You are right, Yes, sensitivity analysis of model this way. If you have a number of input layers or data, calculate partial correlation coefficients and eliminate the input lay or data which has least value of partial correlation, if there is no drastic change in the output layer or output, then eliminate the second least important correlation, and so on, when you find some change in output layer are output data stop. In the case of data you can do it using partial correlation coefficients with the combine output of data, in the case of GIS layer you have to theoretical determine least and most important layers giving ranks to each layer on theoretical basis. Otherwise, you have to create combinations by permutation and try each and find out in which case there is no or little change change in output.
The need for sensitivity analysis come from the fact that the sensitivity of simulations to errors in the individual inputs is needed in order to establish where priorities should be placed in determining required input data. Sensitivity analysis are conducted by changing a given input by a predetermined amount, and, with the other inputs held at their correct values. For each input parameter, simulations are conducted for the correct value and +10, -10, +25, -25. +50, -50, -95, +100 and +200 percent of the correct value.