Regression analysis of the

Although this experiment is written as a dry-lab, it can be adapted to the laboratory. Details are given for the determination of the equilibrium constant for the binding of the Lewis base 1-methylimidazole to the Lewis acid cobalt(II)4-trifluoromethyl-o-phenylene-4,6-methoxysalicylideniminate in toluene. The equilibrium constant is found by a linear regression analysis of the absorbance data to a theoretical equilibrium model. 

Regression analysis of the results gave Eqs. 11 and 12 fora- and P-cyclodextrin systems respectively. 

On the basis of regression analysis of the initial rate data obtained for both isolated reactions (Vila) and (Vllb) and for each of the three reactions proceeding in the coupled system [reactions (Vlla)-(VIIc)], of the set of twenty-five equations, the best equation was always found to be of the... 

Other data support the above picture. Hexanol adsorbs very weakly on Ag(l 10), more weakly than expected, and in any case less than on the (100) face.440 Such a poor adsorption on (110) faces has been explained in terms of steric hindrance caused by the superficial rails of atoms. Consistently, adsorption on the (110) face of Cu is vanishing small.587 Predictions based on a linear regression analysis of the data for pentanol (nine metals) give a value of-12 kJ mol 1 for Cu(l 10) and about -16 kJ mol 1 for Au(110). No data are available for polycrystalline Au, but Au(l 11) is placed in the correct position in the adsorption of hexanol.910 Thus, these data confirm the hydrophilicity sequence Hg < Au < Ag and the crystal face sequence for fee metals (111) < (100) < (110). 

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. 

When pressure is applied to the latex, the UCFT is seen to move to higher temperatures as indicated in Figure 2. It was found that the PMMA latex stabilized by PIB of Mn - 2 x lCrcould be fitted to the same curve as the PVAc latex stabilized by PIB of Mjj 4 x 10. A linear regression analysis of the UCFT as a function of applied pressure gave ... 

Time scaling 2.73 ppmx60 min=163.8 ppm-min C1xt=k (ten Berge et al. 1986) (27.3 ppm)1 60 min=163.8 ppm-min regression analysis of the squirrel monkey lethality data suggested a near linear... 

Two data sets of LC50 values for different time periods of exposure were analyzed using a linear regression analysis of the log-log transformation of a plot of C vs t to derive values of n for monomethylhydrazine. 

Table 15. Multiple regression analysis of the immune system parameters and metal contents in hair (Evstafyeva et al., 2004).

When data are lacking for desired exposure times, scaling across time may be based on the relationship between concentration and exposure duration (Cn xt=k) when a common end point is used (ten Berge et al. 1986). The end points for HCN are incapacitation and lethality. Regression analysis of the data of Sakurai (1989), using incapacitation concentrations for mice for the exposure durations of 5, 10, 20, and 30 min, results in a value for n of 1.6. Regression analysis of the incapacitation data of Purser et al. (1984) for monkeys for the time period of 8 to 19 min results in a value for n of 2.1 (Appendix A, Figure A-l). These studies were of relatively short duration. 

The modeling results showed that for the materials studied, the minimum melt superheat ranges from 0.005 Tm to 0.19Tm, depending on process parameters and material properties. The dependence is quantitatively expressed in a correlation derived from a regression analysis of the numerical results ... 

The DSC exothermic peaks can be used to obtain Xc(tmax) from /max. Figures 20.24 and 20.25 illustrate the linear regression analysis of the... 

When a variable with the values EPC = 1, IPC = 0 is entered into a multiple regression analysis of the number of sperm in the first copulatory sample produced by each couple, it has a regression coefficient significantly different from zero. As soon as hours since last ejaculation is entered into the equation, however, the EPC variable loses significance, suggesting that the reduced number of sperm in EPC ejaculates may be linked to the fact that EPCs may often be preceded by a more recent ejaculation than other ejaculations. 

Similar plots have been obtained for the gas-phase rearrangement of 35 (A = CH3 Aik = ethyl Alk = methyl) and 36 (A = CH3 Aik = methyl Alk = ethyl) in 720 torr methyl chloride in the temperature range from 40 to 120 Regression analysis of the relevant Arrhenius curves leads to the activation parameters listed in Table 22. 

