We deal with a mathematical model of binary statistical experiments, based on statistical data, for the validation of the elementary hypothesis about the presence or absence of a predefined attribute A in the set of elements that make up a complex system. It is assumed that: 1) All the elements that make up the system can gain or lose the given attribute A over time, that is the frequency of the attribute A is a dynamic variable; 2) The basic object of the study are the statistical experiments, which are characterized by relative frequencies of the presence or absence of the attribute A in the sample of fixed volume at each time instant. 3) It is assumed the dependency of (average) results of the next experiment on the average result of the present experiment. This relationship is called the property of persistent regression and used as fundamental condition for the subsequent analysis of the model.