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Chapter 12: Q102E (page 772)

Workplace bullying and intention to leave. Refer to the Human Resource Management Journal (October 2008) study of workplace bullying, Exercise 12.91 (p. 765). Recall that multiple regression was used to model an employee’s intention to leave (y) as a function of bullying (x1, measured on a quantitative scale) and perceived organizational support (measured qualitatively as “low POS,” “neutral POS,” or “high POS”). In Exercise 12.91b, you wrote a model for E(y) as a function of bullying and POS that hypothesizes three parallel straight lines, one for each level of POS. In Exercise 12.91c, you wrote a model for E(y) as a function of bullying and POS that hypothesizes three nonparallel straight lines, one for each level of POS.

a) Explain why the two models are nested. Which is the complete model? Which is the reduced model?

b) Give the null hypothesis for comparing the two models.

c) If you reject H0 in part b, which model do you prefer? Why?

d) If you fail to reject H0 in part b, which model do you prefer? Why?

Short Answer

Expert verified

a) The two models are nested models because the first model is a reduced model because this model represents three parallel lines indicating no interaction. While the other model is a complete model representing three nonparallel lines denoting model with interaction hence added variables representing interaction amongst the variables.

b) The null and alternate hypothesis for comparing the two models can be written as H0: β4 = β5 = 0 while Ha: At least one of β parameters are nonzero.

c) If H0 is rejected in part b, then model with interaction is preferred since the hypothesis testing indicates that the added variables from the interaction model is statistically useful for predicting E(y).

d) If H0 is not rejected in part b, then model without any interaction is preferred since the hypothesis testing indicates that the added variables from the interaction model is not statistically useful for predicting E(y).

Step by step solution

01

Nested and complete model

The two models are nested models because the first model is a reduced model because this model (Ey=β0+β1x1+β2x2+β3x3)represents three parallel lines indicating no interaction. While the other model (Ey=β0+β1x1+β2x2+β3x3+β4x1x3+β5x2x3

)is a complete model representing three nonparallel lines denoting model with interaction hence added variables representing interaction amongst the variables.

02

Hypotheses

The null and alternate hypothesis for comparing the two models can be written as

H0: β4 = β5 = 0while Ha: At least one of β parameters are nonzero.

03

Interpretation of thesis testing

If H0 is rejected in part b, then model with interaction is preferred since the hypothesis testing indicates that the added variables from the interaction model is statistically useful for predicting E(y).

04

Clarification of theorem testing

If H0 is not rejected in part b, then model without any interaction is preferred since the hypothesis testing indicates that the added variables from the interaction model is not statistically useful for predicting E(y).

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Most popular questions from this chapter

Question: Write a second-order model relating the mean of y, E(y), to

a. one quantitative independent variable

b. two quantitative independent variables

c. three quantitative independent variables [Hint: Include allpossible two- way cross-product terms and squared terms.]

It is desired to relate E(y) to a quantitative variable x1and 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—one for each level of the qualitative variable.

Question: Job performance under time pressure. Refer to the Academy of Management Journal (October 2015) study of how time pressure affects team job performance, Exercise 12.89 (p. 765). Recall that the researchers hypothesized a complete second-order model relating team performance (y) to perceived time pressure (x1), and whether or not the team had an effective leader (x2 = 1 if yes, 0 if no):

E(Y)=β0+β1x1+β2x22+β3x2+β4x1x2+β5x12x2

a) How would you determine whether the rate of increase of team performance with time pressure depends on effectiveness of the team leader?

b) For fixed time pressure, how would you determine whether the mean team performance differs for teams with effective and non-effective team leaders?

Question: Write a regression model relating E(y) to a qualitative independent variable that can assume three levels. Interpret all the terms in the model.

Question: Accuracy of software effort estimates. Periodically, software engineers must provide estimates of their effort in developing new software. In the Journal of Empirical Software Engineering (Vol. 9, 2004), multiple regression was used to predict the accuracy of these effort estimates. The dependent variable, defined as the relative error in estimating effort, y = (Actual effort - Estimated effort)/ (Actual effort) was determined for each in a sample of n = 49 software development tasks. Eight independent variables were evaluated as potential predictors of relative error using stepwise regression. Each of these was formulated as a dummy variable, as shown in the table.

Company role of estimator: x1 = 1 if developer, 0 if project leader

Task complexity: x2 = 1 if low, 0 if medium/high

Contract type: x3 = 1 if fixed price, 0 if hourly rate

Customer importance: x4 = 1 if high, 0 if low/medium

Customer priority: x5 = 1 if time of delivery, 0 if cost or quality

Level of knowledge: x6 = 1 if high, 0 if low/medium

Participation: x7 = 1 if estimator participates in work, 0 if not

Previous accuracy: x8 = 1 if more than 20% accurate, 0 if less than 20% accurate

a. In step 1 of the stepwise regression, how many different one-variable models are fit to the data?

b. In step 1, the variable x1 is selected as the best one- variable predictor. How is this determined?

c. In step 2 of the stepwise regression, how many different two-variable models (where x1 is one of the variables) are fit to the data?

d. The only two variables selected for entry into the stepwise regression model were x1 and x8. The stepwise regression yielded the following prediction equation:

Give a practical interpretation of the β estimates multiplied by x1 and x8.

e) Why should a researcher be wary of using the model, part d, as the final model for predicting effort (y)?
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