# Important information about Linear regression and correlation

Quick Stab Collection Agency (QSCA) collects bills in an eastern town. The company specializes in small accounts and avoids risky collections, such as those in which the debtor tends to be chronically late in payments or is known to be hostile.

The business can be very profitable. QSCA buys the rights to collect debts from their original owners at a substantial discount. For example, QSCA might pay $10 for the right to collect a $60 debt. QSCA takes the risk of not collecting the debt at all, of course, but often a single official-looking letter yields full or nearly full payment, particularly for small debts.

Profitability at QSCA depends critically on the number of days to collect the payment and on the size of the bill, as well as on the discount rate offered.

A random sample of accounts closed out during the months of January through June yielded the attached data set.

In this data set, the variable DAYS is the number of days to collect the payment, and BILL is the amount of the overdue bill in dollars, while TYPE =1 for residential accounts and TYPE =0 for commercial accounts.

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Write a brief memo to QSCA management advising them on the relationship, if any, between size of bill and number of days to collect.

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1. Does the size of the bill somehow relate to the number of days the payment is late? If so, how? Find a model that can be used to predict how late a bill may be.

2. Does your answer depend upon whether the customer is a residential or commercial customer? If so, how?

3. Find and explain the regression model using a nontechnical discussion of your forecasting model.

4. Prepare a summary of your findings to present to the company's management.

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#### Solution Preview

Questions you need to answer:

1. Does the size of the bill somehow relate to the number of days the payment is late? If so, how? Find a model that can be used to predict how late a bill may be.

I think that the easiest way to answer these questions is to do two regression analyses - one for business accounts and one for residential accounts. In Excel, I made a scatterplot to visualize the data, and on the plot, I displayed the regression equation and the r-squared value.

The size of the bill does relate to the number of days the payment is late.

This relationship is negative for residential customers - a lower bill is associated with a larger number of days overdue. The linear regression model for these customers is y = 5.6304x - 0.7401, where y is the amount of the bill and x is the number of days overdue.

This relationship is positive for business customers - a lower bill is associated with a lower number of days overdue. The linear regression model for these customers is y = -5.0089- 517.27, where y is the amount of the bill and x is the number ...