# solution

Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine, Exercise 12.19 (p. 726). Recall that you fit a first-order model for heat rate (y) as a function of speed (x1), inlet temperature 1×22, exhaust temperature (x3), cycle pressure ratio (x4), and airflow rate (x5). A Minitab printout with both a 95% confidence interval for E(y) and prediction interval for y for selected values of the xâ€™s is shown below.

a. Interpret the 95% prediction interval for y in the words of the problem.

b. Interpret the 95% confidence interval for E(y) in the words of the problem.

c. Will the confidence interval for E(y) always be narrower than the prediction interval for y? Explain.

Exercise 12.19

Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine, Exercise 7.94 (p. 431). Recall that the heat rate (kilojoules per kilowatt per hour) was measured for each in a sample of 67 gas turbines augmented with high-pressure inlet fogging. In addition, several other variables were measured, including cycle speed (revolutions per minute), inlet temperature (Â°C), exhaust gas temperature (Â°C), cycle pressure ratio, and air mass flow rate (kilograms per second). The data are saved in the file. (The first and last five observations are listed in table below.)

a. Write a first-order model for heat rate (y) as a function of speed, inlet temperature, exhaust temperature, cycle pressure ratio, and airflow rate.

b. Fit the model to the data using the method of least squares.

c. Give practical interpretations of the b estimates.

d. Find the model standard deviation, s, and interpret its value.

e. Conduct a test for overall model utility using Â = .01. f. Find and interpret Ra2Â  .

g. Is there sufficient evidence (at a = .01) to indicate that heat rate (y) is linearly related to inlet temperature?

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