A firm that operates a large, direct-to-consumer sales force would like to put in place a system to monitor the progress of new agents. A key task for agents is to open new accounts; an account is a new customer to the business. The goal is to identify “superstar agents” as rapidly as possible, offer them incentives, and keep them with the company. To build such a system, the firm has been monitoring sales 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 predictors 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) Is the elasticity of profit with respect to the number of accounts statistically significantly more than or less than 0.30 or equal to 0.30?
(b) If the firm could train these sales representatives to increase the number of accounts created by 5%, would this be enough to improve the overall level of profits by 1%?
(c) If a sales representative opens 150 accounts, what level of sales would you predict for this individual? Express your answer as an interval.
(d) Would you expect the sales of about half the sales representatives with this many accounts to be less than the center of the interval formed to answer part (c), and half to be more?