The model has a limit on the time of extrapolation until 2024, because from 2025 on the system of enrollment in the HEI begin to act factors that did not act in the formation of actual data used in the synthesis of the approximation model (1.3). This is a fundamental difference between the third algorithm and the previous two, which take into account the peculiarities of the formation of indicators in the forecasting period.

In **Fig. 1.6** the graphic interpretation of forecasting of the indicator «accepted students to HEIs» by this algorithm is presented.

When using this model to predict the indicator «accepted students to the HEI» outside the interval 2020–2024, its inadequacy seems obvious. See **Table 1.5** column 6 and **Fig. 1.6**.

The adequacy of forecasting according to the first algorithm («mean deviations») can be approximately estimated by the error of determining the MD constant, which is assumed to be equal to 8 %.

The adequacy of forecasting according to the second algorithm is determined by Fisher’s criterion, coefficient of determination, Darbin-Watson criterion and the error of determining the AD constant.

The adequacy of forecasting by the third «extrapolation» algorithm is determined by Fisher’s criterion, coefficient of determination, Darbin-Watson criterion. Regarding the scope of this algorithm, it is determined based on the required forecasting horizon, which is limited by the conditions of the accepted hypothesis.

The value of such fundamental indicators of the education system of Ukraine as the number of teachers, the number of secondary school, the number of scientific and pedagogical staff, the number of HEIs, funding for higher and secondary education largely depend on the integrated indicators of the education system of Ukraine, which are the number of students and the number of people in the HEIs.

To predict the dynamics of these integrated indicators, forecasts have already been made until 2031 on the indicator «students enrolled to the HEIs», but this is not enough. It is necessary to make additional forecast calculations until 2026–2031 on the following indicators:

– children are enrolled in the first grade till 2026;

– received a certificate of basic general secondary education (completed nine grades) till 2029;

– received a certificate of completion of general secondary education (completed eleven clas-ses) till 2031;

– the number of persons released from the HEIs till 2031.

Forecasting the number of students enrolled in the first grade will be carried out according to the first algorithm – the algorithm of «average deviations». To calculate the average deviation of the number of births in a given year from the number enrolled to the first class (AD1G), we will take into account the annual actual deviations from 2015 to 2020. The calculation is performed according to **Table 1.1**, column 5. The average deviation of AD1G is 72.8 thousand people. The forecast values of the indicator «Children enrolled in the first grade» for 2021–2026 are given with an asterisk (*) in column 4 of **Table 1.4**. The deviation of 2014 was not taken into account (column 5 of **Table 1.4**). Because this year, as shown above, there was a restructuring of the education system to the conditions of occupation of the Crimea and parts of Donetsk and Luhansk regions.

Forecasting the number of students who received a certificate of basic general secondary education (completed nine classes) is also carried out according to the algorithm of «average deviations». The indicator «Children enrolled in the first grade» is taken as the base and we take its value from 2005 to 2010, which corresponds to 2014–2019 according to the projected indicator. In **Table 1.4**, columns 4 and 7, respectively. The average deviation of the AD9G is 53.2 thousand people. Predicted values are given with an asterisk (*) in **Table 1.4**, column 7.