In this paper, an attempt has been made to find the correlation between various parameters of the two diode equivalent circuit model of silicon solar cells. The statistical analysis has been done to find the engineering fit models between these parameters. The solar cell parameter data of 82 solar cell samples has been estimated using the Particle Swarm Optimization method from the measured illuminated I-V characteristics of the cells. This data on estimated parameters has been used to find the Pearson's correlation coefficient between different parameters and the significant outcome of this work is that it revealed a high correlation between the first diode's reverse saturation current and its ideality factor and a medium correlation between the second diode's reverse saturation current and its ideality factor in the two-diode equivalent circuit model of a silicon solar cell. An engineering fit model has been suggested between the reverse saturation current and ideality factor of the first diode, based on the data of 82 large area (similar to 154.8 cm(2)) silicon solar cells with AM1.5 conversion efficiency between 15% and 18.4%. The suggested engineering fit between the two would be a method to reduce the number of parameters needed for silicon solar cell modeling and to make it easier for predicting the module output. (C) 2016 Elsevier Ltd. All rights reserved.