Rubber materials have mostly been modeled by utilizing hyperelasticity, which have led to greater understanding and acceptable predictability of their stress-strain response. However, inherent inelastic behavior excluded by approximation has never been characterized by time-dependent parameters such as time, strain-rate, and strain history. We hypothesized that time, stretch rate, and stretch history were prominent factors that induce the inelasticity, and we characterized the inelasticity in terms of those factors using a randomized stretch-controlled testing protocol. We applied the custom randomized testing protocol with the fundamental statistical theory to characterize inelastic behavior imbedded in the high strain material. We hypothesized that time spent testing (T), rate-related stretch history (Ht2), and long-term stretch history (Ht1) give rise to the inelastic deviation from hyperelasticity. We examined the significance, effectiveness, and differences of T, Ht2, and Ht1 by looking at the derived multivariable linear regression models. Distribution of prediction deviation was also examined to see if we missed any other significant variable. Predictability of the multivariable linear regression models was validated by utilizing the unused data from the randomized testing protocol and data from the conventional cyclic testing protocol. We found that the inelasticity of the rubber-like material is highly related to T, Ht2, and Ht1, but not equally influential to all stretches. At smaller deformations, greater inelastic deviation occurs. Inelasticity exponentially decreased over stretch and was nonlinearly related to time. This study successfully determined the elastic/inelastic responses and factors that induce the inelastic response of the rubber-like material. This investigation suggests a way to better describe the elastic/inelastic properties and phenomenological models of rubber-like materials.