Summary:
The SegReg computer program (model) is designed to
perform a segmented (piecewise) linear
regression (in splines) of one dependent variable
(Y, e.g. plant growth, crop yield) on one (X) or
two (X and Z) independent (explanatory) variables
(predictors), e.g. crop growth factors like depth
of water table and soil salinity.

Details:
The segmentation is done by introducing a
breakpoint (breakpoint, threshold, switching
point). Thus one can obtain a broken,
discontinuous, line. Seven types of functions
(0 to 6) are used. Examples are given.
The selection of the best function type and
breakpoint is based on maximizing the statistical
coefficient of explanation (determination) and
performing the test of significance.
The 90% confidence interval (belt) is given as
well as an Anova table for variance analysis.
In December 2008, an amplified version (SegRegA)
was made permitting the use of weight factors,
preferred regression type or type exclusion.
Although it can lead to manipulation, it is
available on request.
More details are found in the program itself.

Start:
The mathematical model starts clicking on
SegReg.Exe.

Documentation:
A paper on the statistical principles of
segmented regression with breakpoint,
including the determination of its confidence
interval, can be inspected
in here.
The construction of confidence intervals of the
regression segments separated by the breakpoint,
and of the breakpoint itself, is described in
this confidence
paper, which also gives an example. The
intervals are made with Student's
tdistribution, see the
ttest program.
The principles of regression analysis in general
can be found in this
lecture note.
Furter, the analysis of variance (Anova) and the
Ftest for segmented linear regression with
breakpoint, as used in SegReg, is briefly
discussed in
this paper.
A lecture note on statistical analysis with
examples of SegReg applications is found
in a document called
Data Analysis.

Acknowledgements
In September 2010, the SegReg program was provided
with new functionalities thanks to a request by
Kirsten Otis.
In March 2011 the confidence belts were improved
thanks to questions raised by Linda Jung.
In October 2012 the confidence block of the
breakpoint for type 2 functions was improved thanks
to questions raised by John Schukman.
In March 2013 the use of a second independent
variable was updated thanks to comments made by
Barbara Mahler.
In November 2013 the calculation of the standard
error and confidence interval of the breakpoint
(BP), as well as of the Y value at BP, was
standardized for the different types of segmented
regression. A description of the mathematics
involved, with examples, can be seen in this
confidence paper.
These changes were motivated by suggestions put
forward by Dawn Noren and Wenhuai Li.
In January 2014 the conditions for Type 2, 3, 4 and
5 were made more strict thanks to an example
provided by John Shukman.


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SegReg
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