Final answer:
The student should plot the data for monthly new customers to identify any association. If the association is linear and positive, the manager has a quantitative basis for a raise. They should also calculate the least-squares line and correlation coefficient to quantify performance.
Step-by-step explanation:
They should first draw a scatter plot using the provided data, with the time (months since hiring) on the x-axis and the number of new customers on the y-axis. After plotting the data, they should look for a pattern to determine whether there is a linear association, a nonlinear association, or no association between the time and number of new customers.
If the scatter plot shows a linear association, with the points roughly forming a straight line with a positive slope, then the manager can argue for a raise based on the consistent growth in customers over time. A nonlinear association might suggest that the manager's performance was variable, and could warrant further analysis. If there is no association, the manager may struggle to justify a raise based on customer growth.
The manager should also calculate the least-squares line (regression line) and the correlation coefficient to provide quantitative evidence of their performance. A significant correlation coefficient indicates a strong relationship between time and new customers, further supporting the case for a raise.