This value is formed under the influence of many factors, among which the most significant are:

– labor migration of parents;

– liberal conditions of admission to some foreign universities (citizens of Ukraine are enrolled not only without control of their level of knowledge, but also without original documents);

– reduction of the number of domestic HEIs;

– increase of requirements to entrants – establishment of the lower limit of competitive points of EIE even for those who enter the contractual form of education;

– increasing the requirements for mastering foreign languages;

– gradual loss of the objective need to obtain higher education for a more or less secure life, especially in the conditions of accessibility of labor migration; – loss of prestige of higher education.

Analysis of the fluctuation of indicators (**Table 1.4** and **Fig. 1.5**) showed that they are essentially random variables with deterministic components – trends. The mechanism of formation of these random variables determines the leading trend of the indicator «number of births» with a shift along the abscissa by the appropriate value. Thus, the abscissa of the indicator «the number of children enrolled to the first grade» is shifted by six years; indicator «number of students who completed nine classes» – for 15 years; indicators «the number of students who graduated from eleven classes» and «students enrolled to HEIs» – for 17 years.

The choice as a trend of the indicator «number of births» is significantly complicated by sharp changes in other indicators, which are due to these reasons. To predict the number of students who have completed nine grades; the number of students who have completed eleven classes and the number of students enrolled to the HEIs is better to take as a guide the indicator «the number of students enrolled to the first grade» at appropriate intervals. For example, to predict the number of students who will be enrolled to the HEIs in 2020–2024, consider how the values of the indicator «the number of students enrolled to the first grade» changed from 2003 to 2013. We take this period, because during it the socio-economic system of Ukraine developed without drastic changes.

There are several prediction algorithms that can be used in this case. Consider the essence of each of them.

The first is to consider the algorithm of «mean deviations», which is based on the hypothesis that the mean deviations between two random variables do not have significant changes throughout the forecast period. The stability of the difference between the number of children enrolled to the first grade and the number of students enrolled to the HEI over four years allows to formulate a hypothesis about the possibility of sufficiently accurate forecasting.

In this case, the deviation of the number of students enrolled to the first grade in the respective year from the number of students enrolled to the HEIs does not exceed its average value by more than 8 %. We will consider 8 % as a measure of forecasting error according to this algorithm.