Bivariate analysis

Molecules and crystals are described by a large number of quantitative indicators. Establishing a correlation between any two indicators is called bivariate analysis, and can be expressed either in a graph or in a linear regression the first problem is obviously to find out which pairs of properties do indeed correlate. 

All bivariate correlations between molecular and crystal properties are only broad and approximate, demonstrating that crystal packing is a complex phenomenon. More often that not, one finds that correlations expected on the basis of simple reasoning do not in fact hold. For example. Fig. 8.10 shows that there is no relationship between central molecular dipole moments and point-charge coulombic lattice energies, not even when both quantities are calculated by the same method (the rescaled EHT method). This is a further confirmation that central dipoles are a very poor indicator of molecular electrostatic properties [27]. 

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Beck, L.A. 1985 Bivariate analysis of trace elements in bone. Journal of Human Evolution 14 493-502. 

Priest (1988,190-94), however, argues that the explosion in product liability litigation has not measurably deterred accidental or job-related death rates. But he recognizes that simple time-series bivariate analysis is rather crude evidence, because there is no coun-terfactual of how many accidents would have occurred if a noliability, first-party-insurance regime had existed. 

Inappropriate use of bivariable analysis to screen risk factors for use in multivariable analysis. Journal of Clinical Epidemiology. 49 907-916... 

VI1. Verhoff, F. H., A Study of the Bivariate Analysis of Dispersed Phase Mixing. Ph.D. thesis. University of Michigan, Ann Arbor (1969). 

To obtain the SRO, we have taken the idea of the bivariate analysis, used to study the molecular ordering at interfaces between liquids and vapors and we have applied it to the study of liquid and plastic phases of CCI4. In order to locate the position of a second molecule from a central one, three orthogonal axis must be defined in relation with the molecular structure. In our case the z-axis is set along the direction of a C-Cl bond, being another C-Cl bond in the zy-plane (see Fig. 4). Using this convention we can calculate the azimuthal... 

This involves consideration of the relationships between more than two variables, and hence, operates as an extension of univariate and bivariate analysis. 

P. Galiatsaton and P. Prinos, Bivariate analysis and joint exceedance probabilities of extreme wave heights and periods, Proc. 31st Int. Conf. Coastal Engineering 2008 (2008), pp. 4121-4133, doi 10.1142/9789814277426 0342. 

Beilken et al. [ 12] have applied a number of instrumental measuring methods to assess the mechanical strength of 12 different meat patties. In all, 20 different physical/chemical properties were measured. The products were tasted twice by 12 panellists divided over 4 sessions in which 6 products were evaluated for 9 textural attributes (rubberiness, chewiness, juiciness, etc.). Beilken etal. [12] subjected the two sets of data, viz. the instrumental data and the sensory data, to separate principal component analyses. The relation between the two data sets, mechanical measurements versus sensory attributes, was studied by their intercorrelations. Although useful information can be derived from such bivariate indicators, a truly multivariate regression analysis may give a simpler overall picture of the relation. 

The goal of EDA is to reveal structures, peculiarities and relationships in data. So, EDA can be seen as a kind of detective work of the data analyst. As a result, methods of data preprocessing, outlier selection and statistical data analysis can be chosen. EDA is especially suitable for interactive proceeding with computers (Buja et al. [1996]). Although graphical methods cannot substitute statistical methods, they can play an essential role in the recognition of relationships. An informative example has been shown by Anscombe [1973] (see also Danzer et al. [2001], p 99) regarding bivariate relationships. 

Fig. 21. Equiprobability ellipses and discriminant lines for statistical linear discriminant analysis (bivariate case)...

Figure 6. Bivariate plot of logic [Eu/Fe] vs logi0 [Mn/Fe], Samples are plotted by groups as determined by a cluster analysis. Group 1 does not have enough samples to form an ellipse.

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