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This chapter introduces the reader to the concepts of data modelling using least-squares, regression analysis through a simplified framework consisting of three iterative steps, model selection, parameter estimation, and model validation, which forms the foundation for all subsequent chapters. Model selection focuses on selecting an appropriate description of the data set given both physical and mathematical constraints. This chapter focuses on deterministic models, while subsequent chapters focus on stochastic or more complex models. Parameter estimations seeks to determine the values of the parameter for the given model and data set. Different approaches, including ordinary, linear regression; weighted, linear regression; and nonlinear regression, are examined in detail. Theoretical results are provided as necessary to illustrate the need for some of the components of the analysis. Also, detailed summaries listing all the required formulae are provided after each section. Finally, model validation, which consists of two components, residual testing and model adequacy testing, is explained in detail. Suggestions for corrective actions are also provided for commonly encountered issues in model validation. Detailed examples are provided to illustrate the different methods and approaches. By the end of the chapter, the reader should be familiar with the regression analysis framework and be able to apply it to complex, real-life examples.
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- Chapter 3