First of all, I realize multiple regression does not really give actually "causal" inferences about the data. Let me explain my current case:
I have four independent variables which I hope (but am not sure) are involved in driving the thing I'm measuring. I wanted to use multiple regression to see how much each of these variables are contributing to my dependent variable, and did so. Supposedly, variable "Number four" is influencing my outcome measure very strongly (beta weight close to 0.7).
However, I've been told this isn't enough, because some of my "independent" variables may in fact be correlated with each-other. In that case, I could think "Variable four" is driving my dependent variable, when really both three and four could be contributing equally. This seems correct, but since I'm new to this I'm unsure.
How can I systemically avoid this problem in the future? What specific procedures would you recommend when using multiple regression to make sure that your "independent" data does not already contain hidden correlations?
Edit: The data itself is a series of network (graph) models of a particular neurological state. I'm measuring the "clustering coefficient" which describes the topology of each network as a whole (dependent variable here), and then seeing if the individual connectivities of four nodes in the larger 100+ network are driving the global clustering values (four independent variables). However, these nodes are part of a network, so sort of by definition it's possible they're correlated to some extent.