  We show how a general formulation of the Fluctuation-Response Relation is
able to describe in detail the connection between response properties to
external perturbations and spontaneous fluctuations in systems with fast and
slow variables. The method is tested by using the 360-variable Lorenz-96 model,
where slow and fast variables are coupled to one another with reciprocal
feedback, and a simplified low dimensional system. In the Fluctuation-Response
context, the influence of the fast dynamics on the slow dynamics relies in a
non trivial behavior of a suitable quadratic response function. This has
important consequences for the modeling of the slow dynamics in terms of a
Langevin equation: beyond a certain intrinsic time interval even the optimal
model can give just statistical prediction.
