Banks monitor the use of credit cards to see whether promotions that encourage customers to charge more have been successful. Banks also monitor balances to seek out fraud or cases of stolen credit card numbers. For these methods to work, we need to be able to anticipate the balance on a credit card next month from things that we know today. A key in-dicator of the balance next month is the balance this month. Those balances that roll over earn the bank high rates of interest, often in the neighborhood of 12% to 24% annually.
The data table for this analysis shows a sample of balances for 923 customers of a national issuer of credit cards, such as Visa and Mastercard. The four columns in the data table are balances over four consecutive months. For this analysis, we’ll focus on the relationship between the balance in the third and fourth months.
(a) The bank would like to predict the balance of a customer in month 4 from the balance in month 3 to within 10% of the actual value. How well must a linear equation describe the data in order to meet this goal?
(b) Explain in management terms how an equation that anticipates the balance next month based on the current balance could be useful in evaluating the success of a marketing program intended to increase customer account balances.
(c) Form the appropriate scatterplot of the balances in months 3 and 4. Does a linear model seem like a decent way to describe the association?
(d) The scatterplot reveals two types of outliers that deviate from the general pattern. What is the explanation for these outliers?
(e) Fit the linear equation using all of the cases. Briefly summarize the estimated slope and intercept as well as the overall summary statistics, R2 and se.
(f) Exclude the cases that have a near-zero balance in either month 3 or month 4 (or both). Interpret “near zero” to mean an account with balance $25 or less. Refit the equation and compare the results to the equation obtained in part (e). Do the results change in a meaningful way?
(g) Inspect the residuals from the equation ft in part (f). Do these suggest simple variation?
(h) Summarize the ft of your equation for management. Explain in clear terms any relevant symbols. (That is, don’t just give a value for r2 and expect that the reader knows regression analysis.)
(i) Is the goal of predicting the balance next month within 10% possible? Indicate, for management, why or why not.