Since many important biological systems or processes are dynamic systems, it is important to study the gene expression patterns over time in a genomic scale in order to capture the dynamic behavior of gene expression. Microarray technologies have made it possible to measure the gene expression levels of essentially all the genes during a given biological process. In order to determine the transcriptional factors (TFs) involved in gene regulation during a given biological process, we propose to develop a functional response model with varying coefficients in order to model the transcriptional effects on gene expression levels and to develop a group smoothly clipped absolute deviation (SCAD) regression procedure for selecting the TFs with varying coefficients that are involved in gene regulation during a biological process.