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We employ the new statistical estimates of the conditional entropy proposed in Bulinski, A. and Kozhevin, A. [2018] for models comprising the widely used logistic regression. Namely, we concentrate on the estimation of mutual information (for two random vectors). Then the important applications for feature selection are discussed. We compare the proposed approach with previous ones (see, e.g., Coelho, F. et al. [2016], Gao, W. et al. [2018]). In particular, the XOR-model introduced in Bulinski, A. and Kozhevin A. [2017] is also considered. The computer simulations in the framework of the logistic regression with Gaussian predictors show the advantages of the developed feature selection method.