Weak correlation model

The weak correlation model Broken symmetry structure... 

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. 

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. 

In an empirical study Vereecke and Van Dierdonck (2002) tested Fer-dow s model and found it to be valid with two exceptions it appears to be too limited in the criteria for adding plants to an existing network and lead factories were also added based on market proximity. In another study Maritan et al. (2004) used autonomy over planning, production and control decisions to validate Ferdow s model but found only weak correlations with planning decisions showing the strongest correlation. 

It is believed that electron correlation plays an important role with the anomalously high resistivity exhibited in marginal metals. Unfortunately, although the Mott-Hubbard model adequately explains behavior on the insulating side of the M-NM transition, on the metallic side, it does so only if the system is far from the transition. Electron dynamics of systems in which U is only slightly less than W (i.e. metallic systems close to the M-NM transition), are not well described by a simple itinerant or localized picture. The study of systems with almost localized electrons is still an area under intense investigation within the condensed matter physics community. A dynamical mean field theory (DMFT) has been developed for the Hubbard model, which enables one to describe both the insulating state and the metallic state, at least for weak correlation. 

A relaxation spectrum similar to that of Fig. 4.2 is obtained for the diffusional motion of a local-jump stochastic model of IV+ 1 beads joined by N links each of length b, if a weak correlation in the direction of nearest neighbor links is taken into account for the probability of jumps (US). On the other hand, relaxation spectra similar to that of the Rouse theory (27) are obtained for the above mentioned model or for stochastic models of lattice chain type (i 14-116) without the correlation. Iwata examined the Brownian motion of more realistic models for vinyl polymers and obtained detailed spectra of relaxation times of the diffusional motion 117-119). However, this type of theory has not gone so far as to predict stationary values of the dynamic viscosity at high frequencies. 

The absence of well defined reflections with a finite /-index (from which the c-axis parameter could have been determined) is attributed by the authors to possible chain position disorder. One source of disorder could be that the chains are only weakly correlated concerning their translational position along the chain direction, a situation reminiscent of a nematic packing. Another possible source could be disorder among a few discrete preferred arrangements. However, both these models should allow for 00/-type reflections. This latter type of... 

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