Hiring (introduced in Chapter 19) A firm that operates a large, direct-to-consumer sales force would like to be able 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 frst 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. Some of these agents were located in new offices, whereas others joined an existing office (see the column labeled Office).
(a) Plot the log of profit on the log of the number of accounts opened for both groups in one scatterplot. Use color-coding or distinct symbols to distinguish the groups. Does the coloring explain an unusual aspect of the “black and white” scatterplot? Does a simple regression that ignores the groups provide a reasonable summary?
(b) Add a dummy variable (coded as + for new offices and 0 for existing offices) and its inter- action with Log Number of Accounts to the model. Does the fit of this model meet the conditions for the MRM? Comment on the consequences of any problem that you identify.
(c) Assuming that the model meets the conditions for the MRM, use the incremental F-test to assess the size of the change in R2. (See the discussion of this test in Exercise 45.) Does the test agree with your visual impression? (The value of kfull for the model with dummy and interaction is 3, with - slopes added. You will need to fit the simple regression to get its R2 for comparison to the multiple regression.)
(d) Compare the conclusion of the incremental F-test to those of the tests of the coefficients of the dummy variable and interaction separately. Do these agree? Explain the similarity or difference.
(e) What do you think about locating new hires in new or existing offices? Would you recommend locating them in one or the other (assuming it could be done without disrupting the current placement procedures)?