# Finding the relation between two dimensions in a multi-dimensional problem

I have a collection of data points. Each point has 6 dimensions (x1, x2,...x6). I want to find a relation between two dimension (e.g. x1 vs x2). What I have been doing so far is look for points where the other dimensions (x3 to x6) are relatively constant, by defining a band. This way I would get several groups of data points where only the two dimensions of interest would change.

I was wondering if there is a better way of analyzing the relationship between these two dimensions. I looked at PCA, but I have a feeling that it does not help me much. If I reduce the problem to two dimensions the axes are basically meaningless.

Can you guys give me some directions to look at?