Mono-Linear Regression

The mono- and di-substituted benzenes, for which the relative swelling power (C as defined in Eq. 14) have been determined thus far, are listed in Tables 2-4. In every case the volume (S) of sorbed liquid per gram of polymer increased linearly with X1/3 as noted in Figs. 9-11, and the square of the correlation coefficient (r) to the line of best fit, determined by linear regression analysis of the set of six S-data points, was in every case r2 > 0.99, and q13 was equal to 1.84 0.09. The corresponding C and oc (calculated therefrom Eq. 15) are also collected in Tables 2-4. These data show clearly that the value a = 2.50 for benzene is greater than that for any benzene derivative listed therein. Any substituent in place of... 

Reciprocal plots (Equation 16) of the experimental data for mono-layers in the expanded state yielded linear regression equations. Representative plots are in Figure 8. Slope and intercept data from regression equations were used to calculate the apparent surface pKa of the fatty acid in the monolayer. These pKa values are tabulated in Table I. The apparent surface pKa was several pH units above the pKa of carboxylic acids dissolved in solution. Thus desorption kinetics generated data for... 

With this equation, it was possible to describe the acid dependences of Dw found for the different mono- and divalent cations studied, within the limits of the approximations introduced. The extraction constants K were obtained as the constant term of the linear regression analysis of the extraction data performed using Eq. (27) in the form ... 

Results of linear regression analyses of the observed toxicities (pTmp) on the toxicities (pTm ) of the corresponding mono-substituted benzene derivaties data given in TABLE 1. 

Figure . PlotoflogkNOM(Eq-3-9) versus [El (ArN02)/0.059 V] for the mono-substituted nitrobenzenes listed in Table 4 in aqueous solutions of Hyde County NOM at pH 7.5 and 5 mM H2S. The regression line log kNOM = 1-0 [EA (ArN02)/0.059 V] + 4.4 is the result of a linear least-squares fit of Eq. 3-8 to the data set given in Table 4. The half-lives indicated on the right-hand side are calculated for an aqueous solution containing 1 mg C/liter of Hyde County NOM adapted from (11).

It finely recovers the basic mono-regression correlation results of Eq. (2.28) and (2.29), thus confirming the validity of the multi-linear matrix formalism reliability nevertheless, it becomes ciunbersome in analytical terms for higher regression forms, for which the actual Spectral-SAR or Spectral-Diagonal SAR successfully overcome, see Chapter 3 of the present volume. For the moment, we go further with the statistical basics analysis. 

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