Representation of Correlation Data on the Hemisphere

FIGURE 4.1 Scree plot eigenvalues 2 of the matrix of correlation coefficients of 23 parameters for 28 solvents, in descending order. Four eigenvalues are greater than unity, with a distinct break before the fifth, suggesting that four independent properties of the solvents are significant. 

FIGURE 4.2 Representation of the 23 parameters on the hemisphere. Squares represent positive vector directions, crosses negative, that is, antipodes. The Cartesian axes corresponding to the three principal components are labeled N(North pole), G (Greenwich meridian on the Equator), and E (90°E on the Equator). 

Because the first PC (N) by construction contains the greatest part (53%) of the variance of all the data, many of the points are loosely scattered about the N axis. Some of the points are grouped as might be expected, but some unexpected similarities and differences appear. Notable groups are as follows  

The group spread from latitude 78°, longitude 13° to latitude 50°, longitude -60°, that measures various blends of (di)polarity and polarizability. The subgroup 

Two parameters related to polarizability, (latitude 31°, longitude 123°) and Marcus s softness parameter n (latitude 20°, longitude 152°) appear fairly close together, plotted as antipodes. 

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