Family plot regression

However, the derivation of Equation 16 failed to take into account the free-volume ("structural") contribution to xy"(35), nor is the effect negligible with some polymer phases (36). In addition, there remains considerable doubt even as to what constitutes a "family" set of data e.g., with polymers that are liquid-crystalline. The characterization of polymer stationary phases via family-plot regressions of "inverse" gas-chromatographic retentions therefore invites further and comprehensive study. 

Published activation parameters, for the radical forming decompositions of the families of initiators, were used to calculate the temperatures at which members of the four reactions react at one- hour and at ten-hour half lives. For a given family of initiators, at a given decomposition rate, the experimental temperatures were plotted by linear regression against the calculated AE(jr) values for the R products of the rate determining step ... 

Equation 13 is the empirical relationship obtained by the linear regression between D/T and terminal pumping numbers (4). It is important to note that a family of curves exists for each D/T ratio when Nq (pumping number) is plotted versus the impeller Reynolds number (5). In the turbulent range (iVRe > 2000), the Nq curves flatten out and thus are independent of the Reynolds number. 

The regression equation has been obtained by plotting standard enthalpy and entropy data of 271 independent experiments performed on 16 different membrane receptor systems belonging to the GPCR and LGICR families. The equation was ... 

Figure 4. Plots of family-regression slopes against % phenyl content for n-hexane (filled circles) and benzene (open circles) with OV stationary phases at 30-80°C.

The WA plot is shown in Figure 13.8 for the stabilized-zirconia powder of Figure 13.7 In(Ai) is plotted as a function of for three reflections of the (0//) family, (Oil), (022) and (033). According to Equation (18), from the intercept and slope of the regression lines, respectively, size Fourier coefficients and microstrain can be obtained for different Fourier lengths, L. 

In the case of 28, Fig. 21 b shows how the data points for the three families of solvents are combined around a single regression line when i (28)niax is plotted against (rr -I- d5), d = -0.231. The correlation equation becomes... 

Table 10.10 lists the data for the regression analysis and, as before, gives the values of the constants in Eq. (10.23) plus the calculated concentrations. The standard deviation in this instance was 0.0035%. The limits of the correction curves are plotted in Fig. 10.12 using the value of the slope and the maximum and minimum background values. The shape of the correction curve looks far more reasonable in this instance, since indeed one would theoretically predict a family of parallel curves. Not so reasonable, however, is the correlation between x-ray and chemical values shown in Fig. 10.13. The scatter of points in this case is certainly not distributed evenly along the 1 1 relationship, and in fact all x-ray data are within 0.0026 of the mean of0.352%. In other words, this method yields approximately the same result in every case, irrespective of the arsenic concentration. 

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