My Math Forum Estimate paid invoices

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 December 5th, 2017, 11:52 PM #1 Newbie   Joined: Dec 2017 From: Stockholm Posts: 2 Thanks: 0 Estimate paid invoices Let’s say we run a charity program to which people can donate by invoice. So people sign up to donate a specific amount and then we send them an invoice and they can choose to pay it whenever they want and also choose not to pay it. Let’s say we run this for some months and now we want to estimate the final paid amount per sign up (ie final meaning at that point in future where everyone who will pay has paid). How to estimate this?
 December 6th, 2017, 04:07 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,163 Thanks: 867 Rough estimate- For each month, divide the amount of money that has been paid so far and divide by the total amount of money pledged. That will give you points on a graph of a "percentage amount paid per time". Extrapolate that function into the future.
 December 6th, 2017, 11:11 AM #3 Newbie   Joined: Dec 2017 From: Stockholm Posts: 2 Thanks: 0 Thanks, but that solution won’t work in our case and maybe I wasn’t clear enough on describing our problem - we need to base the analysis on the sign up date. Let’s say we have this final result: Signup: 2017-10-02, $2000. Paid: 2017-10-08 Signup: 2017-10-10,$4000. Never Paid Signup: 2017-10-16, $4000. Paid: 2017-11-21 Signup: 2017-11-04,$3000. Paid: 2017-11-10 Signup: 2017-11-07, $1000. Never Paid Signup: 2017-11-09,$6000. Paid: 2017-12-30 Let’s say our goal is to calculate paid/signup for November signups. If being able to look into the future we would see it’s $9000/3=$3000. But on today’s date (2017-12-06) we only know of $3000/3=$1000 so then we have to estimate the likelihood of those last \$6000 being paid, and we should be able to do that knowing the historical pattern (October in this example). Now ofcourse a good estimation is not possible with only 6 data points, but imagine we have thousands of data points for many months back. Then it should be possible right? Last edited by Lasselakan; December 6th, 2017 at 11:12 AM. Reason: Formatting
December 6th, 2017, 01:29 PM   #4
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Quote:
 Originally Posted by Lasselakan Thanks, but that solution won’t work in our case and maybe I wasn’t clear enough on describing our problem - we need to base the analysis on the sign up date. Let’s say we have this final result: Signup: 2017-10-02, 2000 dollars. Paid: 2017-10-08 Signup: 2017-10-10, 4000 dollars. Never Paid Signup: 2017-10-16, 4000 dollars. Paid: 2017-11-21 Signup: 2017-11-04, 3000 dollars. Paid: 2017-11-10 Signup: 2017-11-07, 1000 dollars. Never Paid Signup: 2017-11-09, 6000 dollars. Paid: 2017-12-30 Let’s say our goal is to calculate paid/signup for November signups. If being able to look into the future we would see it’s 9000/3= 3000. But on today’s date (2017-12-06) we only know of 3000/3=1000 so then we have to estimate the likelihood of those last 6000 being paid, and we should be able to do that knowing the historical pattern (October in this example). Now of course a good estimation is not possible with only 6 data points, but imagine we have thousands of data points for many months back. Then it should be possible right?
I have cleaned up your post so that it is legible. Please do not use dollar signs on this site. They are interpreted in a special way.

But yes. If you have enough points, you can come up with a robust estimation process.

Here is one way to go about it. Pick a date; track the percentage of commitments fulfilled by quarter following the date. (Four quarters after each pledge date should be ample: I suspect that the percentages will be close to zero after the first two quarters.) You may need to do that two ways: once by number of payments per quarter versus the number of pledges and once by dollar value of payments per quarter versus aggregate dollars pledged. Do that for 20 or 30 pledge dates. Then run a linear regression routine against the data points for the first quarter. If that gives you a high coefficient of correlation, you have a reasonable estimate for what to expect within one quarter of the date of the pledge. You can repeat the process for each quarter.

If this makes no sense, see if someone involved with your organization knows how to run the data analysis package in excel and ask them to look at this answer.

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