Using a training set consisting of twenty-two well-known semiconducting organic polymers, we studied the ability of a simple linear regression supervised machine learning algorithm to accurately predict the bandgap (BG) and ionization potential (IP) of new polymers. We show that using the PBE or PW91 exchange-correlation functionals and this simple linear regression, calculated BGs and IPs can be obtained with average percent errors of less than 3 and 4%, respectively. We then apply this method to predict the BG and IP of a group of new polymers composed of monomers used in the training set and their derivatives in AABB and ABAB orientations.