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I have a series of datasets that are composed of 100 or so variables and a corresponding response variable. I am often faced with the question of trying to attribute differences in the response variable to the 100 or so variables.

My problem is that it is often difficult to compare two or more datasets and attribute the response variable to the 100 or so variables, due the large number of variables.

What do people do when faced with such a problem? What are some common analyses for doing this kind of work? It's preferable if the solution can be explained to people with a non-technical background.

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