Regression analysis between methods

Principal component analysis (PCA) of the soil physico-chemical or the antibiotic resistance data set was performed with the SPSS software. Before PCA, the row MPN values were log-ratio transformed (ter Braak and Smilauer 1998) each MPN was logio -transformed, then, divided by sum of the 16 log-transformed values. Simple linear regression analysis between scores on PCs based on the antibiotic resistance profiles and the soil physico-chemical characteristics was also performed using the SPSS software. To find the PCs that significantly explain variation of SFI or SEF value, multiple regression analysis between SFI or SEF values and PC scores was also performed using the SPSS software. The stepwise method at the default criteria (p=0.05 for inclusion and 0.10 for removal) was chosen. 

Passing and Bablok regression analysis between the methods resulted in biases as predicted in AB agreement (Table 5). The CIs of the intercepts and the slopes did not overlap between the comparison instruments. It can be concluded that although a statistical difference was detected, this was not clinically significant either. Lab A previously reported a therapeutic range of 0.8-1.2 mmol/1, and Lab C a range of 0.5-1.5 mmol/1 with their patient results. Thus, accord-... 

Correlation gas chromatography is an indirect method to determine the enthalpies of vaporization of both solids and liquids [99]. The quantity directly measured is the enthalpy of transference from the condensed state in the column to the gas state. The enthalpy of vaporization is obtained by using the equation obtained by regression analysis between the enthalpies of transference and the... 

Multiple linear regression analysis is a widely used method, in this case assuming that a linear relationship exists between solubility and the 18 input variables. The multilinear regression analy.si.s was performed by the SPSS program [30]. The training set was used to build a model, and the test set was used for the prediction of solubility. The MLRA model provided, for the training set, a correlation coefficient r = 0.92 and a standard deviation of, s = 0,78, and for the test set, r = 0.94 and s = 0.68. 

If the rate law depends on the concentration of more than one component, and it is not possible to use the method of one component being in excess, a linearized least squares method can be used. The purpose of regression analysis is to determine a functional relationship between the dependent variable (e.g., the reaction rate) and the various independent variables (e.g., the concentrations). 

Miller first used Eq. (7-41) to correlate multiple variations, and this approach has more recently been subjected to considerable development. Many cross-interaction constants have been evaluated multiple regression analysis is one technique, but Miller and Dubois et ah discuss other methods. Lee et al. consider Pxy to be a measure of the distance between groups x and y in the transition state... 

We now consider a type of analysis in which the data (which may consist of solvent properties or of solvent effects on rates, equilibria, and spectra) again are expressed as a linear combination of products as in Eq. (8-81), but now the statistical treatment yields estimates of both a, and jc,. This method is called principal component analysis or factor analysis. A key difference between multiple linear regression analysis and principal component analysis (in the chemical setting) is that regression analysis adopts chemical models a priori, whereas in factor analysis the chemical significance of the factors emerges (if desired) as a result of the analysis. We will not explore the statistical procedure, but will cite some results. We have already encountered examples in Section 8.2 on the classification of solvents and in the present section in the form of the Swain et al. treatment leading to Eq. (8-74). 

Beilken et al. [ 12] have applied a number of instrumental measuring methods to assess the mechanical strength of 12 different meat patties. In all, 20 different physical/chemical properties were measured. The products were tasted twice by 12 panellists divided over 4 sessions in which 6 products were evaluated for 9 textural attributes (rubberiness, chewiness, juiciness, etc.). Beilken etal. [12] subjected the two sets of data, viz. the instrumental data and the sensory data, to separate principal component analyses. The relation between the two data sets, mechanical measurements versus sensory attributes, was studied by their intercorrelations. Although useful information can be derived from such bivariate indicators, a truly multivariate regression analysis may give a simpler overall picture of the relation. 

Statistical method to model a mathematical equation that describes the relationship between random variables (usually x and y). The goal of regression analysis is both modelling and predicting. 

Walash et al. [14] described a kinetic spectrophotometric method for determination of several sulfur containing compounds including penicillamine. The method is based on the catalytic effect on the reaction between sodium azide and iodine in aqueous solution, and entails measuring the decrease in the absorbance of iodine at 348 nm by a fixed time method. Regression analysis of the Beer s law plot showed a linear graph over the range of 0.01 0.1 pg/mL for penicillamine with a detection limit of 0.0094 pg/mL. 

