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 8.46 (p. 392). 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 (°C), exhaust gas temperature (°C), cycle pressure ratio, and air mass flow rate (kilograms per second). The first and last five observations of the data are listed in the following table.

a. Write a first-order model for heat rate (y) as a function of speed, inlet temperature, exhaust temperature, cycle pressure ratio, and air mass flow rate.
b. Use the method of least squares to fit the model to the data.
c. Give practical interpretations of the β estimates.
d. Find the standard deviation s of the model, and interpret its value.
e. Find R2α and interpret its value.
f. Is the overall model statistically useful in predicting heat rate (y)? Test, using α = .01.

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Rpm Cpratio Inlet-Temp Exh-Temp Airflow Heatrate 602 27245 9.2 1134 950 14622 13196 12.2 14000 446 15 17384 11085 14.8 1149 1024 537 478 20 27 11948 11289 11.8 13.2 14045 1149 553 29 11964 1066 18910 14.0 532 8 12766 35.0 448 3600 1288 152 8714 2010 10.6 1160 3600 456 84 9469 16000 1232 560 14 11948 13.4 1077 14600 536 12414 ... .... ...