Lung cancer is the top cancer killer worldwide with high mortality rate. Majority belong to non-small cell lung cancers (NSCLCs). The epidermal growth factor receptor (EGFR) has been broadly explored as a drug target for therapy. However, the drug responses are not durable due to the acquired resistance. MicroRNAs (miRNAs) are small noncoding and endogenous molecules that can inhibit mRNA translation initiation and degrade mRNAs. We wonder if some downstream molecules shared by EGFR and the other tyrosine kinase receptors (TKRs) further transduce the signals alternatively, and some miRNAs play the key roles in affecting the expression of these downstream molecules. In this study, we investigated the mRNA:miRNA associations for the direct EGFR downstream molecules in the EGFR signaling pathway shared with the other TKRs, including c-MET (hepatocyte growth factor receptor), Ron (a protein tyrosine kinase related to c-MET), PDGFR (platelet-derived growth factor receptor), and IGF-1R (insulin-like growth factor receptor-1). The multiple linear regression and support vector regression (SVR) models were used to discover the statistically significant and the best weighted miRNAs regulating the mRNAs of these downstream molecules. These two models revealed the similar mRNA:miRNA associations. It was found that the miRNAs significantly affecting the mRNA expressions in the multiple regression model were also those with the largest weights in the SVR model. To conclude, we effectively identified a list of meaningful mRNA:miRNA associations: phospholipase C, gamma 1 (PLCG1) with miR-34a, phosphoinositide-3-kinase, regulatory subunit 2 (PIK3R2) with miR-30a-5p, growth factor receptor-bound protein 2 (GRB2) with miR-27a, and Janus kinase 1 (JAK1) with miR-302b and miR-520e. These associations could make great contributions to explore new mechanism in NSCLCs. These candidate miRNAs may be regarded as the potential drug targets for treating NSCLCs with acquired drug resistance.