Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 TheilSenLine

Source Notebook

Fit a line through a set of points using the Theil–Sen estimator

Contributed by: Rauan Kaldybayev

ResourceFunction["TheilSenLine"][data]

uses the Theil–Sen estimator to fit a line through a set of points represented by data.

ResourceFunction["TheilSenLine"][xlist,ylist]

uses the Theil–Sen estimator to fit a line through a set of points, where xlist and ylist respectively give the x and y coordinates of the points.

ResourceFunction["TheilSenLine"][…,x]

returns an equation for the Theil-Sen line in terms of the variable x.

Details

ResourceFunction["TheilSenLine"][data,x] or ResourceFunction["TheilSenLine"][xlist,ylist,x] returns the equation of a line mx+b, where x is the predictor of the model and can be any symbol.
ResourceFunction["TheilSenLine"][data] or ResourceFunction["TheilSenLine"][xlist,ylist] returns {m,b}.

Examples

Basic Examples (2) 

Fit a line through the points (0,1),(1,1),(2.5,3) using the Theil–Sen estimator:

In[1]:=
ResourceFunction["TheilSenLine"][{{0, 1}, {1, 1}, {2.5, 3}}]
Out[1]=

The output is of the form {m,b}, which represents a line fit of the form y=mx+b. Compare the fitted line to the original points:

In[2]:=
Show[ListPlot[{{0, 1}, {1, 1}, {2.5, 3}}, PlotStyle -> {PointSize -> Large}], Plot[%[[1]] x + %[[2]] // Evaluate, {x, 0, 2.5}, PlotStyle -> ColorData[97, 2]]]
Out[2]=

Scope (2) 

Supply data given in the form of separate lists for the x and y coordinates:

In[3]:=
ResourceFunction["TheilSenLine"][{0, 1, 2.5}, {1, 1, 3}]
Out[3]=

Return a formula for the model by passing the predictor as an additional argument:

In[4]:=
ResourceFunction["TheilSenLine"][{{0, 1}, {1, 1}, {2.5, 3}}, x]
Out[4]=

Publisher

Wolfram Summer Camp

Version History

  • 1.1.0 – 27 February 2023
  • 1.0.1 – 10 February 2023
  • 1.0.0 – 20 July 2021

Source Metadata

  • Citation:
    • Gocic, M., Trajkovic, S., "Analysis of changes in meteorological variables using Mann-Kendall and Sen's slope estimator statistical tests in Serbia." Global and Planetary Change, vol. 100, 172–182, 2013. DOI: 10.1016/j.gloplacha.2012.10.014
    • Sen, P.K., "Estimates of the Regression Coefficient Based on Kendall's Tau." Journal of the American Statistical Association, vol. 63, no. 324, 1379–1389, 1968. DOI: 10.2307/2285891
    • Theil, H., "A rank-invariant method of linear and polynomial regression analysis I." Nederl. Akad. Wetensch. Proc., vol. 53, 386–392, 1950. https://www.nrc.gov/docs/ML1330/ML13304B779.pdf
    • Theil, H., "A rank-invariant method of linear and polynomial regression analysis II." Nederl. Akad. Wetensch. Proc., vol. 53, 521–525, 1950. https://www.nrc.gov/docs/ML1330/ML13304B787.pdf
    • Theil, H., "A rank-invariant method of linear and polynomial regression analysis III." Nederl. Akad. Wetensch. Proc., vol. 53, 1397–1412, 1950. https://www.nrc.gov/docs/ML1330/ML13304B799.pdf

Related Resources

Author Notes

The code for this function is based on a piece of code written by the StackExchange user in answering the question "" on Mathematica Stack Exchange.

License Information