Solution Found!
Agreeableness, gender, and wages. Refer to the Journalof
Chapter 12, Problem 107E(choose chapter or problem)
Agreeableness, gender, and wages. Refer to the Journal of Personality and Social Psychology (Feb. 2012) study of on-the-job agreeableness and wages, Exercise 12.92 (p. 722). The researchers modeled mean income, E(y), as a function of both agreeableness score (\(x_1\)) and a dummy variable for gender (\(x_2=1\) if male, 0 if female). Suppose the researchers theorize that for either gender, income will decrease at a decreasing rate as the agreeableness score increases. Consequently, they want to fit a second-order model.
a. Consider the model, \(E(y)=\beta_0+\beta_1x_1+\beta_2(x_1)^2+\beta_3x_2\). If the researchers' belief is true, what is the expected sign of \(\beta_2\) 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 \(x_1\) and \(x_2\).
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 compare 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 \(\alpha\ =\ .10\).)
Questions & Answers
QUESTION:
Agreeableness, gender, and wages. Refer to the Journal of Personality and Social Psychology (Feb. 2012) study of on-the-job agreeableness and wages, Exercise 12.92 (p. 722). The researchers modeled mean income, E(y), as a function of both agreeableness score (\(x_1\)) and a dummy variable for gender (\(x_2=1\) if male, 0 if female). Suppose the researchers theorize that for either gender, income will decrease at a decreasing rate as the agreeableness score increases. Consequently, they want to fit a second-order model.
a. Consider the model, \(E(y)=\beta_0+\beta_1x_1+\beta_2(x_1)^2+\beta_3x_2\). If the researchers' belief is true, what is the expected sign of \(\beta_2\) 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 \(x_1\) and \(x_2\).
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 compare 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 \(\alpha\ =\ .10\).)
ANSWER:Step 1 of 15
(a)
The model is given by,
where 
