Comparison of correlation coefficient

Comparison of Correlation Coefficient (r) and the Standard Deviation of Calibration Data ... 

When using SC-CSRS 300, the response at varying concentrations is linear, because the analyte is detected as totally dissociated methanesulfonic acid. Figure 4.49 shows the linear calibration plots for ammonium, comparing SC-CSRS 300 with the conventional CSRS 300 over three orders of magnitude (0.1-100 mg/L). Table 4.6 lists the comparison of correlation coefficients for... 

In the case of sugars, which are largely employed in the pharmaceutical field as lyoprotectants for the formulation of proteins used as drugs, it was found that FT-IR spectra of lipase BC co-lyophilized with these additives are more similar to that of lipase BC lyophilized without sugars than to that of the enzyme in water (the comparison of spectra was done on the basis of correlation coefficients between the infrared amide I band) [14]. An analysis of the relative area of the... 

Figure 17.37. Some measured and predicted values of heat transfer coefficients in fluidized beds. 1 Btu/hr(sqft) (°F) = 4.88kcal/(hr)(m )(°C) = 5.678 W/(m )(°C). (a) Comparison of correlations for heat transfer from silica sand with particle size 0.15 mm dia fluidized in air. Conditions are identified in Table 17.19 (Leva, 1959). (b) Wall heat transfer coefficients as function of the superficial fluid velocity, data of Varygin and Martyushin. Particle sizes in microns (1) ferrosilicon, d = 82.5 (2) hematite, d = 173 (3) carborundum, d = 137 (4) quartz sand, d = 140 (5) quartz sand, d = 198 (6) quartz sand, d = 216 (7) quartz sand, d = 428 (8) quartz sand, d = 5 5 (9) quartz sand, d = 650 (10) quartz sand, d = lllO (11) glass spheres, d = 1160. (Zabrodsky et al, 1976, Fig. 10.17). (c) Effect of air velocity and particle physical properties on heat transfer between a fluidized bed and a submerged coil. Mean particle diameter 0.38 mm (I) BAV catalyst (II) iron-chromium catalyst (III) silica gel (IV) quartz (V) marble (Zabrodsky et al., 1976, Fig. 10.20).

Figure 3.15 Comparison of correlations for Z°. The virial-coefficient correlation is representedby the straight lines the Lee/Kesler correlation, by the points. In the region above the dashed line the two correlations differ by less than 2%...

Comparison of full spectra can be achieved by applying correlation or similarity measures. In the case of correlation, the coefficient of correlation between the spectra to be compared is computed (cf. Eq. (5.12)). Ranking the comparisons by the size of correlation coefficients, Table 7.10 provides a hit list that describes the quality of comparison between the unknown and the candidate Ubrary spectrum. In principle, the spectrum with the highest correlation coefficient is the sought-for spectrum. In order to ensure that a certain degree of similarity is reached for the top spectrum of the hit Ust, a threshold for assigning the library spectrum should be specified. 

A comparison of the coefficient of friction with the amount of solvent molecules absorbed in the brushUke structure of PLL-g-PEG is shown in Figiue 6. A strong correlation between coefficient of friction and solvation is observed for both symmetric and asymmetric tri-bointerfaces i.e., the higher the solvation, the lower the coefficient of friction. 

G2(MP2) and G3 levels and were compared with calorimetric measurements [99JOC9328]. Within this comparison, a correlation coefficient of r = 0.9998 and a standard deviation of 0.7 kcal/mol have been obtained for a series of 10 molecules. 

A number of correlation coefficients with droplet concentration and flow entities as input are summarized in Table 19.6. For better comparison, the values on the spray axis have been averaged and the rms value is also calculated. Generally, the correlation values are not higher than 0.3 which means that the droplet concentration is poorly correlated with other flow variables. 

Comparison of Models Only scattered and inconclusive results have been obtained by calculation of the relative performances of the different models as converiers. Both the RTD and the dispersion coefficient require tracer tests for their accurate determination, so neither method can be said to be easier to apply The exception is when one of the cited correlations of Peclet numbers in terms of other groups can be used, although they are rough. The tanks-in-series model, however, provides a mechanism that is readily visualized and is therefore popular. 

