H. Mintzberg's classic book The Nature of Managerial Work (1973) identified the roles found in all managerial jobs. An observational study of 19 managers from a medium-sized manufacturing plant extended Mintzberg's work by investigating which activities successful managers actually perform (Journal of Applied Behavioral Science, Aug. 1985). To measure success, the researchers devised an index based on the manager's length of time in the organization and his or her level within the firm; the higher the index, the more successful the manager. The table on the following page presents data that can be used to determine whether managerial success is related to the extensiveness of a manager's network-building interactions with people outside the manager's work unit. Such interactions include phone and face-to-face meetings with customers and suppliers, attending outside meetings, and doing public relations work.
a. Construct a scatterplot for the data.
b. Find the prediction equation for managerial success.
c. Find s for your prediction equation. Interpret the standard deviation s in the context of this problem.
d. Plot the least squares line on your scatterplot of part a. Does it appear that the number of interactions with outsiders contributes information for the prediction of managerial success? Explain.
e. Conduct a formal statistical hypothesis test to answer the question posed in part d. Use α = .05.
f. Construct a 95% confidence interval for β1. Interpret the interval in the context of the problem.
g. A particular manager was observed for 2 weeks, as in the Journal of Applied Behavioral Science study. She made 55 contacts with people outside her work unit. Predict the value of the manager's success index. Use a 90% prediction interval.
h. A second manager was observed for 2 weeks. This manager made 110 contacts with people outside his work unit. Why should caution be exercised in using the least squares model developed from the given data set to construct a prediction interval for this manager's success index?
i. In the context of this problem, determine the value of x for which the associated prediction interval for y is the narrowest.