The main aim of this paper is to develop a suitable regression analysis model for describing the relationship between the index efficiency and the parameters of the Rival Penalized Competitive Learning Binary Tree (RPCLb-tree). RPCL-b-tree is a hierarchical indexing structure built with a hierarchical RPCL clustering implementation, which transforms the feature space into a sequence of nested clusters. Based on the RPCL-b-tree, the efficient Nearest-Neighbor search for a query can be performed with the branch-and-bound algorithm. The index efficiency of a RPCL-b-tree relates to a set of parameters: leaf node size of the tree, number of retrieved objects per search, feature dimensionality and database size. To formulate this relationship, we develop a nonlinear regression model in this paper. This regression model includes two components. One is used to describe the relationship between index efficiency and the number of retrieved objects per search; another is to describe the rela...