Statistical analysis nonlinear regression

Most laboratories now have access to powerful computers and an extensive array of commercially available data analysis software (e.g., Prism (GraphPad, San Diego, CA), Sigma Plot (San Rafael, CA)). This provides ready access to the use of nonlinear regression techniques for the direct analysis of binding data, together with appropriate statistical analyses. However, there remains a valuable place for the manual methods, which involve linearisation, particularly in the undergraduate arena and these have been rehearsed in the above text. 

Multiple regression analysis is a useful statistical tool for the prediction of the effect of pH, suspension percentage, and composition of soluble and insoluble fractions of oilseed vegetable protein products on foam properties. Similar studies were completed with emulsion properties of cottonseed and peanut seed protein products (23, 24, 29, 30, 31). As observed with the emulsion statistical studies, these regression equations are not optimal, and predicted values outside the range of the experimental data should be used only with caution. Extension of these studies to include nonlinear (curvilinear) multiple regression equations have proven useful in studies on the functionality of peanut seed products (33). 

Seber, G. and Wild, C., Nonlinear Regression Analysis, Wiley Series in Probability and Mathematical Statistics, John Wiley, New York, 1989. 

The Wilson, Margules, and Van Laar procedures described in this example are suitable for manual calculation. However, to take full advantage of all the information available from whatever vapor-liquid equilibrium data are at hand, statistical procedures for estimating the parameters should instead be employed, with the aid of digital computers. These procedures fall within the domain of nonlinear regression analysis. 

All the data analysis methods shown in Fig. 3 involve linear or nonlinear regression of ACF data, (representing data point j of Gi2 g(2K or j 1 ). to fit a proposed model, yjnixlel. The model parameters or amplitudes of a proposed distribution are adjusted until a characteristic function is minimized or maximized. The characteristic function is often the chi-square [Pg.218]

The Arrhenius form of the parameters are used, i.e., ki=Aie, Ki=Aje, and the exponent % were estimated using the nonlinear regression software package SAS (Statistical Analysis Software). The Proc Model (with Marquardt-Levenberg method) and Fit Procedures in SAS were used for this purpose. The results are shown in Table 1 and Table 2. 

Because of their fixed length, descriptors are valuable representations of molecules for use in further statistical calculations. The most important methods used to compare chemical descriptors are linear and nonlinear regression, correlation methods, and correlation matrices. Since patterns in data can be hard to find in data of high dimension, where graphical representation is not available, principal component analysis (PCA) is a powerful tool for analyzing data. PCA can be used to identify patterns in data and to express the data in such a way as to highlight their similarities and differences. Similarities or diversities in data sets and their properties data can be identified with the aid of these techniques. 

Kinetic analysis Statistical data analysis was performed using the Statistica program version 6.0 (30). The usual kinetic models reported in literature to describe kinetic of compoimd formation are zero order [c= cO + kt], first order [c=cO exp (kt)] or second order [1/c = 1/cO + kt] reaction models. The Arrhenius equation k = kref exp (- Eai/R ( 1/T - 1 / Tref))] is usually applied to evaluate the effect of temperature on the reaction rate constant (31). For both levels of oxygen concentration a one step nonlinear regression method was performed and a regression analysis of the residuals was also carried out (32). 

The points marked by an asterisk in Fig. 5-28 are the new ones. When included in a visually weighted fit to the whole data set, they lead to the much lower estimates of and of 10 pmol and 25 pmol L min, respectively. Such changes in estimates brought about by using additional data, from a separate experiment, should alert the investigator to possible systematic artifacts in the outcome. The new analysis also shows the effects of outlying points on the parameter estimates. It alerts us to the idea that modern statistical methods of nonlinear regression analysis should be used to estimate parameter values in circumstances like the present. (We don t have the space to go into this here.)... 

Statgraphics Statistical Graphics Corp. cluster analysis, discriminant analysis, PCA, linear and nonlinear regression... 

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