Recall that the researchers used a quadratic model to relate

Recall that the researchers used a quadratic model to relate y = task performance score (measured on a 30-point scale) to x₁= conscientiousness score (measured on a scale of -3 to +3). In addition, the reasearchers included job complexity in the model, where x₂= { if highly complex job, 0 if not}. The complete model took the form

E(y) = ₀ + ₁x₁ + ₂(x₁)² + ₃x₂ + ₄x₁x₂ + ₅(x₁)²x₂

a. For jobs that are not highly complex, write the equation of the model for E(y) as a function of x₁. (Subsitute x₂ = 0 into the equation.)

b. Refer to part a. What do each of the\'s represent in the model?

c. For highly complex jobs, write the equation of the model for E(y) as a function of x1. (Substitute x2 = 1 into the equation.)

d. Refer to part C. What do each of the\'s represent in the model?

e. Does the model support the researchers\' theory that the curvilinear relationship between task performance score (y) and conscientiousness score (x₁) depends on job complexity (x₂)? Explain.

Solution