Comparisons (49) of measured concentrations of SFg tracer released from a 36-m stack, and those estimated by the PTMPT model for 133 data pairs over PasquiU stabilities varying from B through F, had a linear correlation coefficient of 0.81. Here 89% of the estimated values were within a factor of 3 of the measured concentrations. The calculations were most sensitive to the selection of stability class. Changing the stability classification by one varies the concentration by a factor of 2 to 4. 

Kresge et a/.498 have drawn attention to the fact that detritiation of [3H]-2,4,6-trihydroxy- and [3H]-2,4,6-trimethoxy-benzenes by concentrated aqueous perchloric acid gives correlations of log rate coefficient with — H0 with slopes of 0.80 and 1.14 respectively. Protonation to give the carbon conjugate acids is, however, governed by h0lA0 and h0l 9S, respectively, which suggests that the difference in kinetic acidity dependence is a property of the substrate and should not be interpreted as a major difference in mechanism. The kinetic difference can be eliminated by an appropriate comparison of kinetic and equilibrium acidity dependencies. In equation (230)... 

New questions have arisen in micro-scale flow and heat transfer. The review by Gad-el-Hak (1999) focused on the physical aspect of the breakdown of the Navier-Stokes equations. Mehendale et al. (1999) concluded that since the heat transfer coefficients were based on the inlet and/or outlet fluid temperatures, rather than on the bulk temperatures in almost all studies, comparison of conventional correlations is problematic. Palm (2001) also suggested several possible explanations for the deviations of micro-scale single-phase heat transfer from convectional theory, including surface roughness and entrance effects. 

Fig. 6.32 Comparison of heat transfer coefficient data for R-134s and water with predictions based on Lee and Mudawar correlation. Reprinted from Lee and Mudawar (2005b) with permission...

When comparisons are to be drawn among scales derived with different criteria of physical validity, we believe this point to be especially appropriate. The SD is the explicit variable in the least-squares procedure, after all, while the correlation coefficient is a derivative providing at best a non linear acceptability scale, with good and bad correlations often crowded in the range. 9-1.0. The present work further provides strong confirmation of this conclusion. 

This equation describes the series of lines in Figure 5, the variable parameter being represented by The physical meaning of coefficients aj follows from comparison of eqs.(17), (18) and (19) ao equals logAo and ai=-Eo/ 2.303 RT, the subscripts 0 referring to the standard substituent, az =p ,at the infinite temperature, and as = -/3pco. Hence, 0 is obtained as -aj/a2. Direct correlations of AH and AS with a (176, 197, 198) or other parameters (199, 200) are usually bad and cannot serve to obtain the AH/AS relationship. 

FIGURE 26.42 Comparison of the correlation coefficients between laboratory side force measurements with the six compounds of Table 26.2 on wet, blunt Alumina 180 and a concrete road test track as function of log ajv and log v (left) with function of temperature and log v (right). 

The molecular diffusion coefficients in hquid phase can be estimated from the correlations of WiUce and Chang [47] for organic solutions and Hayduk and Minhas [48] for aqueous solutions, respectively. An extensive comparison of the available correlations is provided by Wild and Charpentier [49]. 

Since the widely accepted in vitro permeability model in the pharmaceutical industry is based on the use of cultured cells, such as Caco-2 or MDCK, it was appropriate to analyze the regression correlation coefficients based on the comparisons of Caco-2 log Pe and the log Pe values based on the human jejunal measurements [56]. 

Experimental conditions and initial rates of oxidation are summarized in Table V. For comparison, initial rates of dry oxidation at the same temperature and pressure of oxygen predicted by Equation 9 are included in parentheses. The predicted dry rate, measured dry rate, and measured wet rates are compared in Figure 2. The logarithms of the initial rates of heat production during wet oxidation increase approximately linearly (correlation coefficient = 0.92) with the logarithm of the partial pressure of oxygen and lead to values of In k = 2.5 and r = 0.9, as compared with values of In k = 4.8 and r = 0.6 for dry oxidation at this temperature. 

---