# Interpreting overlapping arrows on a PCA biplot: does it mean that the variables are redundant?

I'm new in principal component analysis (PCA) and I don't really understand the biplot representation of its results, so I would really appreciate some guidance. Having the example of the illustration shown below. Could I say that variables x1 and x2 are telling me the same, and so there is no need to record the values of one of the two?

In my case variables are geometrical deviations of a part where the points measured are close to each other. Therefore, I would like to know if based on the PCA biplot I could stop measuring the values for x2 if I already measured x1 values.

• I think it is a duplicated question, can you check this post – Haitao Du Jun 15 '16 at 18:25
• This Q asks a specific question about variable redundancy. I don't think it's a duplicate. – amoeba says Reinstate Monica Jun 15 '16 at 19:10
• stats.stackexchange.com/q/224204/3277 is theoretically a similar question (see). – ttnphns Sep 7 '16 at 10:10

X1 and X2 are "redundant" in the sense of linear duplicates of each other if they correlate perfectly ($r=1$). Then the two variable vectors must coincide, be collinear in the space (that space - where variables are drawn as vectors, arrows - is called "subject space").
Finally, if they do coincide or near coincide and therefore redundant for you, could I stop measuring the values for x2 if I already measure x1 values? - you ask. That depends on what you are going to do next after the deletion of one of the two variables. If, for example, you delete the one and go to redo PCA - the PCs will change despite that you deleted a "redundant" measurement.