Purpose:　The　purpose　of　this　paper　is　to　overcome　the　application　limitations　of　other　multi-variable　regression　based　on　polynomials　due　to　the　huge　computation　room　and　time　cost.　Design/methodology/approach:　In　this　paper,　based　on　the　idea　of　feature　selection　and　cascaded　regression,　two　strategies　including　Laguerre　polynomials　and　manifolds　optimization　are　proposed　to　enhance　the　accuracy　of　multi-variable　regression.　Laguerre　polynomials　were　combined　with　the　genetic　algorithm　to　enhance　the　capacity　of　polynomials　approximation　and　the　manifolds　optimization　method　was　introduced　to　solve　the　co-related　optimization　problem.　Findings:　Two　multi-variable　Laguerre　polynomials　regression　methods　are　designed.　Firstly,　Laguerre　polynomials　are　combined　with　feature　selection　method.　Secondly,　manifolds　component　analysis　is　adopted　in　cascaded　Laguerre　polynomials　regression　method.　Two　methods　are　brought　to　enhance　the　accuracy　of　multi-variable　regression　method.　Research　limitations/implications:　With　the　increasing　number　of　variables　in　regression　problem,　the　stable　accuracy　performance　might　not　be　kept　by　using　manifold-based　optimization　method.　Moreover,　the　methods　mentioned　in　this　paper　are　not　suitable　for　the　classification　problem.　Originality/value:　Experiments　are　conducted　on　three　types　of　datasets　to　evaluate　the　performance　of　the　proposed　regression　methods.　The　best　accuracy　was　achieved　by　the　combination　of　cascade,　manifold　optimization　and　Chebyshev　polynomials,　which　implies　that　the　manifolds　optimization　has　stronger　contribution　than　the　genetic　algorithm　and　Laguerre　polynomials.　©　2022,　Emerald　Publishing　Limited.