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I have a large number of continuous independent variables and I want to analyse how they correlate with a continuous dependent variable.

There is one independent variable ("size") which is correlated with the dependent variable ("target") but also more or less strongly correlated with many other independent variables. The reason is that all the independent variables measure e.g. an average or maximum of some property of items in the set.

For example "var1" may be the average weight of an item in a set. "size" is the size of the set itself. Now if I correlate var1 and size with the target variable and it turns out the target depends a bit on the set size, then inevitably it will probably also depend on var1 because larger sets have a bigger chance to contain heavier items and may have a bigger average item weight.

What is the best approach to find out what the actual contribution of each independent variable is without the influence of size? So in the example, is there an approach to find the influence of weight on the target variable?

There is no way to directly correlate the set element properties with the target so some kind of aggregation of the set needs to be done first.

Is there a standard procedure for doing this?

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  • $\begingroup$ There is a standard procedure: regression $\endgroup$ Apr 10 at 4:37
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You could try running PCA with varimax rotation. You would obtain a set of uncorrelated components, where groups of highly correlated variables cluster together in a particular component, which you can see by them having high loadings of similar magnitude in that PC. Perhaps a component can also serve as an aggregation of the set, you could then try PCR instead of regular OLS.

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