Curve fitting with nonlinear regression analysis

Curve Fitting with Nonlinear Regression Analysis... 

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.

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,... 

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. 

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. 

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. 

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