Question 1 : Goal congruence in top management teams. Do chief executive officers (CEOs) and their top managers always agree on the goals of the company? Goal importance congruence between CEOs and vice presidents (VPs) was studied in the Academy of Management Journal (February 2008). The researchers used regression to model a VP's attitude toward the goal of improving efficiency (y) as a function of the two quantitative independent variables, level of CEO leadership (x1) and level of congruence between the CEO and the VP (x2). A complete second-order model in x1 and x2 was fit to data collected for n = 517 top management team members at U.S. credit unions.
(a) Write the complete second-order model for E(y).
(b) The coefficient of determination for the model, part a, was reported as R2 = .14. Interpret this value.
(c) The estimate of the β-value for the (x2)2 term in the model was found to be negative. Interpret this result, practically.
(d) A t-test on the β-value for the interaction term in the model, x1x2, resulted in a p-value of .02. Practically interpret this result, using α = .05.
Question 2: 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 5.8 (p. 271). Consider a model for heat rate (kilojoules per kilowatt per hour) of a gas turbine as a function of cycle speed (revolutions per minute) and cycle pressure ratio. Recall that the data are saved in the GASTURBINE file.
(a) Write a complete second-order model for heat rate (y).
(b) Fit the model to the data and give the least squares prediction equation.
(c) Conduct a global F-test for overall model adequacy.
(d) Based on the prediction equation, graph the relationship between heat rate and cycle pressure ratio when cycle speed is held constant at 5,000 rpm.
(e) Repeat part d when cycle speed is held constant at 15,000 rpm.
(f) Compare the two graphs, parts d and e. What do you observe?