9853

Modeling World Student Populations

This Demonstration shows the actual and projected growth in student populations at primary, secondary, post-secondary, and tertiary levels broken down by country and country groups. Population data is from the years 2000–2012 (where available). The projected growth is then modeled through 2020 using selected modeling methods.
The modeling is performed using either linear or quadratic regression or using a logistic model. While the first two typically produce better fits, the logistic model is perhaps more likely to produce better projections, because it captures something about population dynamics—a claim to be checked in 2020.

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The population data is from UNESCO's Institute of Statistics [1]. A different type of visualization of this data can be found at the World Bank's website [2].
The logistic function (or Verhulst model) is the most "realistic" projection in this Demonstration, in the sense that it captures the population dynamic whereby population growth initially increases before moderating and eventually declining (usually from changes in relative food abundance). It is given by
,
where is the population relative to the environment's carrying capacity and (the Malthusian parameter) is the rate of maximum population growth. The logistic models in this Demonstration are therefore solutions of the following form, with chosen to give the best fit, and is the 1998 population:
.
The Verhulst model can be augmented in several ways to capture richer dynamics not only in population change, but also in chaotic systems, particle physics, machine learning, chemical reactions, and economic innovation.
References
[1] UNESCO. "Public Reports, Education, Table 2: Demographic and Economic Data." (Feb 11, 2013) stats.uis.unesco.org/unesco/TableViewer/tableView.aspx?ReportId=173.
[2] World Bank. "Data Visualizer: Education Statistics." (Feb 11, 2013) devdata.worldbank.org/EdStatsDataVisualizer/Visualizer.html.
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