Phenol and its congeners are known to induce caspase-mediated apoptosis activity and cytotoxicity on various cancer cell lines. Apoptosis, scavenging of radicals, antioxidant, and pro-oxidant characteristics are primarily responsible for the antitumor activities of phenolic compounds. Quantitative structure-activity relationship studies on the cellular apoptosis and cytotoxicity of phenolic compounds have been investigated recently by Selassie and colleagues (J Med Chem; 48:7234, 2005) wherein models were developed for various carcinogenic cell lines. These quantitative structure-activity relationship models are based on few experimentally obtained physicochemical parameters such as Verloop's sterimol descriptor, hydrophobicity, Hammett electronic parameter, and octanol/water partition coefficient. The paper deals with structure-activity relationships of phenols and its derivatives for the development of predictive models from the standpoint of theoretical structural parameters and ridge regression methodology. The quantitative structure-activity relationship studies developed here for the caspase-mediated apoptosis activity and cytotoxicity on murine leukemia cell line (L1210), human promylolytic cell line (HL-60), human breast cancer cell line (MCF-7), parenteral human acute lymphoblastic cells (CCRF-CEM), and multidrug-resistant subline of CCRF-resistant to vinblastine (CEM/VLB) cells utilize physicochemical molecular descriptors calculated solely from the structure of phenolic compounds under investigation along with the descriptors used by Selassie and group. It is seen that such quantitative structure-activity relationships can provide a better quality predictive model for the phenolic compounds. The biological activities of the nine sets of phenolic compounds have been calculated based on ridge regression analysis that clearly gives a better significant correlation compared to the activities predicted by Selassie and co-workers. Counter-propagation artificial neural network studies have been introduced in the present investigation for a better understanding of multidimensional rational patterns in more complex data sets. The counter-propagation artificial neural network studies were performed on the same data set and with the same descriptors as have been carried out in developing ridge regression models and the result of counter-propagation neural network models produces very interesting findings in terms of leave-one-out test. Finally, an attempt has been made for a comparative study of the relative effectiveness of linear statistical methods versus nonlinear techniques, such as counter-propagation neural networks in modeling structure-activity studies of the phenolic compounds.