MicroRNAs (miRNA) exert regulatory actions via base-pairing with their binding sites on target mRNAs. Cooperative-binding, i.e., synergism, among binding sites on a mRNA is biochemically well-characterized. We studied whether this synergism is reflected in global relationship between miRNA-mediated regulatory activity and miRNA-binding-site count on the target mRNAs, i.e., leading to a non-linear relationship between the two. Recently, using our own and public datasets, we have enquired into miRNA regulatory actions: first, we analyzed the power-law distribution pattern of miRNA binding sites; second, strikingly, mRNAs for core miRNA regulatory apparatus proteins have extra-ordinarily high binding site counts, forming self-feedback-control loops; third, we revealed that tumor suppressor mRNAs generally have more sites than oncogene mRNAs; and fourth, we characterized enrichment of miRNA target mRNAs in translationally less-active polysomes relative to more-active polysomes. In these four studies, obvious correlation was observed qualitatively between the extent to which a mRNA is miRNA-regulated and its binding sites count. This paper summarizes the used datasets. We also re-analyzed the correlation by comparative linear and non-linear regression analyses. The results support a non-linear, instead of linear, relationship between the two parameters, conceivably a transcriptome-level reflection of cooperative-binding/synergism among miRNA binding sites on a target mRNA.