The pattern recognition method of clustering is a technique automatically classifying data into clusters. Among clustering methods, c-regression based on fuzzy set theory, called Fuzzy c-Regression (FCR), is proposed to get a linear dataset structure. The most recent clustering is based on rough set theory called rough clustering, which is less descriptive than fuzzy clustering. A typical rough clustering algorithm is Rough k-Regression (RKR). However, RKR has problems because it depends on initial values and has no optimum index, so we do not know whether a clustering result will be optimal. This paper proposes Rough c-Regression (RCR) based on the optimization of an objective function and demonstrates its effectiveness through numerical examples.