Find / measure multiple correlation of mutually correlated vars with a continuous target?


New Member
I have a large dataset of around 100 continuous independent variables and one continuous dependent target variable.

The aim would be to assess the "influence" (correlation) each of the independent variables has on the target.

I know that one independent variable is positively correlated with the target and from background knowledge it is clear
that this variable also is somewhat (though we do not know how much) correlated with many of the other independent variables.

There is likely no proper linear relationship and the error of a linear estimator is not normal. So for checking the pairwise-correlation between all of the independent variables and the target I used Kendall's Tau which showed very high significance but not a big effect size.

What I would like to understand is what would be the best approach to better assess the individual influence (correlation) of the independendent variables with the target, but after "factoring out" the correlation that is just caused by each of those variables being correlated with that one independent variable that is already highly correlated with the target?

Among the 100 varibales there are probably also subsets which are highly correlated among each other, so what is a good way to select a subset of variables which best describes a joint correlation between those variables and the target?

Is there some method that can be applied that would separate out the individual and mutual (rank) correlations of multiple variables on the target?
Is there a good (online) resource or paper to learn more about how to do this properly?