Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of a high-pressure inlet fogging method for a gas turbine engine, presented in Exercise 12.27

(p. 701). Consider a model for the heat rate (kilojoules per kilowatt per hour)

produced by a gas turbine as a function of cycle speed

(revolutions per minute) and cycle pressure ratio.

a. Write a complete second-order model for heat rate (y).

b. Give the null and alternative hypotheses for determining whether the curvature terms in the complete second-order model are statistically useful in predicting the heat rate (y).

c. For the test in part

b, identify the complete and reduced models.

d. Portions of the MINITAB printouts for the two models are shown above. Find the values of SSER, SSEC, and MSEC on the printouts.

e. Compute the value of the test statistics for the test of part b.

f. Find the rejection region for the test of part

b. Use a = .10.
g. State the conclusion of the test in the words of the problem.

Transcribed Image Text:

MINITAB output for Exercise 12.126 Complete Model The regression equation is HEATRATE 15583 +0.078 RPM +8.84 CPRSQ - 523 CPRATIO +0.00445 RP_CPR - 0.000000 RPMSQ S = 563.513 R-Sq 88.5% R-Sq (adj) 87.5% Analysis of Variance Source DF SS MS F P Regression Residual Error Total 5 148526859 61 19370350 55 167897208 29705372 93.55 0.000 317547 Reduced Model The regression equation is HEATRATE 12065 +0.170 RPM = S = 633.842 - 146 CPRATIO - 0.00242 RPM CPR R-Sq 84.9% R-Sq (adj) 84.2% Analysis of Variance Source DF SS MS F _ P 47528857 118.30 0.000 401756 Regression 3 142586570 25310639 66 167897208 Residual Error 63 Total