Recall that y = task performance score (measured on a 30-point scale) was modeled as a function of x1 = conscientiousness score (measured on a scale of -3 to +3) and x2 = {1 if highly complex job, 0 if not) using the complete model
E(y) = β0 + β1x1 + β2(x1)2 + β3x2 + β4x1x2 + β5(x1)2x2
a. Specify the null hypothesis for testing the overall adequacy of the model.
b. Specify the null hypothesis for testing whether task performance score (y) and conscientiousness score (x1) are curvilinearly related.
c. Specify the null hypothesis for testing whether the curvilinear relationship between task performance score (y) and conscientiousness score (x1) depends on job complexity (x2).
d. Explain how each of the tests, parts a-c, should be conducted (i.e., give the forms of the test statistic and the reduced model).
For information: Refer to the Journal of Applied Psychology (Jan. 2011) study of the relationship between task performance and conscientiousness, Exercise 12.94.