So　far,　many　regression　works　have　been　implemented　by　using　linear　regression　methods.　Although　more　accurate　predictions　results　could　be　obtained,　polynomial　regression　is　not　used　as　much　as　compared　to　linear　regression　in　real　applications　due　to　occurrence　of　coefficient　explosion.　To　overcome　this　problem,　two　regression　algorithms　using　Chebyshev　polynomials　of　class　2　based　on　cascade　regression　and　feature　selection　are　proposed　in　this　paper.　In　the　experimental　part,　three　separate　experiments　including　function　interpolation　and　real-case　regression　were　conducted　on　three　datasets　to　test　the　proposed　algorithms.　As　shown　by　the　experimental　results,　the　proposed　algorithms　performed　better　than　other　regression　methods　in　terms　of　both　accuracy　and　processing　time.　(C)　2018　Elsevier　B.V.　All　rights　reserved.