Weak correlation

First, the structure should explain the data. Apart from the energy or target function value returned by the refinement program, this check can be performed with some independent programs (e.g., AQUA/PROCHECK-NMR [90], MOLMOL [91]). The analysis of the deviations from the restraints used in calculating the structures is very useful in the process of assigning the NOE peaks and refining the restraint list. As indicators of the quality of the final structure they are less powerful, because violations have been checked and probably removed. A recent statistical survey of the quality of NMR structures found weak correlations between deviations from NMR restraints and other indicators of structure quality [88]. 

For 4t (Uthe relevant perturbation consists in perturbing the covalent (or neutral) VB structures by their interaction with the ionic ones this is the strongly correlated or magnetic domain. So that the Hartree Fock symmetry breaking occurs in a zone which covers the whole magnetic domain and a significant part of the "weakly" correlated domain... 

The effect of water temperature variation is logarithmically correlated with dispersant effectiveness [585]. Dispersant/oil ratios greater than approximately 1 40 or 1 60 result in a low dispersant effectiveness. Dispersion experiments were conducted to investigate the effects of oil composition. The effectiveness is positively and strongly correlated with the saturate concentration in the oil and is negatively correlated with the contents of aromatic, asphaltene, and polar compounds in the oil. The effectiveness is weakly correlated with the viscosity of the oil. The dispersant effectiveness is limited primarily by the oil composition. 

In a screening study with 78 subjects, the lag phase varied from 34 to 114 min. Interestingly, only a weak correlation was found between the a-tocopherol content and the lag phase (r=0.2, P < 0.01, n = 78). Increasing the a-tocopherol content of individual LDL samples in vitro or by oral supplementation led always to a proportional increase of oxidation resistance, according to the equation y=kx+a. The slope k is the eflScacy of... 

If the inputs are correlated, then the inverse of the covariance matrix does not exist and the OLS coefficients cannot be computed. Even with weakly correlated inputs and a low observations-to-inputs ratio, the covariance matrix can be nearly singular, making the OLS solution extremely sensitive to small changes in the measured data. In such cases, OLS is not appropriate for empirical modeling. 

Figure 18A shows the overlaid multiplicity-edited GHSQC and 60 Hz 1,1-ADEQUATE spectra of posaconazole (47). As will be noted from an inspection of the overlaid spectra, there is an overlap of the C46 and C47 resonances of the aliphatic side chain attached to the triazolone ring that can be seen more clearly in the expansion shown in Figure 18B. In contrast, when the data are subjected to GIC processing with power = 0.5, the overlap between the C46 and C47 resonances is clearly resolved (Figure 18C). In addition, the weak correlation between the C3 and C4 resonances of the tetrahydrofuryl moiety in the structure is also observed despite the fact that this correlation was not visible in the overlaid spectrum shown in A. This feature of the spectrum can be attributed to the sensitivity enhancement inherent to the covariance processing method.50...

Consideration of Weak Correlation. If an inter-needle correlation can no longer be disregarded, two published methods for the analysis of weakly correlated particles may be considered (Cohen and Thomas [201] Porod [206]). 

A weak correlation between octanol/water partition coefficient (logP) and logVDss ft.ee was shown for a set of 36 weak bases, while a similar relationship using VD data for 15 weak acids could not be demonstrated [26]. The correlation was binomial and likely would not be tight enough to enable prospective human... 

High (absolute) correlation coefficient with the v-variable however, note that also variables with a weak correlation can become important if they are able to explain variability of y that is not captured by other regressor variables. A better strategy could thus be based on an iterative procedure, where only in the first step the variable with highest correlation with v is selected. Then a model is computed using the selected variable and the residuals are computed. In the next step the variable with the (absolute) highest correlation coefficient with the residuals is selected, and so on. However, this approach already considers the multivariate data information. 

In summary, it is more common to examine pairs of variables from a profit chain-of-effects model rather than the profit chain in its entirety. A scatter plot or correlation analysis of a pair of profit-chain variables (e.g. satisfaction and loyalty) almost always indicates a weak correlation. The weak correlation is typically interpreted as suggesting a crisis whereby the implied profit chain-of-effects or cascading model is not supported. 

Studies to date have demonstrated an extremely weak correlation (if any) between photochemical-oxidant pollution and hospital admissions. If such correlations do exist, observations must be carried out over considerably longer periods with adequate provisions for controlling confounding variables, such as meteorologic factors. 

Hageman et al. [41] correlated pesticide concentrations in mountain snow from various Western US National Parks with the amount of farmland within a given distance of a sampling site to determine the source of the pesticides. A strong correlation between the two appears for current-use pesticides, showing the importance of local use areas, but a weak correlation applies for historic-use pesticides, indicating that LRT is important. 

NOE theory provides an exact energy functional for two-electron systems [76, 77]. In the weak correlation limit, the total energy is given by... 

Three sets of molecular descriptors that can be computed from a molecular connection table are defined. The descriptors are based on the subdivision and classification of the molecular surface area according to atomic properties (such as contribution to logP, molar refractivity, and partial charge). The resulting 32 descriptors are shown (a) to be weakly correlated with each other (b) to encode many traditional molecular descriptors and (c) to be useful for QSAR, QSPAR, and compound classification. 

In the present work, we will use a relatively low level of theory to derive 32 weakly correlated molecular descriptors, each based on the subdivision and classification of the molecular surface area according to three fundamental properties contribution to ClogP, molar refractivity, and atomic partial charge. The resulting collection will be shown to have applicability in QSAR, QSPR, and compound classification. Moreover, the derived 32 descriptors linearly encode most of the information of a collection of traditional mathematical descriptors used in QSAR and QSPR. 

We have derived three sets of (easily calculated) molecular descriptors based on atomic contributions to logP, molar refractivity, and atomic partial charge. The individual descriptors were found to be weakly correlated with each other... 

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