Editing Piecewise linear function (section)

==Fitting to data==
{{Main|Segmented regression}}
If partitions, and then breakpoints, are already known, [[linear regression]] can be performed independently on these partitions. 
However, continuity is not preserved in that case, and also there is no unique reference model underlying the observed data. A stable algorithm with this case has been derived.<ref name="Golovchenko">{{cite web|last=Golovchenko|first=Nikolai|title=Least-squares Fit of a Continuous Piecewise Linear Function|url=https://drive.google.com/file/d/1M5b5EoGbARlcsRVnG-7D64cpL8Vh76Av/view?usp=sharing|access-date=6 Dec 2012}}</ref>

If partitions are not known, the [[residual sum of squares]] can be used to choose optimal separation points.<ref>{{Cite journal 
| last1 = Vieth | first1 = E. 
| title = Fitting piecewise linear regression functions to biological responses 
| journal = Journal of Applied Physiology 
| volume = 67 
| issue = 1 
| pages = 390–396 
| year = 1989 
| pmid = 2759968
| doi = 10.1152/jappl.1989.67.1.390 
}}</ref> However efficient computation and joint estimation of all model parameters (including the breakpoints) may be obtained by an iterative procedure<ref>{{Cite journal |last=Muggeo |first=V. M. R. |date=2003 |title=Estimating regression models with unknown break-points |journal=Statistics in Medicine |volume=22 |issue=19 |pages=3055–3071 |doi=10.1002/sim.1545 |pmid=12973787|s2cid=36264047 }}</ref> currently implemented in the package <code>segmented</code><ref>{{Cite FTP |last=Muggeo |first=V. M. R. |date=2008 |title=Segmented: an R package to fit regression models with broken-line relationships |url=ftp://200.236.31.12/CRAN/doc/Rnews/Rnews_2008-1.pdf#page=20 |volume=8 |server=R News |url-status=dead |pages=20–25}}</ref> for the [[R (programming language)|R language]]. 

A variant of [[decision tree learning]] called [[model tree]]s learns piecewise linear functions.<ref>{{Cite journal | last1 = Landwehr | first1 = N. | last2 = Hall | first2 = M. | last3 = Frank | first3 = E. | title = Logistic Model Trees | doi = 10.1007/s10994-005-0466-3 | journal = Machine Learning | volume = 59 | issue = 1–2| pages = 161–205 | year = 2005 | s2cid = 6306536 | url = http://www.cs.waikato.ac.nz/~eibe/pubs/LMT.pdf| doi-access = free }}</ref>