Correlation analysis

The calculation of characteristic values causes a high amount of values which contain redundant informations. Due to this the forth partial step will be to reduce this amount of values using extraction methods. This can be realized with statistical methods like cross correlation analysis. 

N.B. Chapman, J. Shorter (Eds.), Advances in Linear Free Energy Relationships, Plenum Press, London, 1972. po] N.B. Chapman, J. Shorter (Eds.), Correlation Analysis in Chemistry, Plenum Press, London, 1978. pi] J. Shorter, Linear Free Energy Relationships (LEER), in Encyclopedia of Computational Chemistry, Vol. 2, P.v.R. Schleyer, N.L. Ailinger, T. Clark,... 

To gain insight into chemometric methods such as correlation analysis, Multiple Linear Regression Analysis, Principal Component Analysis, Principal Component Regression, and Partial Least Squares regression/Projection to Latent Structures... 

A first step in a data analysis process is the detection of relationships between variables. This can be achieved through correlation analysis. 

Figure 9-4. Correlation analysis examples of different values of the correlation coefficient.

An application of correlation analysis is the detection of related chemical de.scriptors when analyzing chemical data, correlation analysis should be used as a first step to identify those descriptors which are interrelated. 1 f two descriptors are strongly correlated, i.e, the correlation coefficient of two descriptors exceeds a certain value, e.g., r > 0.90, one of the descriptors can be excluded from the data set. 

Association deals with the extraction of relationships among members of a data set. The methods applied for association range from rather simple ones, e.g., correlation analysis, to more sophisticated methods like counter-propagation or back-propagation neural networks (see Sections 9.5.5 and 9.5.7). 

Correlation analysis reveals the interdependence between variables. The statistical measure for the interdependence is the correlation coefficient. 

These first components of the autocorrelation coefficient of the seven physicochemical properties were put together with the other 15 descriptors, providing 22 descriptors. Pairwise correlation analysis was then performed a descriptor was eliminated if the correlation coefficient was equal or higher than 0.90, and four descriptors (molecular weight, the number of carbon atoms, and the first component of the 2D autocorrelation coefficient for the atomic polarizability and n-charge) were removed. This left 18 descriptors. 

C. Hansch and A. J. Leo, Substituent Constantsfor Correlation Analysis in Chemistry andBiolog, [Pg.284]

The existing series of substituent constants has been developed by analysis of experimental data. Separation of the various components has usually depended on correlation analysis designed to identify the contributions from various components of... 

When the orbitals have been classified with respect to symmetry, they can be arranged according to energy and the correlation lines can be drawn as in Fig. 11.10. From the orbital correlation diagram, it can be concluded that the thermal concerted cycloadditon reaction between butadiene and ethylene is allowed. All bonding levels of the reactants correlate with product ground-state orbitals. Extension of orbital correlation analysis to cycloaddition reactions involving other numbers of n electrons leads to the conclusion that the suprafacial-suprafacial addition is allowed for systems with 4n + 2 n electrons but forbidden for systems with 4n 7t electrons. 

O. Exner, in Correlation Analysis in Chemistry, N. B. Chapman and B. Shorter, eds. Plenum Press, New York, 1978, Chapter 10. 

Hansch, C, Leo, A Substituent Constants for Correlation Analysis in Chemistry and Biology, John Wiley New York, 1979... 

Shorter, J. "Correlation Analysis of Organic Reactivity Research Studies Press (Wileyl Chicester, 1982. 

Kaiser [140] presents a correlation analysis for flooding in packed towers that is more analytical in the performance approach. It is based on single phase hydraulics. It would have been helpful for the article to present a comparison of results tvith the other more conventional techniques. 

Correlation analysis quantifies the degree to which the value of one variable can be used to predict the value of another. The most frequently used method is the Pearson product-moment correlation coefficient. 

It is known that several intermolecular interactions are responsible for cyclodextrin complexation, acting simultaneously. These interactions are separable from one another by quantitative structure-reactivity analysis. Furthermore, correlations obtained by the analysis can be discussed in direct connection with actual interactions already elucidated experimentally for the action site of cyclodextrin. Thus, the results must serve to make the background of the correlation analysis more concrete. 

Matsui et al.82) have analyzed the same data of log l/Kd(X) for cyclodextrin-phenol systems from a somewhat different standpoint. They computed the minimal van der Waals interaction energies (Emin) for the systems by using the same method as described in a previous section (Table 4). The calculated Emin values were applied, in place of such steric parameters as Ibrnch and B1( to the correlation analysis. The correlations obtained are given in Eqs. 24 to 27. 

