Technical Abstract: Chapter 2 is concerned with how data are analyzed with nonlinear regression methods. It compares nonlinear and linear models for analyzing laboratory data. A tutorial of the linear model is presented, as are the equations of linear regression analysis. Matrix representation of the linear least squares method is derived. Why the error increases when models are linearized, is also discussed. Next the nonlinear regression model is presented, along with the nonlinear regression algorithms. The matrix representation of the nonlinear regression is derived in total. An example of regression analysis for an exponential decay with and without weighting functions is discussed. Finally, sources of software for regression analysis are provided and contrasted.