The paper considers the task of automatic modulation classification, i.e. blind identification of modulation type of unknown signal before reconstructing its information content. This issue is especially important for the conditions of limited bandwidth of communication channels especially when two or more signals occupy the same frequency bandwidth. The proposed method uses linear logistic regression based on features calculated on the base of higher order cumulants of the received signal. The selection of informative features based on the absolute values of regression coefficients is proposed. The simulation results for the classification of composite BPSK/QPSK signals with various channel parameters and noise levels show the advantage of proposed approach with reduced set of features over the application of linear regression based on normal equation.