Forecasting managerial needs. Managers are an important part of any organization’s resource base. Accordingly, the organization should be just as concerned about forecasting its future managerial needs as it is with forecasting its needs for, say, the natural resources used in its production process (Northcraft and Neale, Organizational Behavior: A Management Challenge, 2002). A common forecasting procedure is to model the relationship between sales and the number of managers needed. To develop this relationship, the data shown in the table below are collected from a firm’s records.

a. Test the usefulness of the model. Use a = .05. State your conclusion in the context of the problem.

b. The company projects that it will sell 39 units next month. Use the least squares model to construct a 90% prediction interval for the number of managers needed next month.

c. Interpret the interval in part

b. Use the interval to determine the reliability of the firm’s projection. Units Sold, x Managers, y 5 10 4 11 8 10 7 10 9 9 15 10 20 11 21 17 25 19 24 21 30 22 31 25 36 30 38 30 40 31 41 31 51 32 40 30 48 32 47 32