Refer to Exercise 9.42

(p. 503). in which managerial success, y, was modeled as a function of the number of contacts a manager makes with people outside his or her : work unit, x, during a specific period of time. The data are repeated in the table on page 551. The MINITAB simple linear regression printout is also provided there.

a. A particular manager was observed for two week$.

as in the Journal of Applied Behavioral Scirrru study. She made 55 contacts with people outside her work unit. Predict the value of the manager's suc- cess index. Use a 90% prediction interval.

b. A second manager was observed for two weeks. This manager made 110 contacts with people outside his work unit. Give two reasons why caution should 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.
In the context of this problem, determine the value of x for which the associated prediction interval for y is the narrowest.