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. 673). Recall that you fitted a first-order model for heat rate (y) as a function of speed(x1), inlet temperature (x2), exhaust temperature (x3), cycle pressure ratio (x4), and air mass flow rate (x5). A MINITAB printout with both a 95% confidence interval for E(y) and a prediction interval for y, for selected values of the x's, is shown above.
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.