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In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation , which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a higher risk of producing ...
Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to increase or decrease over time or is influenced by changes in an external factor.
This form of simple trend extrapolation helps to direct attention towards the forces, which can change the projected pattern. A more elaborated curve that uses times series analysis can often reveal surprising historical and current data patterns. The qualitative trend analysis is one of the most demanding and creative methods in Futures Studies.
If the trend can be assumed to be linear, trend analysis can be undertaken within a formal regression analysis, as described in Trend estimation. If the trends have other shapes than linear, trend testing can be done by non-parametric methods, e.g. Mann-Kendall test, which is a version of Kendall rank correlation coefficient.
Human population projections are attempts to extrapolate how human populations will change in the future. [2] These projections are an important input to forecasts of the population's impact on this planet and humanity's future well-being. [3] Models of population growth take trends in human development and apply projections into the future. [4]
Prediction outside this range of the data is known as extrapolation. Performing extrapolation relies strongly on the regression assumptions. The further the extrapolation goes outside the data, the more room there is for the model to fail due to differences between the assumptions and the sample data or the true values.
Futures studies, futures research, futurism research, futurism, or futurology is the systematic, interdisciplinary and holistic study of social/technological advancement, and other environmental trends; often for the purpose of exploring how people will live and work in the future.
Minimum polynomial extrapolation — for vector sequences; Richardson extrapolation; Shanks transformation — similar to Aitken's delta-squared process, but applied to the partial sums; Van Wijngaarden transformation — for accelerating the convergence of an alternating series