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Chapter 12: 124E (page 803)

Personality traits and job performance. Refer to the Journal of Applied Psychology (January 2011) study of the determinants of task performance, Exercise 12.94 (p. 766). In addition to x1 = conscientiousness score and x2 = {1 if highly complex job, 0 if not}, the researchers also used x3 = emotional stability score, x4 = organizational citizenship behavior score, and x5 = counterproductive work behavior score to model y = task performance score. One of their concerns is the level of multicollinearity in the data. Below is a matrix of correlations for all possible pairs of independent variables. Based on this information, do you detect a moderate or high level of multicollinearity? If so, what are your recommendations?

Short Answer

Expert verified

Multicollinearity is checked by checking the correlation amongst the independent variables. If there is high correlation amongst any two independent variables, it is said that the problem of multicollinearity exists in the model.

Step by step solution

01

Multicollinearity check

Multicollinearity is checked by checking the correlation amongst the independent variables. If there is high correlation amongst any two independent variables, it is said that the problem of multicollinearity exists in the model.

02

Application of multicollinearity check 

Based on the table provided in the question, there is a moderate level of multicollinearity between emotional stability (x3) and conscientiousness score (x1) since the correlation coefficient value of 0.62 and between organizational citizenship (x4) and counterproductive work (x5) since the correlation coefficient value is -0.62. For all the other variables the correlation coefficient value is less than 0.25 indicating very low level of multicollinearity.

03

Recommendations to avoid multicollinearity

Recommendations to avoid multicollinearity are

Drop one or more correlated variables from the model

Do not make inferences about E(y) or future y-values to values of x鈥檚 that fall outside the range of the sample data.

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Most popular questions from this chapter

Question: Study of supervisor-targeted aggression. 鈥淢oonlighters鈥� are workers who hold two jobs at the same time. What are the factors that impact the likelihood of a moonlighting worker becoming aggressive toward his/her supervisor? This was the research question of interest in the Journal of Applied Psychology (July 2005). Completed questionnaires were obtained from n = 105 moonlighters, and the data were used to fit several multiple regression models for supervisor-directed aggression score 1y2. Two of the models (with R2-values in parentheses) are given below:

a. Interpret the R2-values for the models.

b. Give the null and alternative hypotheses for comparing the fits of models 1 and 2.

c. Are the two models nested? Explain.

d. The nested F-test for comparing the two models resulted in F = 42.13 and p-value < .001. What can you conclude from these results?

e. A third model was fit, one that hypothesizes all possible pairs of interactions between self-esteem, history of aggression, interactional injustice at primary job, and abusive supervisor at primary job. Give the equation of this model (model 3).

f. A nested F-test to compare models 2 and 3 resulted in a p-value > .10. What can you conclude from this result?

Question: Write a first-order model relating to

  1. Two quantitative independent variables.
  2. Four quantitative independent variables.
  3. Five quantitative independent variables.

Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study on using the volume of chatter on Twitter.com to forecast movie box office revenue, Exercise 12.10 (p. 723). The researchers modelled a movie鈥檚 opening weekend box office revenue (y) as a function of tweet rate (x1 ) and ratio of positive to negative tweets (x2) using a first-order model.

a) Write the equation of an interaction model for E(y) as a function of x1 and x2 .

b) In terms of the尾 in the model, part a, what is the change in revenue (y) for every 1-tweet increase in the tweet rate (x1 ) , holding PN-ratio (x2)constant at a value of 2.5?

c) In terms of the in the model, part a, what is the change in revenue (y) for every 1-tweet increase in the tweet rate (x1 ) , holding PN-ratio (x2)constant at a value of 5.0?

d) In terms of the尾 in the model, part a, what is the change in revenue (y) for every 1-unit increase in the PN-ratio (x2) , holding tweet rate (x1 )constant at a value of 100?

e) Give the null hypothesis for testing whether tweet rate (x1 ) and PN-ratio (x2) interact to affect revenue (y).

Going for it on fourth down in the NFL. Refer to the Chance (Winter 2009) study of fourth-down decisions by coaches in the National Football League (NFL), Exercise 11.69 (p. 679). Recall that statisticians at California State University, Northridge, fit a straight-line model for predicting the number of points scored (y) by a team that has a first-down with a given number of yards (x) from the opposing goal line. A second model fit to data collected on five NFL teams from a recent season was the quadratic regression model, E(y)=尾0+尾1x+尾2x2.The regression yielded the following results: y=6.13+0.141x-0.0009x2,R2=0.226.

a) If possible, give a practical interpretation of each of the b estimates in the model.

b) Give a practical interpretation of the coefficient of determination,R2.

c) In Exercise 11.63, the coefficient of correlation for the straight-line model was reported asR2=0.18. Does this statistic alone indicate that the quadratic model is a better fit than the straight-line model? Explain.

d) What test of hypothesis would you conduct to determine if the quadratic model is a better fit than the straight-line 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?
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