A firm that operates a large, direct-to-consumer sales force would like to build a system to monitor the progress of new agents. The goal is to identify “superstar agents” as rapidly as possible, offer them incentives, and keep them with the company. A key task for agents is to open new accounts; an account is a new customer to the business. To build the system, the firm has monitored activities of new agents over the past two years. The response of interest is the profit to the firm (in dollars) of contracts sold by agents over their first year. Among the possible explanations of this performance is the number of new accounts developed by the agent during the first three months of work. Formulate the SRM with Y given by the natural log of Profit from Sales and X given by the natural log of Number of Accounts.
(a) Locate the most negative residual in the data. Which case is this?
(b) Explain some characteristics that distinguish this employee from the others. (Hint: Consider the data in the Early Commission and Early Selling columns. Both are measured in dollars and measure the quality of business developed in the first three months of working for this firm.)
(c) How does the ft change if this point is set aside, excluded from the original regression? Compare the fitted model both with and without this employee.
(d) Explain the magnitude of the change in the fit. Why does the fit change by so much or so little?