WAGAP 12.107 Agreeableness, gender, and wages. Refer to the Journal of Personality and Social Psychology (February 2012) study of on-the-job agreeableness and wages, Exercise 12.92 (p. 751). The researchers modeled mean income, E(y), as a function of both agreeableness score (x1) and a dummy variable for gender (x2 = 1 if male, 0 if female). Suppose the re- searchers theorize that for either gender, income will de- crease at a decreasing rate as agreeableness score increases. Consequently, they want to fit a second-order model. a. Consider the model, E(y) = B + Bx1 + B(x1) + B3x2. If the researchers' belief is true, what is the ex- pected sign of in the model? b. Draw a sketch of the model, part a, showing how gender impacts the income-agreeableness score relationship. c. Write a complete second-order model for E(y) as a function of x and x2. d. Draw a sketch of the model, part c, showing how gender impacts the income-agreeableness score relationship. e. What null hypothesis would you test in order to com- pare the two models, parts a and c? f. Fit the models to the sample data saved in the file and carry out the test, part e. What do you conclude? (Test using a = .10.) Data for First 10 Individuals in Study Income Agree Score Gender 44,770 3.0 1 51,480 2.9 1 39,600 3.3 1 24,370 3.3 0 15,460 3.6 43,730 3.8 48,330 3.2 25,970 2.5 17,120 3.5 20,140 3.2 O11100