A firm that operates a large, direct-to- consumer sales force would like to implement a sys-tem 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 con-tracts sold by agents over their frst 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 rep-resents a large extrapolation and is consequently not reliable.
(c) Interpret r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) Based on the equation ft 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 ft 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 ft of the least squares line change much? Should it?