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Statistics For Business And Economics
Found in: Page 803
Statistics For Business And Economics

Statistics For Business And Economics

Book edition 13th
Author(s) James T. McClave, P. George Benson, Terry Sincich
Pages 888 pages
ISBN 9780134506593

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Short Answer

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.

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.

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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.

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.

Most popular questions for Math Textbooks

Consider the following data that fit the quadratic model E(y)=β0+β1x+β2x2:

a. Construct a scatterplot for this data. Give the prediction equation and calculate R2 based on the model above.

b. Interpret the value of R2.

c. Justify whether the overall model is significant at the 1% significance level if the data result into a p-value of 0.000514.

Assertiveness and leadership. Management professors at Columbia University examined the relationship between assertiveness and leadership (Journal of Personality and Social Psychology, February 2007). The sample represented 388 people enrolled in a full-time MBA program. Based on answers to a questionnaire, the researchers measured two variables for each subject: assertiveness score (x) and leadership ability score (y). A quadratic regression model was fit to the data, with the following results:

a. Conduct a test of overall model utility. Use α=0.05 .

b. The researchers hypothesized that leadership ability increases at a decreasing rate with assertiveness. Set up the null and alternative hypotheses to test this theory.

  1. Use the reported results to conduct the test, part b. Give your conclusion (at α=0.05 ) in the words of the problem.

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)=β0+β1x1+β2x12+β3x2+β4x1x2+β5x12x2 here x2=1 E(y)=β0+β1x1+β2x12+β3(1)+β4x1(1)+β5(1)2(1) E(y)=(β0+β3) +(β1+β4)x1+(β2+β5)(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’s 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’s represent in the model?

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

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Write a model relating E(y) to one qualitative independent variable that is at four levels. Define all the terms in your model.
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