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Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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How much of a dependent variable is explained by each of a bunch of independent variables?

I can neither sum them all up and scale the results down to 100 % in total, since they don't explain 100 % of the hierarchy (a multiple linear regression model with all of the possibly explaining variables … Scaling down to 90 % wouldn't work either, if I'm not mistaken, because the multiple linear regression model does not (necessarily) weigh the single explanatory variables equally. …