WAGAP 12.107 Agreeableness, gender, and wages. Refer to the Journal of Personality and Social Psychology (February...

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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 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