Empirical linear correlation analysis

Empirical linear correlation analysis has also produced results that may be used in predicting the rates of FeS-mediated pollutant transformation based on pollutant thermodynamic or molecular properties. One study (77) performed linear correlation analysis of log kohs values for 8 halogenated aliphatic molecules with five molecular properties one-electron reduction potentials, lowest unoccupied molecular orbital (LUMO) energies, fi ee energies of formation of aqueous phase radicals formed upon one-electron reduction, gas-phase homo-[ytic bond dissociation enthalpies, and aqueous solubilities. Of these parameters, homolytic bond dissociation enthalpies (7)r.x values) were best correlated with log obs values for FeS reductive dechlorination (R =0.82). The correlation between log obs and 7)r x is illustrated in Figure 4. Another parameter shown... 

The analysis of empirical links between the SA and the general concentration of ozone (GCO) has shown, that during all the active period of the Pinatubo volcano eruption, the coefficient of the linear correlation between SA and GCO was equal to r=0.87 0.07, while the reliability of the linear correlation was P=0.99. 

Differences in the Si MAS NMR shifts of framework silicon atoms located on crystallographically inequivalent T-sites are mainly caused by different local geometries of Si04 tetrahedra. Empirical correlations and theoretical considerations yielded that the Si NMR shifts, 65,-, of Si( wAl) units are linearly correlated with the mean value, a, of the four Si-O-T bond angles. With linear regression analysis, quantitative relationship between the values of 6si and d, sec a,sin (a/2) and cos a/(cos a-1) have been found [1,71-76]. For Si(4Al) units in sodalite,... 

Using the multi-variable linear regression analysis, the author developed empirical expressions for permeability in terms of porosity, specific surface area, and irreducible fluid saturation for four carbonate reservoir rock areas in the USSR. The coefficient of correlation varied from 0.981 to 0.997. 

The results were found to be sensitive to the choice of force field and atomic partial charges used in the simulations, but for the best tested parameters a reasonable correlation between experimental and computed amorphous solubilities was observed [40, 41]. It was shown in Ref. [41] that after reparameterization of the model and introducing an empirical relationship through linear regression analysis of experimental and calculated data = 2.04AG p), amorphous solubility could be... 

Having set the factual effects of liquid velocity, gas velocity and particle size on mass transfer coefficients and interfacial area for Hg -=84mm, correlations were attempted for these characteristic parameters by non-linear regression analysis of the experimental results. Empirical correlations in S.I. units,obtained for... 

The state of the structure of the polymeric material, which is defined by its formation mechanisms, always influences the properties of the indicated materials. Therefore the analysis fulfilled above has a purely applied interest as well. For confirmation of this postulate on Figure 9.4 the dependence of the elasticity modulus E of the considered EP on D p (such a form of the dependence E D ) was chosen for the purpose of its linearisation) is adduced. As one can see, the linear correlation between E and was obtained, described analytically by the following empirical equation [10] ... 

Calibration curve quality. Calibration curve quality is usually evaluated by statistical parameters, such as the correlation coefficient and standard error of estimate, and by empirical indexes, such as the length of the linear range. Using confidence band statistics, curve quality can be better described in terms of confidence band widths at several key concentrations. Other semi-quantitative indexes become redundant. Alternatively, the effects of curve quality can be incorporated into statements of sample analysis data quality. 

Those based on strictly empirical descriptions Mathematical models based on physical and cnemical laws (e.g., mass and energy balances, thermodynamics, chemical reaction kinetics) are frequently employed in optimization applications. These models are conceptually attractive because a general model for any system size can be developed before the system is constructed. On the other hand, an empirical model can be devised that simply correlates input/output data without any physiochemical analysis of the process. For these models, optimization is often used to fit a model to process data, using a procedure called parameter estimation. The well-known least squares curve-fitting procedure is based on optimization theory, assuming that the model parameters are contained linearly in the model. One example is the yield matrix, where the percentage yield of each product in a unit operation is estimated for each feed component... 

Another approach used in the empirical characterization of liquid polarity is the study of the outcome of a chemical reaction. Earle et al. [216] report a preliminary study of the keto-enol tautomerization of pentane-2,4-dione, and create an empirical correlation between the degree of tautomerization and the dielectric constant of molecular liquids. They then predict dielectric constants for a series of ILs based on the observed keto-enol equilibrium the values range from 40 to 50, slightly higher than those of short-chain alcohols. A more detailed study by Angelini et al. [217] considers the tautomerization of a nitroketone complex in a series of five imidazolium-based ILs. The results, parameterized as a linear free energy analysis of the behavior of the equilibrium constant, indicates an overall polarity comparable to that of acetonitrile, consistent with the partitioning and spectroscopic studies referenced above. 

An initial guess of keff can be obtained from moment analysis (Section 6.5.3.1) or empirical correlations. For peak injections in the linear range of the isotherm keff is calculated by Eq. 6.137 if the axial dispersion coefficient is already known (Section 6.5.6.2). Another rough estimation is based on the slope B of the simplified HETP curve (Eq. 6.141) ... 

Bergmann (1847) hrst noted that metabolic rate in mammals appeared to scale with mass to a 2/3 power. Rubner (1883) observed that heat production appeared to be more closely correlated with surface area than with mass, positing the widely cited Rubner s rule or surface law. Huxley (1932) advocated htting metabolic rate to a power function of mass, and based on the most extensive empirical analysis to date, Kleiber (1932) concluded that the exponent was 3/4. By mid-century we had the 3/4 rule. Surface area explanations of metabolic scaling were abandoned. For one thing, they required a 2/3 exponent (representing the linear dimension squared) that did not ht the data. In addition, metabolic rate scaled to body mass by a similar power function in ectotherms, for which the metabolic replacement of surface-mediated heat loss was not relevant. 

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