Correlation coefficients for

The correlation coefficient for this equation was 0.994. Such a paraboHc dependence of activity on the partition coefficient may reflect partitioning of the dmg through several membrane barriers, which enabled the dmg to reach its site of action. 

Color Difference Evaluation. Shade evaluation is comparable in importance to relative strength evaluation for dyes. This is of interest to both dye manufacturer and dye user for purposes of quaUty control. Objective evaluation of color differences is desirable because of the well-known variabihty of observers. A considerable number of color difference formulas that intend to transform the visually nonuniform International Commission on Illumination (CIE) tristimulus color space into a visually uniform space have been proposed over the years. Although many of them have proven to be of considerable practical value (Hunter Lab formula, Friele-MacAdam-Chickering (FMC) formula, Adams-Nickerson formula, etc), none has been found to be satisfactorily accurate for small color difference evaluation. Correlation coefficients for the correlation between average visually determined color difference values and those based on measurement and calculation with a formula are typically of a magnitude of approximately 0.7 or below. In the interest of uniformity of international usage, the CIE has proposed two color difference formulas (CIELAB and CIELUV) one of which (CIELAB) is particularly suitable for appHcation on textiles (see Color). 

An idea of the scale of turbulence can be obtained by measuring instantaneous values of velocities at two different points within the fluid and examining how the correlation coefficient for the two sets of values changes as the distance between the points is increased. 

VanArendonk, M. D., and Skogerboe, R. K., Correlation Coefficients for Evaluation of Analytical Calibration Curves, Anal. Chem. 53, 1981, 2349-2350. 

The slopes, Y-intercepts and squares of correlation coefficients for the linear regression analyses of the T versus AE(ir) plots (equation 7) for reactions 1-4 for one-hour and ten-hour half life rates of decomposition to form free radical products are given in Table II. 

If the T values of Table I are first fitted against EA values, without first fitting with EE(v) values, poor linea correlations result. For example, for tKe one-hour half-life temperatures of reactions 1 and 4, the squares of the correlation coefficients for these linear regression analyses are only 0.51 and 0.55, respectively. 

The kinetic parameters are listed in Table 1. The linearity of lnAr l/r plot is revealed by the correlation coefficient. For all reactions but the deactivation, the rate constants follow the Arrhenius law satisfactorily, implying catalyst deactivation may involve more than one elementary steps. 

Each of these data sets is skewed, yet each can be transformed to normality. With no transformation applied, the probability plot correlation coefficients for the Co, Fe, and Sc data sets are 0.855, 0.857, and 0.987, respectively. For Co and Fe, the hypothesis of normality is rejected at the 0.5 percent level (12). On the other hand, the maximum probability plot correlation coefficients are 0.993, 0.990, and 0.993 for Co, Fe, and Sc, respectively. The maxima occur at (X,t) (0,0.0048), (0,0.42), and (0.457,0), respectively. These maxima are so high that they provide no evidence that the range of transformations is inadequate. Note that the (, x) values at which the maxima occur correspond to log transformations with a shift for the Co and Fe and nearly a square-root transformation for the Sc. 

The mechanistic simulation ACAT model was modified to account automatically for the change in small intestinal and colon k as a function of the local (pH-dependent) log D of the drug molecule. The rank order of %HIA from GastroPlus was directly compared with rank order experimental %HIA with this correction for the log D of each molecule in each of the pH environments of the small intestine. A significant Spearman rank correlation coefficient for the mechanistic simulation-based method of 0.58 (p < 0.001) was found. The mechanistic simulation produced 71% of %HIA predictions within 25% of the experimental values. 

Figure 1-2 Projecting each point of the three-dimensional MND onto any of the planes defined by two axes of the coordinate system (or, more generally, any plane passing through the coordinate system) results in the projected points being represented by a two-dimensional MND). The correlation coefficients for the projections in all planes are needed to fully describe the original MND.

The next item we will look at is the correlation coefficient. The correlation coefficient for Table 25-1C is identical to that in Table 25-1B. There is nothing particularly noteworthy about this, except that the correlation coefficient is useless as a means of distinguishing between the two cases obviously, since we obtain the same result in both situations, we cannot tell from the value of the correlation coefficient which situation we are dealing with. 

A method and Worksheet for comparing correlation coefficients for different size populations at user selected confidence levels. 

Several software packages contain simple command lines for performing matrix computations directly and thus are conveniently capable of computing the correlation coefficient, for example as in r2 (Equation 59-8). 

The confidence limits for a correlation coefficient for a given number of X, Y pairs (n) at a specified confidence limit is calculated as Z2 (Equation 60-16). 

In summary, for any stated value of the population correlation (p) the z statistic is denoted as Z(p), and the corresponding correlation confidence limits can be determined. For our example, the Z statistic of 0.6366 corresponding to the lower correlation coefficient confidence limit is shown in the graphic below (Graphic 60-6a) as having a p value of 0.562575 this represents the lower confidence limit for the correlation coefficient for this example. 

Fig. B.l Relations between the linear and partial correlation coefficients for two variables and a controlling variable. Lines denote causal relations between the variables.

As an indication of the accuracy of the technique the correlation coefficients for the calibration curves indicate a precision of 0.2% or better. The standard deviation of the measurement samples is 0.70%. 

As is the total surface area and a ... d are all positive. The correlation coefficients for Eqs. (9) and (10) are 0.990 and 0.954, respectively. When applying such expressions it is, of course, imperative that the surface quantities are evaluated at the same computational levels as were used in their development. 

We will now use these equations to find expressions for the correlation coefficients for cases with and without mean scalar gradients. 

Figure 4.14. Predictions of the multi-variate SR model for Re, = 90 and Sc = (1, 1/8) with collinear mean scalar gradients and no backscatter (cb = 0). For these initial conditions, the scalars are uncorrelated pap(0) = gap(0) = 0. The correlation coefficient for the dissipation range, pD, is included for comparison with pap. 

Because phytate intakes were essentially constant, but calcium intake varied with caloric needs, a range of phytate/calcium molar ratios resulted with each phytate level. The correlation coefficient for apparent absorption and dietary phytate/zinc molar ratio was 0.62, P<0.01. The equation of the regression line was y =... 

Vs,mm and Vs are negative, this means that each term except e is promoting solvation. Equation (10) is one of the few GIPF relationships that include Vmin, the overall most negative value of the electrostatic potential. The correlation coefficient for Eq. (10) is R = 0.988 the average absolute deviation from experiment is 0.27 kcal/mole for AGsoivation values varying over 9.59 kcal/mole. 

A second use of this type of analysis has been presented by Stewart and Benkovic (1995). They showed that the observed rate accelerations for some 60 antibody-catalysed processes can be predicted from the ratio of equilibrium binding constants to the catalytic antibodies for the reaction substrate, Km, and for the TSA used to raise the antibody, Kt. In particular, this approach supports a rationalization of product selectivity shown by many antibody catalysts for disfavoured reactions (Section 6) and predictions of the extent of rate accelerations that may be ultimately achieved by abzymes. They also used the analysis to highlight some differences between mechanism of catalysis by enzymes and abzymes (Stewart and Benkovic, 1995). It is interesting to note that the data plotted (Fig. 17) show a high degree of scatter with a correlation coefficient for the linear fit of only 0.6 and with a slope of 0.46, very different from the theoretical slope of unity. Perhaps of greatest significance are the... 

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