When paper which was applied as insulation in oil-filled transformer was aged by thermal, its electrical, mechanical and chemical characteristics were changed and deteriorated. Therefore operating temperature was more higher, damage of paper was more quicker. Insulating paper which was generally made with cellulose was degraded, polymer of long length chain was decomposed as a monomer and CO, $CO_2$ gas and/or by-product such as furfural was produced from paper at the same time. In according with detection these gas and furfural by dissolved gas analysis(DGA) and high performance liquid chromatography(HPLC), we have investigated effects of CO, $CO_2$ gas and furfural on insulation of paper. Also we have analyzed for correlation between furfural and CO, $CO_2$ gas using linear regression method that was known as useful, credible statistical analysis.