Multiple transcription factors coordinately control transcriptional regulation of genes in eukaryotes. Although many computational methods consider the identification of individual transcription factor binding sites (TFBSs), very few focus on the interactions between these sites. We consider finding TFBSs and their context specific interactions using microarray gene expression data. We devise a hybrid approach called LogicMotif composed of a TFBS identification method combined with the new regression methodology logic regression. LogicMotif has two steps: First, potential binding sites are identified from transcription control regions of genes of interest. Various available methods can be used in this step when the genes of interest can be divided into groups such as up-and downregulated. For this step, we also develop a simple univariate regression and extension method MFURE to extract candidate TFBSs from a large number of genes in the availability of microarray gene expression data. MFURE provides an alternative method for this step when partitioning of the genes into disjoint groups is not preferred. This first step aims to identify individual sites within gene groups of interest or sites that are correlated with the gene expression outcome. In the second step, logic regression is used to build a predictive model of outcome of interest (either gene expression or up- and down-regulation) using these potential sites. This 2-fold approach creates a rich diverse set of potential binding sites in the first step and builds regression or classification models in the second step using logic regression that is particularly good at identifying complex interactions.