Solution Found!
Goal congruence in top management teams. Do chief
Chapter 12, Problem 59E(choose chapter or problem)
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 (Feb.2008). The researchers used regression to model a VPs attitude toward the goal of improving efficiency (y) as a function of the two quantitative independent variables level of CEO leadership (\(x_1\)) and level of congruence between the CEO and the VP (\(x_2\)). A complete second-order model in \(x_1\) and \(x_2\) 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 \(R^2 = .14\). Interpret this value.
c. The estimate of the β-value for the \((x_2)^2\) term in the model was found to be negative. Interpret this result, practically.
d. A t-test on the \(\beta\)-value for the interaction term in the model, \(x_1x_2\), resulted in a p-value of .02. Practically interpret this result, using \(\alpha\ =\ .05\).
Questions & Answers
QUESTION:
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 (Feb.2008). The researchers used regression to model a VPs attitude toward the goal of improving efficiency (y) as a function of the two quantitative independent variables level of CEO leadership (\(x_1\)) and level of congruence between the CEO and the VP (\(x_2\)). A complete second-order model in \(x_1\) and \(x_2\) 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 \(R^2 = .14\). Interpret this value.
c. The estimate of the β-value for the \((x_2)^2\) term in the model was found to be negative. Interpret this result, practically.
d. A t-test on the \(\beta\)-value for the interaction term in the model, \(x_1x_2\), resulted in a p-value of .02. Practically interpret this result, using \(\alpha\ =\ .05\).
ANSWER:Step 1 of 4
a) The complete second-order model is
Comments on the parameters
y-intercept , the value of E(y) when
Changing and causes the surface to shift along the - and -axes
Controls the rotation of the surface
Signs and values of these parameters control the type of surface and the
rates of curvature.