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Chapter 12: 140SE (page 807)

It is desired to relate E(y) to a quantitative variable x1 and a qualitative variable at three levels.

  1. Write a first-order model.
  2. Write a model that will graph as three different second- order curves鈥攐ne for each level of the qualitative variable.

Short Answer

Expert verified
  1. A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written as E(y)=尾0+尾1xx+尾2xx+尾3x3.
  2. Graph

Step by step solution

01

First-order model

A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written asE(y)=尾0+尾1xx+尾2xx+尾3x3,

Where x1 is the quantitative variable

And x2 and x颅3 represent level 1 and level 2 of the qualitative variable.

02

Graph

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Most popular questions from this chapter

Question: Personality traits and job performance. Refer to the Journal of Applied Psychology (January 2011) study of the relationship between task performance and conscientiousness, Exercise 12.94 (p. 766). 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)=尾0+尾1x1+尾2(x1)2+尾3x2+尾4x1x2+尾5(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).

Explain how each of the tests, parts a鈥揷, should be conducted (i.e., give the forms of the test statistic and the reduced model).

Question: Job performance under time pressure. Time pressure is common at firms that must meet hard and fast deadlines. How do employees working in teams perform when they perceive time pressure? And, can this performance improve with a strong team leader? These were the research questions of interest in a study published in the Academy of Management Journal (October, 2015). Data were collected on n = 139 project teams working for a software company in India. Among the many variables recorded were team performance (y, measured on a 7-point scale), perceived time pressure (, measured on a 7-point scale), and whether or not the team had a strong and effective team leader (x2 = 1 if yes, 0 if no). The researchers hypothesized a curvilinear relationship between team performance (y) and perceived time pressure (), with different-shaped curves depending on whether or not the team had an effective leader (x2). A model for E(y) that supports this theory is the complete second-order model:E(y)=尾0+尾1x1+尾2x12+尾3x2+尾4x1x2+尾5x12x2

a. Write the equation for E(y) as a function of x1 when the team leader is not effective (x2= 0).

b. Write the equation for E(y) as a function ofwhen the team leader is effective (x2= 1).

c. The researchers reported the following b-estimates:.

尾0^=4.5,尾1^=0.13,尾3^=0.15,尾4^=0.15and尾5^=0.29Use these estimates to sketch the two equations, parts a and b. What is the nature of the curvilinear relationship when the team leaders is not effective? Effective?

Explain why stepwise regression is used. What is its value in the model-building process?

Question: Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the impact of reality TV shows on one鈥檚 desire to undergo cosmetic surgery, Exercise 12.17 (p. 725). Recall that psychologists used multiple regression to model desire to have cosmetic surgery (y) as a function of gender(x1) , self-esteem(x2) , body satisfaction(x3) , and impression of reality TV (x4). The SPSS printout below shows a confidence interval for E(y) for each of the first five students in the study.

  1. Interpret the confidence interval for E(y) for student 1.
  2. Interpret the confidence interval for E(y) for student 4

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. 747). Recall that the researchers used a quadratic model to relate y = task performance score (measured on a 30-point scale) to x1 = conscientiousness score (measured on a scale of -3 to +3). In addition, the researchers included job complexity in the model, where x2 = {1 if highly complex job, 0 if not}. The complete model took the form

E(y)=尾0+尾1x1+尾2x12+尾3x2+尾4x1x2+尾5x12x2herex2=1E(y)=尾0+尾1x1+尾2x12+尾3(1)+尾4x1(1)+尾5(1)2(1)E(y)=(尾0+尾3)+(尾1+尾4)x1+(尾2+尾5)(x1)2

a. For jobs that are not highly complex, write the equation of the model for E1y2 as a function of x1. (Substitute x2 = 0 into the equation.)

b. Refer to part a. What do each of the b鈥檚 represent in the model?

c. For highly complex jobs, write the equation of the model for E(y) as a function of x1. (Substitute x2 = 1 into the equation.)

d. Refer to part c. What do each of the b鈥檚 represent in the model?

e. Does the model support the researchers鈥� theory that the curvilinear relationship between task performance score (y) and conscientiousness score (x1) depends on job complexity (x2)? Explain.
See all solutions

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