Methyl regression equations

We have also correlated rate constants for the reaction of 3- or 4-substituted N,N-dimethylanilines with methyl iodide, 3- or 4-substituted benzoic acids with diphenyldia-zomethane and 3- or 4-substituted benzoyl chlorides with aniline with the MYT equation. The best regression equations obtained are ... 

The same method has been applied to the iododealkylation of Ak1SnAk2 with Ak2 equal to Me or Et. Again, f was defined as log k2 for the methyl group. Correlation of the data set with equation 25 gave regression equation 27 ... 

The regression equation constants found from enthalpy-of-formation data for the 1-chloro31a and l-iodoalkanes31b, and the 2-methyl-2-chloroalkanes are close enough to those generated from direct enthalpy-of-vaporization measurements to conclude that the selected values are reasonably accurate, at least with respect to their differences. 

Methyl Salicylate and Ethyl Salicylate Linear Regression Equations... 

Finally, as an example involving an N-H acid, limiting F nmr shifts. A, of 5-fluoroindole (22) with HBA bases in CCI4 (relative to N-methyl-5-fluo-roindole internal standard), as reported by Mitsky, Joris, and Taft (146), are also nicely linear with 8. The regression equation for 14 bases (3,13,23,24,25,26,29,41,48,70,72,75,83,84, plus one zero-zero point for neat CCI4) is... 

Both simple linear regression (SLR) and PLS equations were tested for accuracy and precision. The SEP values for methyl oleate, glucose, glutamate, and ammonium were, respectively, 0.65 (and 0.68, 0.57 three models), 1.35, 0.61, and 0.016. For an immensely complex system, these values are outstanding. 

To verify such a steric effect a quantitative structure-property relationship study (QSPR) on a series of distinct solute-selector pairs, namely various DNB-amino acid/quinine carbamate CSPpairs with different carbamate residues (Rso) and distinct amino acid residues (Rsa), has been set up [59], To provide a quantitative measure of the effect of the steric bulkiness on the separation factors within this solute-selector series, a-values were correlated by multiple linear and nonlinear regression analysis with the Taft s steric parameter Es that represents a quantitative estimation of the steric bulkiness of a substituent (Note s,sa indicates the independent variable describing the bulkiness of the amino acid residue and i s.so that of the carbamate residue). For example, the steric bulkiness increases in the order methyl < ethyl < n-propyl < n-butyl < i-propyl < cyclohexyl < -butyl < iec.-butyl < t-butyl < 1-adamantyl < phenyl < trityl and simultaneously, the s drops from -1.24 to -6.03. In other words, the smaller the Es, the more bulky is the substituent. The obtained QSPR equation reads as follows ... 

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. ... 

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. ... 

Figure 5.29 illustrates the pH-rate constant profile for the hydrolysis of L-phenylalanine methyl ester (weak base, pKa = 7.11) at 25°C. When attempts are made to simulate the experimental data with Equation (5.167) over a wide range of pH values, the model seldom fits well, because the values of kobs differ by several orders of magnitude and nonlinear regression analysis does not converge. Therefore, it is recommended that the kinetic values be within less than a few orders of magnitude. A localized and stepwise simulation process is recommended. At very low or high pH, Equation (5.167) simplifies to... 

Cerveny et al. (7J) report hydrogenation of nine olefinic substrates (1-hexene, ethyl acrylate, allyl phenyl ether, allylbenzene, 3-butene-l-ol, 2-butene-l-ol, 3-butene-2-ol, 2-methyl-2-propene-l-ol, l-heptene-4-ol) in seven solvents (cyclohexane, diethyl ether, toluene, methanol, benzene, ethyl acetate, and 1,4-dioxane) on 5% Pt on silica gel. No linear relation could be proved for any of the substrates when Eq. (21) was applied to the set of data obtained in the hydrogenations. In all cases correlation points for benzene and toluene did not fit. On omitting these points, experimental data satisfied Eq. (21), but linear regression gave a nonzero absolute term q on the righthand side of the equation ... 

We have determined LD50 values of 28 BP analogs for the housefly by injection after pretreatment with pb. The most toxic compound was 3-methyl-4-n-propyl BP (compound 3). Their toxicity was greatly dependent on the nature of the bridgehead substituent. The following equation has been derived by multiple regression analysis of some of those synergized toxicity data for a series of 4-substituted BPs (jJ) ... 

Figure 8.15 Examples of GC/EIMS calibration curves that are nonlinear as a result of cross-contributions between the analyte (butalbital) and SIS (butalbital-D5), both as the methylated derivatives. The SIS was present in all calibration solutions at a concentration of 200 ng mL . The mjz values (all for fragment ions) monitored were (a) analyte 196, SIS 201 (b) analyte 138, SIS 143. See main text for data on cross-contributions. In both cases the curves represent nonlinear least-squares regression fits of the data to Equation [8.89], accounting for cross-contributions in both directions. Reproduced from Whiting, /. Anal. Toxicol. 25, 179 (2001), with permission of Preston Publications, A Division of Preston Industries, Inc.

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