Method regression

VLE data are correlated by any one of thirteen equations representing the excess Gibbs energy in the liquid phase. These equations contain from two to five adjustable binary parameters these are estimated by a nonlinear regression method based on the maximum-likelihood principle (Anderson et al., 1978). 

The constants of rate equations of single reactions often can be found by one of the linearization schemes of Fig. 7-1. Nonhnear regression methods can treat any land of rate equation, even models made up of differential and algebraic equations together, for instance... 

Multiple regression analysis can be executed by various programs. The one shown in the Appendix is from Mathcad 6 Plus, the regress method. Taking the log of the rates first and averaging later gives somewhat different result. 

Pd4oCu4oP2o, Pd5oCu3oP2o, and Pd6oCu2oP20 alloys were measured by resonant ultrasound spectroscopy (RUS). In this technique, the spectrum of mechanical resonances for a parallelepiped sample is measured and compared with a theoretical spectrum calculated for a given set of elastic constants. The true set of elastic constants is calculated by a recursive regression method that matches the two spectra [28,29]. 

Search for the overall optimum within the available parameter space Factorial, simplex, regression, and brute-force techniques. The classical, the brute-force, and the factorial methods are applicable to the optimization of the experiment. The simplex and various regression methods can be used to optimize both the experiment and fit models to data. 

This technique is invasive however, the particle can be designed to be neutrally buoyant so that it well represents the flow of the phase of interest. An array of detectors is positioned around the reactor vessel. Calibration must be performed by positioning the particle in the vessel at a number of known locations and recording each of the detector counts. During actual measurements, the y-ray emissions from the particle are monitored over many hours as it moves freely in the system maintained at steady state. Least-squares regression methods can be applied to evaluate the temporal position of the particle and thus velocity field [13, 14]. This technique offers modest spatial resolutions of 2-5 mm and sampling frequencies up to 25 Hz. 

Orth D.S. (1990) Preservative evaluation and testing the linear regression method. In Guide to Microbiological Control in Pharmaceuticals (eds S.P. Denyer R.M. Baird), pp. 304-312. Chichester Ellis Horwood. 

The similarity in approach to LDA (Section 33.2.2) and PLS (Section 33.2.8) should be pointed out. Neural classification networks are related to neural regression networks in the same way that PLS can be applied both for regression and classification and that LDA can be described as a regression application. This can be generalized all regression methods can be applied in pattern recognition. One must expect, for instance, that methods such as ACE and MARS (see Chapter 11) will be used for this purpose in chemometrics. 

Section 35.4), reduced rank regression (Section 35.5), principal components regression (Section 35.6), partial least squares regression (Section 35.7) and continuum regression methods (Section 35.8). 

I. E. Frank, Intermediate least-squares regression method. Chemom. Intell. Lab. Syst., 1 (1987) 233-242. 

Other Nonlinear Regression Methods for Algebraic Models... 

Freund, R.J. and P.D. Minton, Regression Methods, Marcel Dekker, New York, NY, 1979. 

We can distinguish the algorithms in two kinds for the regressions and the classification. Regression methods get a continuous value. Classifiers find the category, for instance the toxicity class, of elements of a population. 

Hoskuldsson A (1988) PLS regression methods. Chemom 2 211 Huber PJ (1981) Robust statistics. Wiley, New York... 

In addition to the three methods described above, nonlinear regression methods or other transform approaches may be used to determine the dispersion parameter. For a more complete treatment of the use of transform methods, consult the articles by Hopkins et al. (15) and Ostergaard and Michelsen (14). 

An important feature of the logistic regression method is that although the input modelling data (P0) are binary, the calculated probability (P) is a continuous function. 

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