Cluster structure in (multicollinear) data can be utilized by pattern recognition methods in order to find adequate subspaces for nonlinear regression. When regressing a particular severely nonlinear function, it is demonstrated that this approach is superior to polynomial PLS. It is also demonstrated that for nonlinear functions, the choice of regression explained variables onto the explaining variables, or vice-versa, is not arbitrary. Numerical experiments indicate that the classical statistical model is more powerful than the inverse regression approach.