This paper proposes the use of a specific mathematical model to represent the relationship between rat behavior and sociality (degree of friendliness with the robot) in the robot-rat interaction system. To validate the model, we conducted social interaction test between a rat-like robot and real, live rats. A rat-like robot called WR-4 capable of generating friendly or neutral behaviors among rats serves as partner to the rats in the interaction. Meanwhile, we performed Principal Component Analysis to specify the mathematical model. The experimental results show that this mathematical model allows quantitative estimation of rat sociality. Likewise, the results reveal that rat sociality can be analyzed and modified in this robot-rat interaction system.