Nonlinear regression for

Complex Rate Equations Complex rate equations may require individual treatment, although the examples in Fig. 7-2 are aU hn-earizable. A perfectly general procedure is nonlinear regression. For instance, when r =f(C, a, b,. . . ) where a,h,. . , ) are the constants to be found, the condition is... 

E. F. Vonesh and R. L. Carter, Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 46 673-687 (1992). 

The glass-transition experimental data obtained with the DSC showed a great reduction in Tg with the increase in moisture content. In the water activity domain studied (0.11 < < 0.90), Gordon-Taylor model (Equation 62.2) was adequate to adjust the experimental data. In Equation 62.2, and are the mass fraction of solids and water, fc is a constant derived experimentally for the solid component, and Tg, Tgs, and Tgw are the glass-transition temperatures for the mixture, the bone-dry solid components, and pure water (— 135°C), respectively. The model parameters, estimated by nonlinear regression for freeze-dried camu-camu natural pulp... 

Jandel Corporation, 1995. Transforms nonlinear regressions for windows, user s manual. Jandel Corp., San Rafael, CA. 

The attraction of the ALS algorithm for general multilinear models is its use of linear least-squares steps. However, these steps become nonlinear regressions for any way containing a nonlinear parametric model, and most parametric models in spectroscopy will be nonlinear. Thus, the ALS approach is unattractive for most situations in which the dependence of the spectral intensity of any component on any experimental variable is described by a specific mathematical function. 

Isotherm experiments, which determine E for a wide range of m, can be analyzed to find and Ej. Equation (6.18) can be linearized in several different ways to avoid the need for using a nonlinear regression for data analysis. The double reciprocal of the Langmuir equation produces the Lineweaver-Burke equation, which is often used to fit adsorption data. 

The situation is more complex in multiple eind/or nonlinear regression. For these cases, predictors with maximal correlation coefficients to Y do not necessarily form... 

APPENDIX 6-A Nonlinear Regression for AIBN Decomposition 197 APPENDIX 6-A NONLINEAR REGRESSION FOR AIBN DECOMPOSITION... 

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