Extrapolation Introduction

Extrapolation can be similar to interpolation if we assume that the function behaves similarly to existing data. Since the next point has not yet been bracketed there is always the possibility that the behaviour changes, depending on the application. Simple extrapolation predicts existing data to fit into the best model.

• Linear

  Used when data increases or decreases at a steady rate, or only two data points.

• Power

  Measurements increase at a specific rate, problems at zero and negative x-values.

• Quadratic

  Starting to build our data and fitting three points.

• Cubic Spline

  Similar to quadratic but using more prediction of how the function grows.

• Exponential

  Data changes at increasingly higher rates, and there are no negative or zero x-values.

• Logarithmic

  Data changes swiftly, there are no negative or zero x-values.

• Polynomial

  Can only be used with more data. Often used as an extension to other methods.

Without a well fitting model expect the results to be unpredicable. If the data is coming from field readings be aware of outliers.

Comparing the results of fitting the least squares line and polynomial to the data.

If the data should be linear then the projected point for an x-axis value of 2 is shown (green point), and the polynomial should be ignored.