Non-linearity is a relation which cannot be explained as a linear combination of its variable inputs. In other words, the result does not change in proportion to a change in one of the inputs.
Non-linearity is a common problem when examining cause and effect relationships. Such instances require complex modeling and assumption to provide explanations for nonlinear events. Non-linearity without explanation can lead to random and unexpected results such as chaos.
Nonlinear regression is a common form of regression analysis used in the financial sector to model nonlinear data against independent variables in order to explain their relationship. Although the parameters of the model are not linear, nonlinear regression can adjust the data using successive approximation methods to provide explanatory results.