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Chapter 12: Q126E (page 803)

Accuracy of software effort estimates. Refer to the Journal of Empirical Software Engineering (Vol. 9, 2004) study of the accuracy of new software effort estimates, Exercise 12.114 (p. 781). Recall that stepwise regression was used to develop a model for the relative error in estimating effort (y) as a function of company role of estimator (x1 = 1 if developer, 0 if project leader) and previous accuracy (x8 = 1 if more than 20% accurate, 0 if less than 20% accurate). The stepwise regression yielded the prediction equation y^= 0.12 - 0.28x1+ 0.27x8. The researcher is concerned that the sign of the estimated β multiplied by x1 is the opposite from what is expected. (The researcher expects a project leader to have a smaller relative error of estimation than a developer.) Give at least one reason why this phenomenon occurred.

Short Answer

Expert verified

The estimated sign for β for x1 is positive (the developer has a larger relative error of estimation than a project leader) but the prediction equation estimated using step-wise regression is negative sign of x1. A possible reason for the same could be the existence of multicollinearity in the model.

Step by step solution

01

Reason for opposite sign

The estimated sign for β for x1 is positive (the developer has a larger relative error of estimation than a project leader) but the prediction equation estimated using step-wise regression is negative sign of x1. A possible reason for the same could be the existence of multicollinearity in the model.

02

Rationale behind opposite sign

Since there is high degree of correlation amongst relative error in estimating effort (y) and company role of estimator (x1) the β estimates will not be true parameter indicators and will be biased.

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Most popular questions from this chapter

Question: Consumer behavior while waiting in line. The Journal of Consumer Research (November 2003) published a study of consumer behavior while waiting in a queue. A sample of n = 148 college students was asked to imagine that they were waiting in line at a post office to mail a package and that the estimated waiting time is 10 minutes or less. After a 10-minute wait, students were asked about their level of negative feelings (annoyed, anxious) on a scale of 1 (strongly disagree) to 9 (strongly agree). Before answering, however, the students were informed about how many people were ahead of them and behind them in the line. The researchers used regression to relate negative feelings score (y) to number ahead in line (x1) and number behind in line (x2).

a.The researchers fit an interaction model to the data. Write the hypothesized equation of this model.

b. In the words of the problem, explain what it means to say that “x1 and x2 interact to affect y.”

c. A t-test for the interaction β in the model resulted in a p-value greater than 0.25. Interpret this result.

d. From their analysis, the researchers concluded that “the greater the number of people ahead, the higher the negative feeling score” and “the greater the number of people behind, the lower the negative feeling score.” Use this information to determine the signs of β1 and β2 in the model.

Suppose you fit the model y =β0+β1x1+β1x22+β3x2+β4x1x2+εto n = 25 data points with the following results:

β^0=1.26,β^1= -2.43,β^2=0.05,β^3=0.62,β^4=1.81sβ^1=1.21,sβ^2=0.16,sβ^3=0.26, sβ^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: β1 = 0 against Ha: β1 < 0. Use α = .05.

  3. Test H0: β2 = 0 against Ha: β2 > 0. Use α = .05.

  4. Test H0: β3 = 0 against Ha: β3 ≠ 0. Use α = .05.

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: Manipulating rates of return with stock splits. Some firms have been accused of using stock splits to manipulate their stock prices before being acquired by another firm. An article in Financial Management (Winter 2008) investigated the impact of stock splits on long-run stock performance for acquiring firms. A simplified version of the model fit by the researchers follows:

E(y)=β0+β1x1+β2x2+β3x1x2

where

y = Firm’s 3-year buy-and-hold return rate (%)

x1 = {1 if stock split prior to acquisition, 0 if not}

x2 = {1 if firm’s discretionary accrual is high, 0 if discretionary accrual is low}

a. In terms of the β’s in the model, what is the mean buy and- hold return rate (BAR) for a firm with no stock split and a high discretionary accrual (DA)?

b. In terms of the β’s in the model, what is the mean BAR for a firm with no stock split and a low DA?

c. For firms with no stock split, find the difference between the mean BAR for firms with high and low DA. (Hint: Use your answers to parts a and b.)

d. Repeat part c for firms with a stock split.

e. Note that the differences, parts c and d, are not the same. Explain why this illustrates the notion of interaction between x1 and x2.

f. A test for H0: β3 = 0 yielded a p-value of 0.027. Using α = .05, interpret this result.

g. The researchers reported that the estimated values of both β2 and β3 are negative. Consequently, they conclude that “high-DA acquirers perform worse compared with low-DA acquirers. Moreover, the underperformance is even greater if high-DA acquirers have a stock split before acquisition.” Do you agree?

Question: Study of supervisor-targeted aggression. “Moonlighters” 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?
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