Fig. 6.13 Measurement of FAC data for a range of pyrimethamine concentrations applied to sol-gel-entrapped dehydrofolate reductase (A) overlay of breakthrough curves and (B) nonlinear regression analysis of the fit to the measured breakthrough volumes from A [28]. Adapted with permission from the American Chemical Society.

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.

Pihlaja and Rossi [83ACSA(B)289] prepared l,3-dioxan-2-one and all of its methyl derivatives, recorded their C NMR spectra, and derived the methyl substituent shift parameters by a multiple linear regression analysis of the anancomeric and two equivalent chair conformers (Table X). With these values, the authors estimated the conformational equilibria for two unequally populated chair conformations (Nos. 2, 3, 9, 11, and 14 in Table X). A consistent picture of the predominance of the chair conformation and the corresponding chair chair equilibria in l,3-dioxan-2-ones was obtained in complete agreement with earlier H NMR results. 

Inhibition of enzyme activity by a chemical species that binds slowly and is tight-binding as well has a low dissociation constant). Such inhibitors require special kinetic analysis . The most common method of obtaining the inhibition parameters is by nonlinear regression analysis of the progress curves. 

The enthalpy of formation of methyl n-pentyl ether is unavailable from experiment, but a value of —316 kJmoP is obtained from the linear regression analysis of the known enthalpies of formation of methyl n-alkyl ethers vs. the number of carbon atoms in the ethers . The methylene increment of —25.3 kJmoP for this homologous ether series is nearly identical to the methylene increment for n-alkanes. Because the experimental protodelithiation enthalpies for the two primary lithio ethers are identical, the methylene increment in that homologous series as calculated here is necessarily identical to that of the homologous methoxy ethers. As calculated from the methylene increment or from equation 16, the enthalpy of formation of 5-lithiopentyl methyl ether is ca —309 kJmol. ... 

Regression analysis of the pH-metric mobility data to obtain pKa. 

There are liquid enthalpy of formation values for the methyl ethers for R = Me, -Pr, w-Bu and w-decyl. Additional enthalpies can be extrapolated for the R = Et and w-Pen species from the linear regression analysis of the enthalpies of formation vs. number of carbons . However, the regression constants from this same analysis immediately reveal that any assumption of thermoneutrality for equation 12 is incorrect. The slope of —25.3 0.1 kJmol for the methyl ethers is much too different from the slope for the peroxide series for there to be a constant difference between enthalpies of formation for two compounds with the same R substitution (the two alcohol enthalpies of formation in equation 12 are constant). As expected, the derived enthalpies of reaction for equation 12 increase with increasing number of carbons 13.9, 21.4, 24.0 and 25.6 kJmol. ... 

The three saturated long-chain tert-butyl peresters are members of a homologons series, and as such, the weighted least-squares regression analysis of the enthalpies of formation V5. number of carbons yields a methylene increment of —26.7 kJmol , a typical valne for liquids. The methylene increment for the terf-butyl esters of the Cg, Cjo, Cn and C14 acids is —28.0 kJmol. The closeness of these two values ensures that the enthalpies of formal reaction 16 will be nearly constant. For the three pairs from Table 3, the value is —70.3 8.1 kJmol. The standard deviation from the mean is quite large because the arithmetic difference for the C12 ester and perester, —79.5 kJmol, is quite a bit more negative than the differences for the Cio and C14 pairs, —64.4 and —66.9 kJmol, respectively. Unfortunately, the acids and esters are in different phases and so we are reluctant to attempt any comparison between them, such as a formal hydrolysis reaction or disproportionation with hydrogen peroxide. 

Equations 27 and 28 present the extension of the Szyszkowski-Langmuir model to the adsorption of one-surfactant systems with aggregation at the interface. For the formation of dimmers on the surface, n = 2 and Eqs. 27 and 28 can be expanded to obtain the Frumkin equation of adsorption state. In general, the surface aggregation model described by Eqs. 27 and 28 contains four free parameters, including coi, n, b and Fc, which can be obtained by regression analysis of the data for surface tension versus surfactant concentration in the solution. 

To achieve these various best fits, statistical methods are employed. A regression analysis of the effects of various substituents on a molecule using the Hansch approach... 

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