Fu et al. [16] analyzed a set of 57 compounds previously used by Lombardo and other workers also. Their molecular geometries were optimized using the semiempirical self-consistent field molecular orbital calculation AMI method. Polar molecular surface areas and molecular volumes were calculated by the Monte Carlo method. The stepwise multiple regression analysis was used to obtain the correlation equations between the log BB values of the training set compounds and their structural parameters. The following model was generated after removing one outlier (Eq. 50) ... 

Figure 12 shows the classical method of obtaining the Mark-Houwink coefficients, K and a, by plotting the log [n](v) vs. log M(v) for this polymer in THF at 50°C. The data points used for the plot in Figure 12 are indicated by the area between the arrows in Figure 10. Linear regression analysis of the data resulted in K o =1.86x10" and a o =0.662 with a correlation coefficient or t =u.9996 for NBS 70o polystyrene.

The first work on pKa determination by zone electrophoresis using paper strips was described by Waldron-Edward in 1965 (15). Also, Kiso et al. in 1968 showed the relationship between pH, mobility, and p/C, using a hyperbolic tangent function (16). Unfortunately, these methods had not been widely accepted because of the manual operation and lower reproducibility of the paper electrophoresis format. The automated capillary electrophoresis (CE) instrument allows rapid and accurate pKa determination. Beckers et al. showed that thermodynamic pATt, (pATf) and absolute ionic mobility values of several monovalent weak acids were determined accurately using effective mobility and activity at two pH points (17). Cai et al. reported pKa values of two monovalent weak bases and p-aminobenzoic acid (18). Cleveland et al. established the thermodynamic pKa determination method using nonlinear regression analysis for monovalent compounds (19). We derived the general equation and applied it to multivalent compounds (20). Until then, there were many reports on pKa determination by CE for cephalosporins (21), sulfonated azo-dyes (22), ropinirole and its impurities (23), cyto-kinins (24), and so on. 

A relatively recent development in QSAR research is molecular reference (MOLREF). This molecular modelling technique is a method that compares the structures of any number of test molecules with a reference molecule, in a quantitative structure-activity relationship study (27). Partial least squares regression analysis was used in molecular reference to analyse the relation between X- and Y-matrices. In this paper, forty-two disubstituted benzene compounds were tested for toxicity to Daphnia... 

Blair et al. (1998) performed a retrospective cohort mortality study of 14 457 workers employed for at least one year between 1952 and 1956 at an aircraft maintenance facility in the United States. Among this cohort were 6737 workers who had been exposed to carbon tetrachloride (Stewart et al., 1991). The methods used for this study are described in greater detail in the monograph on dichloromethane. An extensive exposure assessment was performed to classify exposure to trichloroethylene quantitatively and to classify exposure (ever/never) to other chemicals qualitatively (Stewart et al., 1991). Risks from chemicals other than trichloroethylene w ere examined in a Poisson regression analysis of cancer incidence data. Among women, exposure to carbon tetrachloride was associated with an increased risk of non-Hodgkin lymphoma (relative risk (RR), 3.3 95% CI,... 

Briefly, the method involves determining the capacity factors (retention time corrected for an unretained substance) for a suitable set of reference substances (having known K(k values) using RP-HPLC. The relationship between the capacity factors and Kol for the reference or calibration compounds is determined from regression analysis of a log-log plot of the two properties. The capacity factors of compounds having unknown Koc values then are determined using the identical experimental conditions, and Koc values then are calculated from the regression expression. 

Algebraic expressions for terms M and C were derived using Dewar s PMO method (for C in a version similar to the co-technique [57] in order to calculate carbocation stabilization energies). The size factor S is simply a cubic function of the number of carbon atoms [97], The three independent variables of the model were assumed to be linearly related to the experimental Iball indices (vide supra). By multilinear regression analysis (sample size = 26) an equation was derived for calculating Iball indices from the three theoretical parameters. The correlation coefficient for the linear relation between calculated and experimental Iball indices is r = 0.961. 

Two procedures were tested in developing a method for measuring blood flow. Based on obtained results determine whether there exists linear correlation between the procedures, and if there is, give the linear regression analysis of variance. 

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