is there a method like PLS-DA, but for a quantitative Y value?

Hi guys,

I am looking for a statistical method like PLS-DA but for quantitative Y

For a normal PLS-DA, we have X (n*p) matrix which contains quantity data and Y (n) vector with qualitative information such as treatment/control or difference group. So PLS-DA will give us an optimal number of components and variables which maximize the separation between matrix and qualitative groups.

But what if we replace the Y value by quantitative value like fold-change? I know PLS which searches the best choice of components to maximize the correlation between 2 matrices, so is there any statistical tools already targeting this question?

Thanks in advance