INDEX correlation coefficients

Linear regression analysis was performed on the relation of G"(s) versus PICO abrasion index. Figure 16.10 plots the correlation coefficient as a function of strain employed in the measurement of loss modulus. The regression results show poor correlation at low strain with increasing correlations at higher strains. These correlations were performed on 189 data points. 

The technology of proximity indices has been available and in use for some time. There are two general types of proximity indices (Jain and Dubes, 1988) that can be distinguished based on how changes in similarity are reflected. The more closely two patterns resemble each other, the larger their similarity index (e.g., correlation coefficient) and the smaller their dissimilarity index (e.g., Euclidean distance). A proximity index between the ith and th patterns is denoted by D(i, j) and obeys the following three relations ... 

Index i is Student s I distribution parameter l( is the correlation coefficient, / is the degrees of freedom ot a sample. 

Fields et al. 33) examined the closely related bis (trifluoromethyl) phosphine (Table 14) and found a similar increase in Vp.H with increasing polarity of the solvent. They noted a correlation between /P H and the proton chemical shift (confidence limit of the correlation coefficient was 99.9 %). Again hydrogen bonding was suggested as the principle causative factor since correlations with dielectric constant or refractive index were not found. The two-bond 2/P F was noted to decrease while the three-bond 3/H F coupling constant was solvent invariant (vide infra). 

A set of n = 209 polycyclic aromatic compounds (PAC) was used in this example. The chemical structures have been drawn manually by a structure editor software approximate 3D-structures including all H-atoms have been made by software Corina (Corina 2004), and software Dragon, version 5.3 (Dragon 2004), has been applied to compute 1630 molecular descriptors. These descriptors cover a great diversity of chemical structures and therefore many descriptors are irrelevant for a selected class of compounds as the PACs in this example. By a simple variable selection, descriptors which are constant or almost constant (all but a maximum of five values constant), and descriptors with a correlation coefficient >0.95 to another descriptor have been eliminated. The resulting m = 467 descriptors have been used as x-variables. The y-variable to be modeled is the Lee retention index (Lee et al. 1979) which is based on the reference values 200, 300, 400, and 500 for the compounds naphthalene, phenanthrene, chrysene, and picene, respectively. 

The data containing 324 descriptor values of 88 molecules was given as an input to VSMP program, to build models based on three and four descriptors, keeping the interdescriptor correlation below 0.75. The best three-descriptors model, Eq. 80, was based on descriptors 254 (atomic type E-state index), 311 (AlogP98), and 320 (2D Van der Waals surface area) with a correlation coefficient, r, of 0.8425, and the cross-validated correlation coefficient, q, of 0.8239. The correlation coefficients of the other two VSMP models, Eqs. 81 and 82 were 0.8411 and 0.8329, respectively. Significantly, the descriptors 254 and 311 were selected in all the best three-descriptors models of VSMP. The three descriptors, in the models 80, 81, and 82 were 320, 144 (Kappa shape index of order 1), and 30 (topological Xu index), respectively. 

Calibration curve quality. Calibration curve quality is usually evaluated by statistical parameters, such as the correlation coefficient and standard error of estimate, and by empirical indexes, such as the length of the linear range. Using confidence band statistics, curve quality can be better described in terms of confidence band widths at several key concentrations. Other semi-quantitative indexes become redundant. Alternatively, the effects of curve quality can be incorporated into statements of sample analysis data quality. 

Fields can be utilized in virtual screening applications for assessing the similarity (alignment) or complementarity (docking) of molecules. Two similarity measures have achieved the most attention. These are the so-called Garbo- [195] and Hodgkin indexes [196] respectively. Others are Pearson s product moment correlation coefficient [169] and Spearman s rank correlation coefficient [169]. 

The most prevalent among the similarity coefficients is the so-called cosine similarity index or correlation coefficient. For the field functions discussed in Subheading 2.4. it is usually called the Carbo similarity index, and this nomenclature will be used here as well,... 

