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What methods are commonly used in mathematical modeling to study the relationship between what and what?
If it's just a relationship

Then Granger causality test.

If you want an equation.

Then linear regression can get the equation.

The correlation coefficient is obtained by correlation analysis.

The proportional weight is obtained by principal component analysis.

Of course, the above is mathematical.

The mathematical model is wonderful, and your topic is not clear. The mathematical model will study the relationship between an object and an object, so none of the above methods are applicable.

The most universal relationship should be conditional probability.