It sounds like you have some fundamental methematical questions about PCA.  If your library has a copy of A User's Guide to Principal Components by J. Edward Jackson (1991), I highly recommend it. It is easy to read and very applied.   I can't answer all your questions, but I think there are some problems with your SAS code. First, that 'proc princomp' syntax seems to match PROC FACTOR, not PRINCOMP.  The DATA step also contains errors, I believe.   My advice is to start with a basic PCA. Since your variable appear to be comparable, you might want to use the PCA of the covariance matrix. This will eliminate the scaling issue as well as the rotation transformation.  Then perform a regression on the 3 PCA factors and compare the results and predicted values with a regression analysis on the original variables. You should be able to figure out how the two regressions are related.    Lastly, if you want the most help from this forum, I encourage you to either include data or use data from the PROC PRINCOMP documentation or from SASHELP data sets.  That way you can ask specific questions and we can reproduce what you are seeing. ... View more