Curve fitting, nonlinear regression analysis

Therefore, plotting the ALIS MS response from a titration series versus the total ligand concentration yields a saturation binding curve that can be fit to this equation by nonlinear regression analysis to yield the of the ligand of interest. 

Duplicate injections shown. (A) Fitting the data by nonlinear regression analysis yields a of 5.6 1.0 pM. (B) Data from A, plotted as a sigmoidal curve to better show the fit at low titrant concentrations. (C) Residuals plotted as absolute and (D) as percent of signal. 

Fig. 6.13 Measurement of FAC data for a range of pyrimethamine concentrations applied to sol-gel-entrapped dehydrofolate reductase (A) overlay of breakthrough curves and (B) nonlinear regression analysis of the fit to the measured breakthrough volumes from A [28]. Adapted with permission from the American Chemical Society.

Nonlinear regression analysis of the dependence of c2(r) upon (r), a transform of the radial distance i leads to evaluation of the reference thermodynamic activity, Mzzz(rf), and the osmotic second virial coefficient, Au/Mi, expressed on a weight basis (litre/g) rather than a molar basis (litre/mol). Furthermore, the values of Miy v/ and ps can be obtained by curve-fitting the sedimentation equilibrium distribution for low biopolymer concentrations (M fr) cf for all r) to the equations (5.36) and (5.37) in order to deduce the quantity [Mj( 1 - v/ps)] from the coefficient of the exponent (Winzor et al., 2001 Deszczynski et al., 2006). 

This process is partially overlapped with the next process, the j3 relaxation. To analyze the loss permittivity in the subglass zone in a more detailed way, the fitting of the loss factor permittivity by means of usual equations is a good way to get confidence about this process [69], Following procedures described above Fig. 2.42 represent the lost factor data and deconvolution in two Fuoss Kirwood [69] as function of temperature at 10.3 Hz for P4THPMA. In Fig. 2.43 show the y and relaxations that result from the application of the multiple nonlinear regression analysis to the loss factor against temperature. The sum of the two calculated relaxations is very close to that in the experimental curve. 

This method has two major disadvantages. First, it requires two fitting steps, i.e. the nonlinear regression of each individual curve with the pseudo-first order exponential equation and a linear fit of the obtained kobs values vs. the analyte concentration. Second, the two parameters kobs and A f in the exponential equation (Eq. 11) are not independent of each other, which is a major prerequisite for nonlinear regression analysis. 

Curve Fitting with Nonlinear Regression Analysis... 

A comparison of the two-compartment first-order absorption model fit to measured plasma concentration data from a traditional method of residuals analysis and a nonlinear regression analysis is provided in Figure 10.99. This figure illustrates the fact that both methods offer a very reasonable fit to the measured data. It also demonstrates that there is not a large difference between the fit provided by the two different techniques. Close examination does reveal, however, that the nonlinear regression analysis does provide a more universal fit to all the data points. This is likely due to the fact that nonlinear regression fits all the points simultaneously, whereas the method of residuals analysis fits the data in a piecewise manner with different data points used for different regions of the curve. 

Overlapping peaks can be quantitatively analyzed by constructing mathematically a sjmthetic chromatogram which is fitted to the experimental one by iterative, nonlinear regression analysis. This method, called curve fitting, requires two assumptions. 

One motivation of performing simulations is the interpretation of experimental data, e.g. voltammograms or chronoamperometric data, by estimation of physical parameters. This can be achieved by fitting simulated curves to experimental ones in a nonlinear regression analysis process. The user provides a model to the simulation program and an objective function is then minimized by systematic variation of the model parameter. The best fit is achieved when a global minimum of the object... 

There are three parameters in Eq. (60) q, b, and q. Their values are evaluated in fitting the model to the experimental excess adsorption data by nonlinear regression analysis. Each parameter is a fimction of temperature, as shown in Figs. 18-20. The amount adsorbed as predicted by the model is shown by the curves in Fig. 5. The model fits the experimental isotherms very well, even for the one near the critical temperature. The fitness of the model is measured by the total disagreement defined as the following ... 

The time course of HPOD formation was examined with nonlinear regression analysis over a 6 h period at 15°C using IMM-LOX that contained 3.0 mg protein. Curve fit estimates were obtained using Equation 1,... 

Parameter estimates for y, and S were obtained by nonlinear regression analysis of the stress and strain curves using the non-linear curve fitting tool in the software program OriginPro . These values were then used to calculate G, G" and / from Equations (4)-(6). 

Toward these ends, the kinetics of a wider set of reaction schemes is presented in the text, to make the solutions available for convenient reference. The steady-state approach is covered more extensively, and the mathematics of other approximations ( improved steady-state and prior-equilibrium) is given and compared. Coverage of data analysis and curve fitting has been greatly expanded, with an emphasis on nonlinear least-squares regression. 

If poor initial parameter estimates are used, it becomes likely that the nonlinear regression will not be able to find an acceptable fit, or it may stride off on a mathematical tangent and arrive at a nonsensical fit to the data. It turns out that the values determined by traditional methods of residual analyses typically offer excellent starting estimates for the model parameters. Hence the traditional data analysis methods described in this chapter remain highly useful, even when nonlinear regression curve fitting is employed as the final step of parameter evaluation. 

The most common fitting analysis employed is to fit the experimental data to nonlinear least squares regression analysis (NLLS). This analysis is employed for a single decay curve obtained at set experimental parameters, such as fixed excitation and emission wavelengths and fixed concentrations of probe, supramolecular structure, and quencher. The experimental data are fitted to equations derived from assumed mechanistic models. The fitting procedure, which... 

---