Factor Analysis HELP plots

If we plot concentrations in a three dimensional space, a point represents a sample as shown in Figure 1. In fact, the space necessary to show all of the points is really only two dimensional, since the amount of lead and bromine are directly interrelated. By a simple axis rotation shown in Figure 2, it can be seen that all of the points lie in a plane defined by the iron axis and a line that defines the lead-bromine relationship. For more complex systems, factor analysis will help to identify the true dimensionality of the system being studied and permit the determination of these interelemental relationships. With this information, it is then possible to determine the mass contribution of the particle sources to the total observed mass. 

Any variation of the slope for linear plots of Y / Sz)j versus 5ip/ Sz)j along a series of lanthanide complexes j implies that the ratio of the geometrical factor Gi/G changes, hence the structure of the complex does too. The systematic application of nuclear relaxation measurements (Eqs. (28) and (29)) for obtaining R Fj-iuclei distances, combined with the detailed analysis of NMR paramagnetic shifts with the help of the two nuclei method (Eq. (37), detection of isostructural series) as well... 

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