Current methods of neural machine translation may generate sentences with different levels of quality. Methods for automatically evaluating translation output from machine translation can be broadly classified into two types: a method that uses human post-edited translations for training an evaluation model, and a method that uses a reference translation that is the correct answer during evaluation. On the one hand, it is difficult to prepare post-edited translations because it is necessary to tag each word in comparison with the original translated sentences. On the other hand, users who actually employ the machine translation system do not have a correct reference translation. Therefore, we propose a method that trains the evaluation model without using human post-edited sentences and in the test set, estimates the quality of output sentences without using reference translations. We define some indices and predict the quality of translations with a regression model. For the quality of the translated sentences, we employ the BLEU score calculated from the number of word [Formula: see text]-gram matches between the translated sentence and the reference translation. After that, we compute the correlation between quality scores predicted by our method and BLEU actually computed from references. According to the experimental results, the correlation with BLEU is the highest when XGBoost uses all the indices. Moreover, looking at each index, we find that the sentence log-likelihood and the model uncertainty, which are based on the joint probability of generating the translated sentence, are important in BLEU estimation.