Earlier studies have shown that pure quantum mechanical effects on the "light" methyl radical at low temperature minimize the anisotropy of CW EPR spectra to a high resolution character, and new experiments under different conditions display a small additional electron paramagnetic resonance (EPR) line-shape anisotropy. In this work the effects of the solid H-2 quantum matrix and three other typical solid noble-gas matrices on the spectral anisotropy and the hyperfine interaction (hfi) constant of trapped methyl radicals presented as matrix shifts (deviation from the value in free space) are studied in some detail. Experimental EPR data at liquid-He temperatures were used to explore the dependence of the additional broadening and the spectral anisotropy of the hosted methyl radicals and to correlate the experimental spectral anisotropy to the matrix radical interaction. Models correlating the spectral anisotropy and the matrix shift of the hyperfine (hf) coupling constant to the van der Waals (vdW) attraction and/or to the repulsive Pauli exclusion (RPE) forces between the host matrix molecules and the methyl radical were constructed. It was shown that both vdW and RPE forces must be involved to explain these matrix effects, but while the RPE is the major source for the extra anisotropy, its contribution to the if shift was also important but not dominant.