extrapolation

Examples of extrapolation in the following topics:

• Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

  • Some problems with multiple regression include multicollinearity, variable selection, and improper extrapolation assumptions.
  • Typically, the quality of a particular method of extrapolation is limited by the assumptions about the regression function made by the method.
  • If the method assumes the data are smooth, then a non-smooth regression function will be poorly extrapolated.
  • Even for proper assumptions about the function, the extrapolation can diverge strongly from the regression function.
  • This divergence is a specific property of extrapolation methods and is only circumvented when the functional forms assumed by the extrapolation method (inadvertently or intentionally due to additional information) accurately represent the nature of the function being extrapolated.

• Extrapolation is treacherous

  • Applying a model estimate to values outside of the realm of the original data is called extrapolation.
  • If we extrapolate, we are making an unreliable bet that the approximate linear relationship will be valid in places where it has not been analyzed.

• The Regression Method

  • Extrapolation is also frequently used, in which data points beyond the known range of values is predicted.
  • An example of extrapolation, where data outside the known range of values is predicted.
  • The red points are assumed known and the extrapolation problem consists of giving a meaningful value to the blue box at $x=7$.

• Predictions and Probabilistic Models

  • Prediction outside this range of the data is known as extrapolation.
  • Performing extrapolation relies strongly on the regression assumptions.
  • This means that any extrapolation is particularly reliant on the assumptions being made about the structural form of the regression relationship.
  • The implications of this step of choosing an appropriate functional form for the regression can be great when extrapolation is considered.
  • At a minimum, it can ensure that any extrapolation arising from a fitted model is "realistic" (or in accord with what is known).

• Samples

  • Samples are collected and statistics are calculated from the samples so that one can make inferences or extrapolations from the sample to the population.

• A Graph of Averages

  • The line is a model that can be used to make predictions, whether it is interpolation or extrapolation.

• Using Chance in Survey Work

  • Information about the relationship between sample and population is limited, making it difficult to extrapolate from the sample to the population.

• Fundamentals of Statistics

  • It can include extrapolation and interpolation of time series or spatial data, and can also include data mining.

• Applications of Statistics

  • It can include extrapolation and interpolation of time series or spatial data and can also include data mining.

• The Literary Digest Poll

  • It is erroneous to assume that the responders and the non-responders had the same views and merely to extrapolate the former on to the latter.