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 researchers included job complexity in the model, where x2 = {1 if highly complex job, 0 if not}. The complete model took the form
E(y) = β0 + β1x1 + β2(x1)2 + β3x2 + β4x1x2 + β5(x1)2x2
a. For jobs that are not highly complex, write the equation of the model for E(y) as a function of x1. (Substitute x2 = 0 into the equation.)
b. Refer to part a. What do each of the β'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 β'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.
For Information: Refer to the Journal of Applied Psychology (Jan. 2011) study of the relationship between task performance and conscientiousness, Exercise 12.54.