Reviewing the empirical and theoretical parameter relationships between various parameters is a good way to understand more about contact binary systems. In this investigation, two-dimensional (2D) relationships for P–MV(system), P–L1,2, M1,2–L1,2, and q–Lratio were revisited. The sample used is related to 118 contact binary systems with an orbital period shorter than 0.6 days whose absolute parameters were estimated based on the Gaia Data Release 3 parallax. We reviewed previous studies on 2D relationships and updated six parameter relationships. Therefore, Markov chain Monte Carlo and Machine Learning methods were used, and the outcomes were compared. We selected 22 contact binary systems from eight previous studies for comparison, which had light curve solutions using spectroscopic data. The results show that the systems are in good agreement with the results of this study.

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