Linear models have been applied in various applications to determine the relationship between the response and the feature variables as well as to facilitate prediction. However, the explanatory and residual conditions assumed by linear model pose huge performance challenges in the face of datasets that do not met the conditions. This study systematical reviewed how the linear models could be shifted to non-linear models using three different methods: Polynomial regression, Step functions, and Generalized Additive Models (GAMs). To build higher performance predictive models, the research uncovered that non-linear model of 3 to 4 degrees of polynomial regression methods are expected to perform better than linear model. And that the coefficient values in linear models are no longer necessary in non-linear models. It further revealed that the step functions improved the global structure of polynomial regressions by breaking the range of the predictor variable ???? into bins, and converting the continuous variable ???? into an ordered categorical variable, making it very popular in biostatistics and epidemiology studies. Finally, we found that Generalized Additive Models introduced a complete shift from parametric model to non-parametric model, replacing each linear component with a nonlinear function of the variable ????, while maintaining additivity.
