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I am trying to get idea how variables of my data correspond to target variable (binary class).

In regression, Pearson r statistic is quite good to get sense of variable relationship. Also I can use it for classification, treating classes 0 and 1 as real values but it's a risky trick.

My question: is there any equivalent statistic saying which variable is good for classification task ? Thanks

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The Pearson Chi-Squared test may give you what you need: https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test

This is a good resource for analyzing categorical data: https://en.wikipedia.org/wiki/List_of_analyses_of_categorical_data

Also, confusion matrices can be very helpful: https://en.wikipedia.org/wiki/Confusion_matrix

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