Nonlinear Regression Modeling for Engineering Applications: Modeling, Model Validation, and Enabling Design of Experiments
9 The Distortion of Linearizing Transforms
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Unconstrained linear regression, see Equations 1.1 to 1.8, has some desired attributes over nonlinear optimization. Linear regression is guaranteed to find a solution, to find a unique solution, and to find a solution within a time interval that can be specified based on problem dimension. First learned, frequently reinforced, and less complex in concepts, linear regression is better understood than nonlinear regression. More commonly used, it is more familiar to both user and the user’s audience. As a result, we often seek to linearize coefficient expression in models that are nonlinear in the coefficients. Most commonly log, reciprocal, square root, and similar functional transformations are used.