This chapter discusses parametric regression and sensitivity analysis, emphasizing the importance of mathematical modeling in representing physical systems and predicting behavior. Regression is presented as an essential tool for estimating relationships between variables and reducing computational effort in complex systems. Sensitivity analysis complements this process by identifying the influence of input variables on system outcomes, allowing adjustments, simplifications, and improved simulation efficiency. Various methods, including local and global analysis, conditional variance, total effects, and visual approaches such as spider diagrams and scatter plots, are detailed with applications in scenarios involving uncertainties. The parameterization of the system, exemplified by a direct current motor, illustrates the use of optimization and regression techniques to identify unknown parameters. Hybrid and statistical methods are also discussed for exploring variable spaces and assessing the impact of variations on outcomes, contributing to improved modeling, forecasting, and system performance.