In applications, large datasets of parallel situations are encountered more and more often. It is necessary to check whether they are collected from multiple regression models before further modeling, estimation and inference. A novel metric for such heterogeneity is proposed based on the projection strategy, whose strength is then borrowed to form a new test for the equivalence of a large number of unknown regression models that is fully data-driven. Asymptotic normality of the proposed test is constructed. The testing procedure is further applied to identify outlying datasets whose regression models deviate from the majority. Extensive numerical studies demonstrate that our methods have satisfactory performance. A R package hetero:regis developed to implement the proposed methods.