The second algorithm is also based on the hypothesis that the mean deviations between two random variables do not have significant changes throughout the forecast period, but with one significant addition.
In the interval 2003–2013, the actual data of the indicator «children enrolled to the first grade» are approximated using the statistical package StatGraphicsCenturion. We have a polynomial:
where t takes a value from 1 to 11, which corresponds to the years 2003–2013 abscissa Fig. 1.5 for the indicator «children admitted to the first grade»; P1 – the value of the indicator «children accepted to the first grade».
The model is statistically qualitative according to Fisher’s criterion and coefficient of determination.
In the interval 2014–2020 with the help of the same package is an approximation of the actual data of the indicator «children accepted to the first grade». We have a polynomial:
According to the coefficient of determination and the Darbin-Watson criterion, the model is statistically qualitative.
According to this algorithm, the forecast data of the indicator «students enrolled to the HEI» in the interval 2020–2024 are calculated using polynomial (1.1) in which the free member is reduced by 128.8 thousand people:
where t takes the value 7–11, which corresponds to 2020–2024.
In the interval 2025–2031, the forecast data of the indicator «students enrolled to the HEI» are calculated using polynomial (1.2), but the free member of this polynomial is reduced by 128.8 thousand people:
where t takes the value 1–7, which corresponds to 2025–2031 years.
The results of calculations by the second algorithm are also presented in Table 1.5, but in column 5.
In Fig. 1.6 the graphic interpretation of forecasting of the indicator «accepted students to HEIs» by the second algorithm is presented.
The third «extrapolation» algorithm is based on the hypothesis that the process described by the actual data and approximated by statistical models does not change over time under the influence of factors that did not act on the interval of obtaining actual data. With the help of the statistical package StatGraphicsCenturion we will approximate the actual data of the indicator «students accepted to the HEI» in the interval 2014–2019. We have a polynomial:
where PS – the number of students enrolled to the HEIs; t – varies from 1 to 6, which corresponds to the interval 2014–2019, where the approximation process is implemented, and from the values of t from 7 to 11, which corresponds to the time interval from 2020 to 2024, the extrapolation process is implemented. The results of the calculations are presented in Table 1.5 column 6.
The model is statistically qualitative according to Fisher’s criterion, coefficient of determination and Darbin-Watson criterion.