sensitivity analysis with existing data

Hello,

I'm very new to the realm of sensitivity analysis and I'm trying to understand how each of my input parameters is effecting my system's output. For example, my system has several input parameters and I want to understand how each input is driving the change in my output.

Since I only have logged input and output data and no knowledge of the actual system, I need to picture my system as a black box. Is it possible to perform a sensitivity analysis with this sort of set up?

Any help is deeply appreciated. Mitch