Application of Regression Concepts

Poor Sensitivity Modulus The Bode magnitude representation is singularly incapable of distinguishing between impedance models unless they provide extremely poor fits to impedance data. 

Real The real impedance representation is similarly insensitive to fit quality. 

Modest Sensitivity Complex-impedance-plane These plots are sensitive only for large impedance values. Impedance data at high-frequency values are typically obscured. 

Imaginary The imaginary impedance representation is modestly sensitive to fit quality. 

Log-imaginary These plots emphasize small values, and values of the slope that differ from 1 may suggest the need for new models. 

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A disadvantage is that multiple regression, by definition, only allows application of the CA concept there is no possibility to compare the response with the IA concept. In addition, the researcher is limited to using 1 type of concentration-response curve for the complete data set through the choice of the link function. It may, however, be more appropriate to use different types of concentration-response curves for the different mixture components. Finally, deviations from CA can be properly tested for through the interaction parameters, but concentration-ratio- or concentration-level-dependent deviations from CA cannot be detected. 

Although calibrating or classifying spectra are merely two different applications of the mathemati-cal/statistical technique of regression, historically they have evolved independently, with different goals and requirements. Whenever possible attempts will be made to connect the two by drawing attention to common concepts and methods that only differ in their terminology and emphasis. Occasionally, for the sake of simplicity in presentation, discussion will cover certain aspects and peculiarities of the two disciplines separately. 

These techniques span the entire field from multiple linear regression (MLR)-type methods and various forms of neural network architectures to rule-based techniques of different kinds. These approaches also span from single models to multiple models, that is, consensus or ensemble modeling. Terms like machine learning and data or information fusion are also frequently encountered in this area of research, as well as the concepts of applicability domain and validation. 

Saebo S, Martens M, Martens H. Three-block data modeling by endo- and exo-LPLS regression. In Vinzi VE, Chin WM, Henseler J, et al., editors. Handbook of Partial Least Squares Concepts, Methods and Applications. Heidelberg Springer 2010. p 359-379. 

In the past, people was apt to think that the best way to increase the prediction ability of the mathematical models obtained from data processing is to find a function to fit the training data set as close as possible. In other words, best training could assure best prediction result. But this concept has been found to be not correct in the practice of the application work of artificial neural networks or nonlinear regression with polynomial equations. Therefore, it has become an imminent task to find a strict mathematical theory for solving the problem of overfitting [68]. 

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