I have two sets of variables in the same dataset. Say DATA_free and DATA_exp. DATA_exp, however, consists of variables which are very expensive/difficult to obtain whereas DATA_free are always available easily.
I was wondering if it was possible to use Canonical Correlation Analysis between these two sets of variables so that I can find a linear combination of variables in DATA_free that best explains what DATA_exp does, in hopes that, if the correlation between the two linear combinations is high enough I could stop relying on DATA_exp to compute my results.
Is this reasonable? Any advice/example you could give me? Is this theoretically correct?