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Chapter 12: Q139SE (page 807)
Write a model relating E(y) to one qualitative independent variable that is at four levels. Define all the terms in your model.
Mathematically, the model in one qualitative independent variable with 4 levels can be written as
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Question: Personality traits and job performance. Refer to the Journal of Applied Psychology (January 2011) study of the relationship between task performance and conscientiousness, Exercise 12.94 (p. 766). Recall that y = task performance score (measured on a 30-point scale) was modeled as a function of x1 = conscientiousness score (measured on a scale of -3 to +3) and x2 = {1 if highly complex job, 0 if not} using the complete model
a. Specify the null hypothesis for testing the overall adequacy of the model.
b. Specify the null hypothesis for testing whether task performance score (y) and conscientiousness score (x1) are curvilinearly related.
c. Specify the null hypothesis for testing whether the curvilinear relationship between task performance score (y) and conscientiousness score (x1) depends on job complexity (x2).
Explain how each of the tests, parts a鈥揷, should be conducted (i.e., give the forms of the test statistic and the reduced model).
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 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?
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 = 0.12 - 0.28x1+ 0.27x8. The researcher is concerned that the sign of the estimated 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.
Question: There are six independent variables, x1, x2, x3, x4, x5, and x6, that might be useful in predicting a response y. A total of n = 50 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful. The software fits all possible one-variable models of the form
where xi is the ith independent variable, i = 1, 2, 鈥�, 6. The information in the table is provided from the computer printout.
a. Which independent variable is declared the best one variable predictor of y? Explain.
b. Would this variable be included in the model at this stage? Explain.
c. Describe the next phase that a stepwise procedure would execute.
The first-order model was fit to n = 19 data points. A residual plot for the model is provided below. Is the need for a quadratic term in the model evident from the residual plot? Explain.
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