Multivariate　polynomial　regression　(MPR)　is　a　traditional　machine　learning　method.　it　has　been　widely　used　in　the　past　decades.　However,　the　high-order　interaction　information　in　its　model　is　incomplete.　Moreover,　it　is　difficult　to　visually　understand　its　decision　logic　and　to　determine　which　factor　contributes　more　to　the　result.　In　this　work,　we　propose　a　special　set　of　power　terms　named　ergodic　set,　which　considers　more　complete　high-order　interaction　information.　Based　on　this　set,　Ergodic　Set　Regression　(ESR)　and　Curve　Ergodic　Set　Regression　(CESR)　models　are　constructed,　the　first　model　for　accurately　prediction　and　another　model　for　visualizing　the　influences　of　various　factors　on　result.　The　experiment　results　on　a　small-scale　data　set　show　that　the　performance　of　ESR　is　better　than　that　of　MPR　and　even　some　neural　networks　methods　dedicated　to　small-scale　data　sets.　CESR　shows　the　influence　curve　of　each　factor　on　result　with　the　premise　of　obtaining　certain　accuracy.　©　2022　IEEE.