Regression analysis, non-linear

A non-linear regression analysis is employed using die Solver in Microsoft Excel spreadsheet to determine die values of and in die following examples. Example 1-5 (Chapter 1) involves the enzymatic reaction in the conversion of urea to ammonia and carbon dioxide and Example 11-1 deals with the interconversion of D-glyceraldehyde 3-Phosphate and dihydroxyacetone phosphate. The Solver (EXAMPLEll-l.xls and EXAMPLEll-3.xls) uses the Michaehs-Menten (MM) formula to compute v i- The residual sums of squares between Vg(,j, and v j is then calculated. Using guessed values of and the Solver uses a search optimization technique to determine MM parameters. The values of and in Example 11-1 are ... 

The authors are indebted to Messrs. L.T. Hillegers and A.G. Swenker for assistance in the non-linear regression analysis and the parameter estimation, to Mr. J.H.M. Palmen for experimental help, to Mr. G. Schuler for drawing the figures and to Mrs. 

A non-linear regression analysis of the data listed in the table is made by Li [211]. By comparison between the regression coefficients the following are concluded (1) The pH has the most significant effect on the mean size, the influence of the TiCI4 concentration takes second place, while the temperature has little effect and (2) Similarly, the pH and the TiCl4 concentration exhibit the most significant influences on the yield of titanium. 

Vindimian, E., Robaut, C. and Fillion, G. (1983) A method for co-operative and non co-operative binding studies using non-linear regression analysis on a microcomputer, Journal of Applied Biochemistry 5, 261-268. 

Table III presents the values of the second order rate constants for the HDS and HDN data. The values of the rate constants for HDS and HDN of Raw Anthracene Oil using Nalcomo 474 catalyst were obtained by applying the same non-linear regression analysis technique to the data of Sooter (2) and Satchell(3). The comparison of the rate constants leads one to the same conclusions as shown by Figures 5 and 6.

Non-linear regression analysis of the data for these two mechanisms are shown in Table 1 below. 

The kinetic and deactivation models were fitted by non-linear regression analysis against the experimental data using the Modest software, especially designed for the various tasks -simulations, parameter estimation, sensitivity analysis, optimal design of experiments, performance optimization - encountered in mathematical modelling [6], The main interest was to describe the epoxide conversion. The kinetic model could explain the data as can be seen in Fig. 1 and 2, which represent the data sets obtained at 70 °C and 75°C, respectively. The model could also explain the data for hydrogenated alkyltetrahydroanthraquinone. 

The Arrhenius equation did not describe very well the influence of temperature on viscosity data of concentrated apple and grape juices in the range 60-68 °Brix (Rao et al., 1984, 1986). From non-linear regression analysis, it was determined that the empirical Fulcher equation (see Ferry, 1980 p. 289, Soesanto and Williams, 1981) described the viscosity versus temperature data on those juice samples better than the Arrhenius model (Rao et al., 1986) ... 

There are many published computer programs and commercial software packages that perform non-linear regression analysis, but you can obtain the same results very easily by using the Solver. When applied to the same data set, the Solver gives the same results as commercial software packages. 

Other software packages that can be used to perform non-linear regression analysis are MathCad (MathSoft, Inc., 201 Broadway, Cambridge, MA 02139) and MatLab (Mathworks Inc., 24 Prime Park Way, Natick, MA 01760). 

Both the Precision and Tolerance options apply only to problems with constraints. The Precision parameter determines the amount by which a constraint can be violated. The Tolerance parameter is similar to the Precision parameter, but applies only to problems with integer solutions. Since adding constraints to a model that involves minimization of the error-square sum is not recommended, neither the Precision nor the Tolerance parameter is of use in non-linear regression analysis. 

NonLin.xls illustrates the use of the Solver to perform multiple non-linear regression analysis. 

For all mathematical models that are not naturally straight lines, non-linear regression analysis is often the best approach. The observed data and the corresponding dependent variable can be analyzed without transformation. Thus, the data and the error or variance are not distorted during the analysis. If necessary, clearly defined weighting schemes can be applied. Furthermore, multiple observation sets can be readily accommodated. 

SAAMII is provided as a compiled program for Windows or Macintosh systems and performs non-linear regression analysis. It has a graphical user interface for model specification. 

Peck, C.C. Sheiner, L.B. Nichols, A.I. The problem of choosing weights in non-linear regression analysis of pharmacokinetic data. Drug Metab. Rev. 1984,15, 133-148. 

Mode) parameters were estimated by non-linear regression analysis. The sum of squares between the experimental and calculated instantaneous weight fractions was minimised. Estimated values of the model parameters together with standard deviations (SD) are detailed in Table 5. 

Fig. 6 Influence of HP-p-CD concentration on the fluorescence intensity (measured at Aem = 513 nm) of a 10-5 M 9-methyl- 12H-benzo [a]phenothiazine water/ethanol 99 1, v/v, mixture. The solid line was calculated through the use of Eq. 4, assuming a 1 1 stoichiometry and using Too and JCf values obtained from a non-linear regression analysis (from [19], with permission)...

Vyazovkin and Lesnikovich [42] have emphasized that the majority of NIK methods involve linearization of the appropriate rate equation, usually through a logarithmic transformation which distorts the Gaussian distribution of errors. Thus non-linear methods are preferable [89]. Militky and Sest [90] and Madarasz et al. [91] have outlined routine procedures for non-linear regression analysis of equation (5.5) above by transforming the relationship ... 

Linear analysis was carried out using Excel and the non linear regression analysis was carried out with NLREG (Version 5.2 Phillip H. Sherrod 1991-2001). 

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