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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 multi-variate, probabilistic one.
I think the better solution is to measure each KPI separately and independently.
Regressions look at the relationships between variables. For any dependent variable “Y”, what set of independent variables “Xs“ contributes to the variation Y.
From your explanation, it has broken down: but in basic statistical model Y is the dependent variable, X1–Xn represent a set of n independent variables and A1–An are the coefficient constants corresponding to X1–Xn
But you don’t have any coefficient, so linear regression can’t be used. I also suggest measuring each KPI separately and independently. Measure the company’s success versus a set of targets, or objectives, or you use time measurement.
If you just want an indication of how the different variables relate to each other, linear regression can work if your data satisfies the assumptions of linear regression: the variables are linearly related to each other, and the variation is homoskedastic. If you've got reason to believe that the variables aren't linearly related to each other, you can try adding in additional terms where the values of one of the variables have been modified by a mathematical function (e.g. an x^2 term).
It's also possible to use machine learning models to generate predictions for the value of a variable given the values of other variables, but what you gain in predictive accuracy you typically lose in explainability. Depending on use case, this might or might not be a trade-off you're willing to make.
