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Please correct me if I am wrong as I am not good at R. I think I can find a linear combination maximizing correlation between predictors and dependent variables by running partial least squares analysis with standardized X without intercept and standardized Y matrix.

But how can I do that with pls or any other package in R? Does it do that with default settings?

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    $\begingroup$ Do you mean canonical correlation analysis? $\endgroup$ – whuber Apr 2 '12 at 19:47
  • $\begingroup$ similar but partial least squares analysis is little different from CCA. $\endgroup$ – Tae-Sung Shin Apr 2 '12 at 19:52
  • $\begingroup$ In English, "little different" means not different in any important respect whereas "a little different" means sufficiently different to matter! I am guessing that the "but" construction implies you intended to write "a little different." That points out an ambiguity in the question: do you seek an optimal linear combination using any technique whatever or is it a requirement to use "partial least squares analysis"? The question as phrased can be read in the first sense but your comment hints that maybe you have the second sense in mind. Could you clarify? $\endgroup$ – whuber Apr 2 '12 at 19:57
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    $\begingroup$ @whuber it does not matter which analysis to use. And thanks for grammar correction. $\endgroup$ – Tae-Sung Shin Apr 2 '12 at 20:35
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No, PLS package does not maximize correlation between scores and response values in default settings. I couldn't so far find whether the package has that functionality or not although manual mentioned about it with a sentence.

And you are right. You need to deal with standardized matrices to do PLS for the correlation maximization.

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