In these equations, Dmax is the larger of the summed values of STERIMOL parameters, Bj, for the opposite pair 68). It expresses the maximum total width of substituents. The coefficients of the ct° terms in Eqs. 37 to 39 were virtually equal to that in Eq. 40. This means that the a° terms essentially represent the hydrolytic reactivity of an ester itself and are virtually independent of cyclodextrin catalysis. The catalytic effect of cyclodextrin is only involved in the Dmax term. Interestingly, the coefficient of Draax was negative in Eq. 37 and positive in Eq. 38. This fact indicates that bulky substituents at the meta position are favorable, while those at the para position unfavorable, for the rate acceleration in the (S-cyclodextrin catalysis. Similar results have been obtained for a-cyclodextrin catalysis, but not for (S-cyclodextrin catalysis, by Silipo and Hansch described above. Equation 39 suggests the existence of an optimum diameter for the proper fit of m-substituents in the cavity of a-cyclodextrin. The optimum Dmax value was estimated from Eq. 39 as 4.4 A, which is approximately equivalent to the diameter of the a-cyclodextrin cavity. The situation is shown in Fig. 8. A similar parabolic relationship would be obtained for (5-cyclodextrin catalysis, too, if the correlation analysis involved phenyl acetates with such bulky substituents that they cannot be included within the (5-cyclodextrin cavity. 

A few examples have been reported in which no steric parameter is involved in the correlation analysis of cyclodextrin catalysis. Straub and Bender 108) showed that the maximal catalytic rate constant, k2, for the (5-cyclodextrin-catalyzed decarboxylation of substituted phenylcyanoacetic acid anions (J) is correlated simply by the Hammett a parameter. 

Exner, O. (1988) Correlation Analysis in Organic Chemistry. Plenum, New York [7.2]. 

The correlation analysis of spectroscopic properties in terms of a,- and crR-type parameters has been very important. Substituent effects on 19F NMR shielding in... 

The correlation analysis of infrared data has been much examined by Katritzky, Topsom and colleagues69,70. Thus, the intensities of the v16 ring-stretching bands of mono- and di-substituted benzenes may be correlated with the oR° values of the substituents and these correlations may be used to find new oR° values. 

Finally we mention the very recent development of a scale of directional substituent polarizability parameters from ab initio calculations of polarizability potentials135. It is expected that this scale of oa values will prove of considerable utility in correlation analysis, often in association with oF values. The o, value of S02Me is given as — 0.62 cf. H, 0.00 N02, - 0.26 COMe, - 0.55 SMe, - 0.68 t-Bu, - 0.75. 

This section is largely based on the previous account in Ref. 11, in which certain material was adapted (by kind permission of the Oxford University Press) from J. Shorter, Correlation Analysis in Organic Chemistry An Introduction to Linear Free-Energy Relationships, Chap. 2, Oxford Chemistry Series, 1973. 

J. Shorter, Correlation Analysis of Organic Reactivity, Chap. 1, Research Studies Press, Wiley, Chichester, 1982. 

The symbol and sign conventions used for substituent effects in this chapter are those most frequently used by writers on correlation analysis in organic chemistry. / or R effects which withdraw electrons from the ring are regarded as positive. See Ref. 48, pp. 229-230 for a more detailed consideration of symbol and sign conventions. 

For reviews, see Klumpp, G.W. Reactivity in Organic Chemistry Wiley NY, 1982. p. 167 Bell, R.R in Chapman Shorter Correlation Analysis in Chemistry Recent Advances Rlenum Press 1978, p. 55 Kresge, A.J. Chem. Soc. Rev., 1973, 2, 475. 

This is not the only equation that has been devised in an attempt to correlate nucleophilic reactivity. For reviews of attempts to express nucleophilic power quantitatively, see Ritchie, C.D. Pure Appl. Chem., 1978, 50, 1281 Duboc, C. in Chapman Shorter Correlation Analysis in Chemistry Recent Advances, Plenum NY, 1978, p. 313 Ibne-Rasa, K.M. J. Chem. Educ., 1967, 44, 89. See also Hoz, S. Speizman, D. J. Org. Chem., 1983, 48, 2904 Kawazoe, Y. Ninomiya, S. Kohda, K. Kimoto, H. Tetrahedron Lett., 1986, 27, 2897 Kevill, D.N. Fujimoto, E.K. J. Chem. Res. (S), 1988, 408. 

The correlation analysis between the 30 most representative pharmaceutical compounds and the daily measured flow (Fig. 8) shows a variable behavior and... 

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