Solving the problem is an important part of optimization. An equally important part is the analysis of the solution where several questions can arise. For a scheduling problem, is it possible to obtain a better solution by increasing the capacity of a resource? What happens to the objective value if we start a specific task earlier? Answering such questions is important to provide explanations and increase the acceptability of a solution. A lot of research has been done on sensitivity analysis, but few techniques can be applied to constraint programming. We present a new method for sensitivity analysis applied to constraint programming. It collects information, during the search, about the propagation of the CUMULATIVE constraint, the filtering of the variables, and the solution returned by the solver. Using machine learning algorithms, we predict if increasing/decreasing the capacity of the cumulative resource allows a better solution. We also predict the impact on the objective value of forcing a task to finish earlier. We experimentally validate our method with the RCPSP problem.