The purpose of this analysis is to assist the Quick Stab Collection Agency (QSCA) in determining if the amount or size of a bill collection is directly related to the number of days the bill is late. In order to support the validity of this relationship, a statistical analysis on the data provided will support the relationship with 95% confidence. These findings will give us a better understanding of the QSCA’s business and provide key insights on the relationships between the data being evaluated. Introduction:
Determining whether the amount of a bill has an effect on the number of days the bill is late is the key focal point of this analysis. This information will be valuable for the business to develop efficiency and profitability within the account services team. In addition, the final output of the analysis can be applied to many situations, such as insights into customer trends in bill payment, financing, and the current economic impact on the bill collection business. This analysis will help confirm the importance of paying a bill on time and should be supported by the client services team in their management of bill acquisitions.
We are currently faced with a challenging economy and our support of motivating clients to expedite their bill payments will help our business and our customer’s personal and internal finances. To validate the relationship between the amount of a bill and the number of days late it is for both commercial and residential accounts, we apply a linear regression method to generate an accurate statistical analysis of the data. By using this form of analysis, we will be able to answer the following questions with the information provided. Does the size of the bill somehow relate to the number of days the payment is late? If so, how? Does the model show the correlation between the size of the bill and the number of days the bill is late? Does the relationship between days late and the amount of the bill differ between commercial and residential accounts?
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 96 accounts closed out during the months of January through June yielded the following: The variable of DAYS for each account equals the number of days to collect the payment. * The variable BILL for each account, equals the amount of the overdue bill in dollars TYPE – 1, identifies residential accounts, and TYPE – 0 identifies commercial accounts.
By conducting a descriptive analysis on the data for both residential and commercial accounts, we find that the mean number for days late for a bill is approximately 50 days. The mean for the number of bills due is approximately $174 dollars. If we conduct a descriptive by customer type, we find that: The mean days late for commercial accounts is approximately 68 days. The mean days late for residential accounts is approximately 31 days. The mean bill amount for both commercial and residential is the same. Three regression analyses were performed for business accounts, residential accounts and combined.
To visualize the data, a scatterplot was produced to visualize the data. Included in the scatter plot are the calculated regression equations and the r-squared values for each analysis are displayed – see appendix. Per the tight linear grouping of data points in the regression analysis, we can determine that size of the bill does relate to the number of days the payment is late. The relationship is positive for residential accounts, meaning a higher bill amount has an association with a larger number of days overdue.
The linear regression model for these accounts is y = 5. 630 x – 0. 740, (y) is the amount of the bill, and (x) is the number of days overdue. This means that for every 1-day increase in the days overdue, the amount of the associated bill increases by $5. 63. The relationship is negative for commercial accounts, meaning a higher bill has an association with a lower number of days overdue. The linear regression model for these customers is y = -5. 009 x + 517. 274, (y) is the amount of the bill and (x) is the number of days overdue. This means that for every 1 day increase in the days overdue, the amount of the associated bill decreases by $5. 01.
The correlation is very strong for both accounts, (r2 = 0. 933 or 93. 3% variation is explained in the data for residential accounts and r2 = 0. 957 or 95. 7% variation is explained in data for commercial accounts). For both kinds of accounts, bills around $250 – $300 have a tendency to be about 50 days late. Residential accounts that have bills less than $250 tend to pay before 50 days. Commercial accounts with bills less than $250 generally pay after 50 days.
Per the data provided in the regression analysis, it is recommended that management improve the training of account managers to motivate their clients to pay their bills in time. Account managers can offer their clients to take advantage of discount rates as an incentive to expedite their payments.
It is recommended that we focus on commercial accounts since there may be more opportunity to increase the slope on the regression line to close late payments on low bill amounts. Due to recent economic trends, it may be more difficult to improve payments high balance residential accounts. Though, it is still important to promote discount rates to shorten the number of days late for payments. The account management team should set goals to shorten the number of days late for bills on both account types. This will improve profitability for the Quick Stab Collection Agency.
Conclusions and Summary:
Through this analysis, we have identified a linear relationship between the amount of a bill and the number of days that the bill is overdue. This relationship is found both within residential accounts and business accounts. Residential accounts appear to have outstanding bill amounts between $50 and $300, and approximately 0 to 50 days late. Higher delinquency bills were associated with larger account balances due, and the less overdue bills were associated with smaller account balances due.
Commercial accounts also seemed to have outstanding account balances between $50 and $300, but their accounts had greater amounts of time before payments, between 40 and 100 days late. Overdue bills seemed to be more associated with smaller amounts due, and the less overdue bills were associated with larger amounts due. This is interesting since the smallest account of only $60 was 99 days late. This seems to provide an opportunity for QSCA to decrease the time of payment for low commercial account balances. These results do not necessarily evidence that the size of a bill causes lateness.
The analysis is just showing that there is a relationship between the size of a bill and the number of days overdue among a large number of customers. There are several factors that may attribute to the late payment of bills and further research should be conducted to build off of these findings.
Bruce L. Bowerman, R. T. (2004). Essentials of Business Statistics. New York: McGraw-Hill Companies, Inc.