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This paper presents a simple and novel curve fitting approach for generating simple gene regulatory subnetworks from time series gene expression data. Microarray experiments simultaneously generate massive data sets and help immensely in the large-scale study of gene expression patterns. Initial biclustering reduces the search space in the high-dimensional microarray data. The least-squares error between fitting of gene pairs is minimized to extract a set of gene-gene interactions, involving transcriptional regulation of genes. The higher error values are eliminated to retain only the strong interacting gene pairs in the resultant gene regulatory subnetwork. Next the algorithm is extended to a generalized framework to enhance its capability. The methodology takes care of the higher-order dependencies involving multiple genes co-regulating a single gene, while eliminating the need for user-defined parameters. It has been applied to the time-series Yeast data, and the experimental results biologically validated using standard databases and literature.