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My understanding of PLS regression is that we find an eigen vector such that it maximises the covariance between X(matrix of independent variables) and Y(vector/matrix of dependent variable) i.e. find factors by computing SVD on (X'Y) matrix.

In my dataset there are 5 independent variables and 1 dependent variable (dimension of X is (n x 5) & dimension of Y is (n x 1) ). Matrix X'Y will have dimension (5 x 1) on which when I compute SVD, I will have just 1 left singular vector,right singular vector, singular value each.

Why do I see 5 factors in the result of pls package?

Note:

  • X' here refers to transpose of X matrix
  • I am using proc pls procedure in sas
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