Herein, multivariate Lagrange's interpolation polynomial (MLIP) and multivariate least square (MLS) methods are used to derive linear and higher-order polynomials for two varied applications. (1) For an effective fabrication of Pectin degrading Fe3 O4 -SiO2 Nanobiocatalyst activity (IU/mg). Here, the three parameters namely: pH value, pectinase loading and temperature as independent variables are optimized for the maximal of anobiocatalyst activity as a dependent variable. (2) For a passive system reliability estimation of decay heat removal (DHR) of a nuclear power plant. The success criteria of the system depend on three types temperature that do not exceed their respective design safety limits and are considered as dependent variables and 14 significant parameters were used as independent variables. Statistically, the validation of these multivariate polynomials are done by testing of hypothesis. Comparative study of the proposed approach gives significance results in the first application have the optimum conditions for maximum activity using linear MLIP method is: 58.64 with pH = 4, pL = 250 and Temp = 4°C. The maximum activity using second order MLIP method is 59.825 and method of MLS is 59.8249 with the optimized values of an independent variables pH = 4, pL = 300 and Temp = 8°C depicted in Table 1. In DHR system, the significance results are obtained and depicted in Table 2.