The "geochemical effect of lanthanides" is a new concept proposed by the authors during the past decade. This concept reflects lanthanide shrinkage in elemental geochemistry, and it is statistically quantifiable. However, the geological significance of the various parameters of the equations obtained following quantization is not entirely clear. Cooperation and discussions from scholars in related research fields of rare earth elements in geology are required. In the present paper, from the perspective of coal geochemistry, the metamorphic coal seam of C2 series in Fengfeng Mine of Handan Coalfield in Hebei Province, China was used as an example. The geochemical significance of parameters in geochemical effect regression equation for lanthanides was evaluated, and two new formulas (regression equations) that characterized the geochemical behaviors of lanthanides were proposed. On this basis, concepts related to the geochemical effect of lanthanides, such as "individual parameters", "parameters in common", "two-sided parameters", and the "deviation value" of lanthanides, were proposed. In this study, it was proved that the goodness of fit for all types of function regression equations for lanthanides and the radii of their trivalent ions, and the "deviation value" of lanthanides, were all "individual parameters" that could indicate the post-modified geological environment of C2 coal seam, such as the influence from magmatic-hydrothermal fluids. A covariant figure was constructed according to these individual parameters and other indexes, and the C2 coal seam in Handan was effectively divided into two different metamorphic series of A (C2 coal seam uninfluenced or slightly influenced by magmatic-hydrothermal fluids) and B (C2 coal seam strongly influenced and evidently changed by magmatic-hydrothermal fluids). Consequently, the scientific significance of all the parameters for lanthanides in an identifying series of metamorphic coals within the geochemical effect regression equation was further clarified.