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Chapter 12: Q106E (page 773)

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?

Short Answer

Expert verified

Answer

a. The R2 values for the two models are 0.101 and 0.555 respectively. Higher value of R2denotes that the model is a good fit for the data and that approximately what percentage of the variation in the variables is explained by the model. This number is very less for model 1 (only 10%) indicating that the model is not a good fit while for model 2 the value of R2 is 55.5% which is still able to explain around 55% variation in the model.

b. The null and alternate hypothesis to test whether the complete model contributes more information for the prediction of y than the reduced model can be written as

H0: 尾5 = 尾6 = 尾7 = 尾8 = 0 whileHa: At least one of 尾 parameters are nonzero.

c. Two models are nested if one model contains all the terms of the second model and at least one additional term. IN the question model 1 contains 4 terms while model 2 contains 9 terms where 4 are additional terms (尾5, 尾6, 尾7, and 尾8). Hence the two models are nested models where model 1 is reduced model and model 2 is complete model.

d. The nested F-test for comparing the two models resulted in F = 42.13 and p-value < .001. H0 is rejected if p-value < 伪. For 伪 = 0.10 or 0.05, p-value <0.001 is very less. Hence, H0 is rejected.

e. The equation for model 3 with all possible pairs of interaction can be written as 尾0+尾1x1+尾2x2+尾3x3+尾4x4+尾5x5+尾6x6+尾7x7+尾8x8+尾9x5x6+尾10x7x8+尾11x5x7+尾12x5x8+尾13x6x7+尾14x6x8..

f. The nested F-test for comparing model 2 and 3 resulted in p-value > .10. H0 is rejected if p-value < 伪. For 伪 = 0.10 or 0.05, p-value > 0.10. Hence, H0 is not rejected.

Step by step solution

01

Interpretation of R2

The R2 values for the two models are 0.101 and 0.555 respectively. Higher value of R2denotes that the model is a good fit for the data and that approximately what percentage of the variation in the variables is explained by the model. This number is very less for model 1 (only 10%) indicating that the model is not a good fit while for model 2 the value of R2 is 55.5% which is still able to explain around 55% variation in the model.

02

Hypotheses

The null and alternate hypothesis to test whether the complete model contributes more information for the prediction of y than the reduced model can be written as

H0: 尾5 = 尾6 = 尾7 = 尾8 = 0 whileHa: At least one of 尾 parameters are nonzero.

03

Nested models

Two models are nested if one model contains all the terms of the second model and at least one additional term. IN the question model 1 contains 4 terms while model 2 contains 9 terms where 4 are additional terms (尾5, 尾6, 尾7, and 尾8). Hence the two models are nested models where model 1 is reduced model and model 2 is complete model.

04

Hypothesis testing

The nested F-test for comparing the two models resulted in F = 42.13 andp-value < .001.

H0 is rejected if p-value < 伪. For 伪 = 0.10 or 0.05, p-value <0.001 is very less

Hence, H0 is rejected.

05

Model 3 equation

The equation for model 3 with all possible pairs of interaction can be written as尾0+尾1x1+尾2x2+尾3x3+尾4x4+尾5x5+尾6x6+尾7x7+尾8x8+尾9x5x6+尾10x7x8+尾11x5x7+尾12x5x8+尾13x6x7+尾14x6x8..

06

Hypothesis testing

The nested F-test for comparing model 2 and 3 resulted in p-value > .10.

H0 is rejected if p-value < 伪. For 伪 = 0.10 or 0.05, p-value > 0.10.

Thus, H0 is not rejected.

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Most popular questions from this chapter

Suppose you fit the model y =尾0+尾1x1+尾1x22+尾3x2+尾4x1x2+蔚to n = 25 data points with the following results:

尾^0=1.26,尾^1= -2.43,尾^2=0.05,尾^3=0.62,尾^4=1.81s尾^1=1.21,s尾^2=0.16,s尾^3=0.26, s尾^4=1.49SSE=0.41 and R2=0.83

  1. Is there sufficient evidence to conclude that at least one of the parameters b1, b2, b3, or b4 is nonzero? Test using a = .05.

  2. Test H0: 尾1 = 0 against Ha: 尾1 < 0. Use 伪 = .05.

  3. Test H0: 尾2 = 0 against Ha: 尾2 > 0. Use 伪 = .05.

  4. Test H0: 尾3 = 0 against Ha: 尾3 鈮� 0. Use 伪 = .05.

To model the relationship between y, a dependent variable, and x, an independent variable, a researcher has taken one measurement on y at each of three different x-values. Drawing on his mathematical expertise, the researcher realizes that he can fit the second-order model Ey=尾0+尾1x+尾2x2 and it will pass exactly through all three points, yielding SSE = 0. The researcher, delighted with the excellent fit of the model, eagerly sets out to use it to make inferences. What problems will he encounter in attempting to make inferences?

Question: Shared leadership in airplane crews. Refer to the Human Factors (March 2014) study of shared leadership by the cockpit and cabin crews of a commercial airplane, Exercise 8.14 (p. 466). Recall that simulated flights were taken by 84 six-person crews, where each crew consisted of a 2-person cockpit (captain and first officer) and a 4-person cabin team (three flight attendants and a purser.) During the simulation, smoke appeared in the cabin and the reactions of the crew were monitored for teamwork. One key variable in the study was the team goal attainment score, measured on a 0 to 60-point scale. Multiple regression analysis was used to model team goal attainment (y) as a function of the independent variables job experience of purser (x1), job experience of head flight attendant (x2), gender of purser (x3), gender of head flight attendant (x4), leadership score of purser (x5), and leadership score of head flight attendant (x6).

a. Write a complete, first-order model for E(y) as a function of the six independent variables.

b. Consider a test of whether the leadership score of either the purser or the head flight attendant (or both) is statistically useful for predicting team goal attainment. Give the null and alternative hypotheses as well as the reduced model for this test.

c. The two models were fit to the data for the n = 60 successful cabin crews with the following results: R2 = .02 for reduced model, R2 = .25 for complete model. On the basis of this information only, give your opinion regarding the null hypothesis for successful cabin crews.

d. The p-value of the subset F-test for comparing the two models for successful cabin crews was reported in the article as p 6 .05. Formally test the null hypothesis using 伪 = .05. What do you conclude?

e. The two models were also fit to the data for the n = 24 unsuccessful cabin crews with the following results: R2 = .14 for reduced model, R2 = .15 for complete model. On the basis of this information only, give your opinion regarding the null hypothesis for unsuccessful cabin crews.

f. The p-value of the subset F-test for comparing the two models for unsuccessful cabin crews was reported in the article as p < .10. Formally test the null hypothesis using 伪 = .05. What do you conclude?

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: Suppose you fit the first-order multiple regression model y=尾0+尾1x1+尾2x2+蔚 to n=25 data points and obtain the prediction equationy^=6.4+3.1x1+0.92x2 . The estimated standard deviations of the sampling distributions of 尾1 and 尾2are 2.3 and .27, respectively
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