This question follows this question, in particular @amoeba's clarifying answer and the plot from the SAS documentation included. I'm especially interested in knowing

  1. if $\mathbf{X}, \mathbf{Y}$ are unwhitened, what would the CCA axis look like in the plot comparing the different methods? How is that interpreted?
  2. Is whitening generally recommended? When would it be recommended?
  3. Given that $\mathbf{X}, \mathbf{Y}$ are standardised/z-scored (is this pertinent to method choice?), how should one choose between the methods, esp. RRR, CCA, PLS? I presume it is dependent on the objective/question to be answered. Would I be correct in understanding that one should choose RRR if the question is what linear combinations of $\mathbf{X}$ components best explain the $\mathbf{Y}$? What exactly then are the questions for PLS and CCA?
  4. Is the ideal method choice dependent on the amount of data points available or other properties of the data?

Thank you for your time.


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