent confident that it will avoid paying a fine. Note: In the exercises of Chapter 14, we will use multiple regression analysis to predict y accurately enough so that the company is likely to avoid paying a fine.

a. Report (as shown on the computer output) a point estimate of and a 95 percent confidence interval for the mean natural gas 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 natural gas consumption in a single week that has an average hourly temperature of 40° F.

c. Remembering that s = .6542; SSxx = 1,404.355; x-bar = 43.98; and n = 8hand calculate the distance value when x0 = 40. Remembering that the distance value equals (sy/s)2, use s and from the computer output to calculate (within rounding) the distance value using this formula. Note that, because MINITAB rounds sy, the first hand calculation is the more accurate calculation of the distance value.

d. Remembering that for the natural gas consumption data and 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 and order 10.721 MMcf of natural gas to be shipped to the city by a pipeline transmission system. The company will have to pay a fine to the transmission system if the city’s actual gas usage 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 company 95 percent confident that it will avoid paying a fine. Note: In the exercises of Chapter 14, we will use multiple regression analysis to predict y accurately enough so that the company is likely to avoid paying a fine.

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