Hiring A firm that operates a large, direct-toconsumer sales force would like to implement 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 2 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 3 months of work.
(a) Create a scatterplot for Profit from Sales on Number of Accounts. Does a line seem to be a good summary of the association between these variables?
(b) Estimate the least squares linear equation for Profit from Sales on Number of Accounts. Interpret the fitted intercept and slope; be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable.
(c) Interpret
and
associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) Based on the equation fit in part (b), what is the gain in profit to the firm of getting agents to open 100 additional accounts in the first 3 months? Do you think that this is a reasonable estimate?
(e) Plot the residuals from the regression fit in part (b) on the sizes of the files. Does this plot show random variation?
(f) Exclude the data for agents who open 75 or fewer accounts in the first 3 months. Does the fit of the least squares line change much? Should it?