Multiple correlation coefficient an index which measures the joint effect of several variables on some response. 

Figure 7. Comparison of the index that we developed (called index ) and the Canadian PEEP index. The correlation coefficient between the two indexes is 0.95. In both cases we draw a regression line to show the good agreement between the experts judgements and the indexes.

The use of the icterus index, as described by Meulengracht, for the assessment of jaundice has fallen into disrepute because of the errors caused by the presence of lipochromes, carotenoids, and other yellow pigments. Josephson (J6) in his survey found that the correlation coefficient between icterus index and serum bilirubin concentration was 0.69 in 360 healthy subjects and 0.84 in 40 jaundiced subjects. In newborn infants however, bilirubin is the only yellow pigment likely to be present and the possibility of determining serum bilirubin concentrations by direct measurement has again been re-examined. Abelson and Boggs (Al) diluted serum from infants with erythroblastosis 1 in 50 and studied the absorption curves. They found that in addition to the bili-... 

In Fig. 18.3 the parameter p is plotted versus Tg, as an index of the molecular stiffness of the polymer. The data show a considerable scattering, but the general course is unmistakable (Van Krevelen, 1972). The drawn curve corresponds to the following equation, as obtained by linear regression (correlation coefficient is only 0.86) of all data ... 

Statistical parameters, when available, indicating the significance of each of the descriptor s contribution to the final regression equation are listed under its corresponding term in the equation. These include the standard errors written as values, the Student t test values, and the VIF. The significance of the equation will be indicated by the sample size, n the variance explained, r the standard error of the estimate, s the Fisher index, F and the cross-validated correlation coefficient, q. When known, outliers will be mentioned. The equations are followed by a discussion of the physical significance of the descriptor terms. 

Chemometric methods such as analysis of correlation coefficients, cluster analysis or neural network analysis are used, for example, in the classification of fragments of glass on the basis of their elemental composition or refractive index. Such methods allow the test material to be classified into the appropriate group of products on the basis of the measured parameter. 

Figure 2.2. Pairwise percentage sequence identity for 33 cupredoxins plotted against (A) hydrophobic MIF similarity index and (B) electrostatic potential similarity index. The linear regression correlation coefficients...

Data on complex formation constants -log k were taken from Irving and Williams (1953), MoeUer et al. (1965), Izatt et al. (1971), Euria (1972), Kiss et al. (1991), and Mizerski (1997), plus values scattered elsewhere in the literature, while E (L) values are derived from Lever (1990). This means that a potential (-shift) scale based on the Ru(II/III) redox couple is used rather than the older ones from the Chatt workgroup which draw upon Mo(0/I)-, Mn(I/II)- and similar low-valent couples (it should be pointed out that these concerning trani-[Mo" (dppe)j(Nj)L] with L = Hal F to I, ChCN- Ch=O, S or Se, N, CO, PR3, RCN, CS(NH ), etc. and dppe = 1,2-bis-diphenylphosphinoethane can be linked to Lever s scale by linear correlation with very high correlation coefficients (Franzle 2005, unpublished)). The index nd (denticity n) corresponds to the... 

Programme algorithms are considered in detail elsewhere e.g. [54] but in general a similarity index or correlation coefficient has to be calculated for each fit due to variations in spectral data. The latter arise from the differences in spectra on different instruments or under different conditions, from additional components in unresolved GC-peaks and from discrepancies due to concentration changes. A yes/no answer can be more closely approached when all spectra are unique and completely reproducible. The best fits within specified correlations are normally printed out and further criteria have to be applied to these to obtain the final answer. This would be straightforward assuming the correct spectrum was on file. In cases where this is not so, some indication of the class and type of compound may be suggested from the list of best fits. 

Mathews correlation coefficient (Cx) It is the correlation coefficient between positive predicted and observed as well as negative predicted residues. This index is particular for a specific structure x and the formula is... 

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