Yes. In the simplified linear setting we're considering... If you want to do dimension reduction and only have X, use PCA. If you want to do dimension reducti

Yes. In the simplified linear setting we're considering... If you want to do dimension reduction and only have X, use PCA. If you want to do dimension reduction and also have a "y", consider PLS or CCA (canonical correlation analysis). Some background: https://www.cs.cmu.edu/~tom/10701_sp11/slides/CCA_tutorial.pdf https://www.cs.cmu.edu/~tom/10701_sp11/slides/CCA_tutorial.p...