Regression analysis application

The stationary case is given by the description shown below in Fig. 2.2. It is a sketch of the way by which complex formation constants are traced back to and correlated with E (L) using the most simple approach of linear regression analysis (applications in Figs. 2.2 and 2.15). There are two terms in Eq. 2.4 one of which (c) describes an intrinsic binding stability... 

The models are applicable to large data sets with a rapid calculation speed, a wide range of compounds can be processed. Neural networks provided better models than multilinear regression analysis. 

Blanco and co-workers" reported several examples of the application of multiwavelength linear regression analysis for the simultaneous determination of mixtures containing two components with overlapping spectra. For each of the following, determine the molar concentration of each analyte in the mixture. 

If a standard method is available, the performance of a new method can be evaluated by comparing results with those obtained with an approved standard method. The comparison should be done at a minimum of three concentrations to evaluate the applicability of the new method for different amounts of analyte. Alternatively, we can plot the results obtained by the new method against those obtained by the approved standard method. A linear regression analysis should give a slope of 1 and ay-intercept of 0 if the results of the two methods are equivalent. 

Bates DM, Watts DG. Nonlinear regression analysis and applications, New York, Wiley, 1988. 

Bates, D.M. and Watts. D.G., 1991, Nonlinear Regression Analysis and its Applications , J.Wiley, New York. 

The total residual sum of squares, taken over all elements of E, achieves its minimum when each column Cj separately has minimum sum of squares. The latter occurs if each (univariate) column of Y is fitted by X in the least-squares way. Consequently, the least-squares minimization of E is obtained if each separate dependent variable is fitted by multiple regression on X. In other words the multivariate regression analysis is essentially identical to a set of univariate regressions. Thus, from a methodological point of view nothing new is added and we may refer to Chapter 10 for a more thorough discussion of theory and application of multiple regression. 

R. F. Gunst and R.L. Mason, Regression Analysis and its Application A Data-Oriented Approach. Marcel Dekker, New York, 1980. 

Belohlav, Z., P. Zamostny, P. Kluson, and J. Volf, "Application of Random-Search Algorithm for Regression Analysis of Catalytic Hydrogenations", CanJ. Chem. Eng., 75, 735-742 (1997). 

Regression analysis comparing the number of days from spraying to analysis and the parathion spray residue show no significant relationship. The difference in parathion residue due to the 1/r, W, and y4-pound applications was not significant. All residues were only a fraction of 1 p.p.m. 

The relationship between average ADFR and application rate (AR) was tested using linear regression analysis and the model ADFR = a + b AR. All data concerning high-volume applications (n = 8) and low-volume applications (n = 4) were used, separately or together. The results of these regression analyses are presented in Table 2. 

This classification of bonds allowed the application of logistic regression analysis (LoRA), which proved of particular benefit for arriving at a function quantifying chemical reactivity. In this method, the binary classification (breakable or non-breakable, represented by 1/0, respectively) is taken as an initial probability P0, which is modelled by the following functional dependence (Eqs. 7 and 8) where f is a linear function, and x. are the parameters considered to be relevant to the problem. The coefficients c. are determined to maximize the fit of the calculated probability of breaking (P) as closely as possible to the initial classification (P0). 

Bates, D. M. and D. G. Watts. Nonlinear Regression Analysis and Its Applications. Wiley, New York (1988). 

Without having conducted a full elasticity analysis across the entire portfolio, the analysis helps to prove market perceptions such as a higher elasticity exist in one market compared to another market or comparing elasticity between products being perceived to have a different elasticity. The statistical quality of the linear regression analysis in selected months is considered as good in terms of the number of customers involved and the R-squared value proving the applicability of the approach. 

Sen, A. Srivastava, M. (1990). Regression Analysis. Theory, Methods, and Applications. New York Springer-Verlag. 

Sparks (1989) discusses the application of various kinetic equations to earth materials based on the analysis of a large number of reported studies. Even though different equations describe rate data satisfactorily. Sparks (1989) uses hnear regression analysis to show that no single equation best describes every study. 

At this point it was clear that the highest potential for increased activity was by substitution in the 2-position of the biphenyl alcohol. We prepared the sequence of compounds shown in Table 1. Substituents were again chosen to maximize the parameter space covered within the relatively stringent synthetic limitations of the biphenyl substitution pattern. The application of regression analysis to the data for these compounds provided no clear relationship between structure and activity when the parameters in our standard data base were used. The best linear fit was found for B4, the STERIMOL maximum radius. However, the correlation coefficient was only 0.625. 

To test the applicability of statistical techniques for determination of the species contributions to the scattering coefficient, a one-year study was conducted in 1979 at China Lake, California. Filter samples of aerosol particles smaller than 2 ym aerodynamic diameter were analyzed for total fine mass, major chemical species, and the time average particle absorption coefficient, bg. At the same time and location, bgp was measured with a sensitive nephelometer. A total of 61 samples were analyzed. Multiple regression analysis was applied to the average particle scattering coefficient and mass concentrations for each filter sample to estimate aj and each species contribution to light scattering, bgn-j. Supplementary measurements of the chemical-size distribution were used for theoretical estimates of each b pj as a test of the effectiveness of the statistical approach. 

Principles and Applications of Partial Least Squares (PLS) Regression Analysis... 

The statistical methods available make use of the pattern and magnitude of the differences among our experimental results, to tell us what is the chance of being wrong in drawing certain conclusions. There are many techniques available, but by far the majority of applications in chemical experimentation may best be treated by analysis of variance and regression analysis. 

The main application for computers in statistical calculations has been in the field of correlation studies. The technique of multiple-regression analysis is now widely used to examine the effects of one or more independent variables on a dependent variable. This important statistical... 

---