Choosing a research method, what would you recommend?

Question

Analytics

Hi guys,
I would appreciate your opinion on the following topic. For each client (Client ID) I have a set of data:

- Geographical zone ID
- Probability of the client being in this zone
- Distance from this zone to the nearest ATM
- Average monthly account balance

So, for each client, I have three zones where he \it can wobble with the appropriate probability. I also know the distance from this zone to the nearest ATM, and I also know the average monthly account balance. I need to check how the residual depends on this data set (Zone - Probability - Distance to ATM).
The hypothesis is that the closer the ATM is to the client, the larger the average monthly balances, but I would like to check whether there is a correlation, and if it is, look at the type of dependence. What's the best way to do it?
Maybe collapse this set into a single number, like: p1s1 + p2s2 + p3 * s3 (p - probability, s - distance to ATM), well, for these two numerical variables (this number and the remainder) check the correlation, then regression? Or maybe you know the standard methods?

Thank you.