How to approach this: Percentage change in one KPI leading to change in other KPIs?

I want to know how can I approach or model this problem. I have 7 KPIs (3 of them dependent on each other) and one main KPI (total 8 KPIs). I want to understand effect of these 7 KPIs on the main KPIs.
End goal is to make the statement, if you vary KPI_1 by xx.xx %, main_KPI will vary by yy.yy%. Can I model this with linear regression, find coefficients or is there any better approach?

Most KPIs, if not all, are related in some way to other KPIs. What you would have to establish, which is likely impossible, is that one KPI is necessary and sufficient to move another KPI in a very tightly controlled way. Firstly, you can only establish that kind of cause and effect with a very tightly controlled, randomized trial study.
In most cases, you wouldn't even be able to establish that one KPI was even necessary to move the other. Finally, even if you have a decent correlation between two KPIs, you would impact the second KPI in a very probabilistic way where a formula or algorithm would yield a rather deterministic result. That's not valid when we live in a multivariate, probabilistic one.
I think the better solution is to measure each KPI separately and independently.