Power transformers are one of the most significant and expensive equipment in power systems that are exposed to electrical, thermal, and chemical tensions. The transformer health index is a measure that uses test data and field inspections to assess the condition and determine the remaining life of the transformer. The purpose of this article as a new idea is to determine the relationships between electrical, physical, and chemical parameters of transformer oil, dissolved gases, and the transformer health index. One of the advantages of using the regression method in analyzing transformer data compared to the other methods to evaluate the transformer health index is determining the influence of the parameters that have the most impact on each other. Some achievements of this article are as follows: (1) introducing moisture content as the parameter that plays an effective role in reducing dielectric oil breakdown voltage and improving the transformer health index; (2) determining the inverse relationship between acidity and furfural components; (3) determining furfural as a parameter with the greatest role in reducing the Interfacial tension (IFT) of oil (molecular interconnection); (4) determining CO gas as the parameter with the most role in the production of furfural component; (5) determining C2H2 gas as the parameter with the most role in producing the acid component. For example, with a 1 ppm increase in the moisture component, the oil breakdown voltage decreases by 0.583 kV in the compound, growth, exponential, and logistic regressions, or with a 1 ppm increase in the furfural component, the oil interfacial tension decreases by 0.644 mN/m in power regression. In this article, the curve estimation regression method is used and the results are plotted by SPSS statistical software to analyze the interaction between different transformer parameters. To perform the simulations, test data related to 120 transformers have been considered.