Chapter 12: 139SE (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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The Minitab printout below was obtained from fitting the modelto n = 15 data points.
a) What is the prediction equation?
b) Give an estimate of the slope of the line relating y to x1 when x2 =10 .
c) Plot the prediction equation for the case when x2 =1 . Do this twice more on the same graph for the cases when x2 =3 and x2 =5 .
d) Explain what it means to say that x1and x2interact. Explain why your graph of part c suggests that x1and x2interact.
e) Specify the null and alternative hypotheses you would use to test whetherx1andx2interact.
f)Conduct the hypothesis test of part e using .
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.
Write a model that relates E(y) to two independent variables—one quantitative and one qualitative at four levels. Construct a model that allows the associated response curves to be second-order but does not allow for interaction between the two independent variables.
Question: Company donations to charity. The amount a company donates to a charitable organization is often restricted by financial inflexibility at the firm. One measure of financial inflexibility is the ratio of restricted assets to total firm assets. A study published in the Journal of Management Accounting Research (Vol. 27, 2015) investigated the link between donation amount and this ratio. Data were collected on donations to 115,333 charities over a recent 10-year period, resulting in a sample of 419,225 firm-years. The researchers fit the quadratic model,, where y = natural logarithm of total donations to charity by a firm in a year and x = ratio of restricted assets to the firm’s total assets in the previous year. [Note: This model is a simplified version of the actual model fit by the researchers.]
Question: Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the impact of reality TV shows on one’s desire to undergo cosmetic surgery, Exercise 12.17 (p. 725). Recall that psychologists used multiple regression to model desire to have cosmetic surgery (y) as a function of gender , self-esteem , body satisfaction , and impression of reality TV . The SPSS printout below shows a confidence interval for E(y) for each of the first five students in the study.
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