# How does partial least squares algorithm return more than one factor?

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