Personality traits and job performance. Refer to

QUESTION:

Personality traits and job performance. Refer to the Journal of Applied Psychology (Jan. 2011) study of the relationship between task performance and conscientiousness, Exercise 12.54 (p. 704). Recall that the researchers used a quadratic model to relate y =  task performance score (measured on a 30 -point scale) to \(x_1=\) conscientiousness score (measured on a scale of -3 to +3). In addition, the researchers included job complexity in the model, where \(x_2\) = {1 if highly complex job, 0 if not }. The complete model took the form

\(E(y)=\beta_0+\beta_1 x_1+\beta_2\left(x_1\right)^2+\beta_3 x_2+\beta_4 x_1 x_2+\beta_5\left(x_1\right)^2 x_2\)

a. For jobs that are not highly complex, write the equation of the model for \(\mathrm{E}(\mathrm{y})\) as a function of \(x_1\). (Substitute \(x_2=0\) into the equation.)

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

c. For highly complex jobs, write the equation of the model for \(\mathrm{E}(\mathrm{y})\) as a function of \(x_1\). (Substitute \(x_2=1\) into the equation.)

d. Refer to part c. What do each of the \(\beta\)'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 ( \(\left.x_1\right)\) depends on job complexity \(\left(x_2\right)\)? Explain.