Write the complete second-order model for E(y).

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.

• Write the complete second-order model for E(y).
• The coefficient of determination for the model, part a, was reported as R² = .14. Interpret this value.
• The estimate of the β-value for the (x₂)² term in the model was found to be negative. Interpret this result, practically.
• 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.