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.
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Details:
The segmentation is done by introducing a breakpoint
(break-point, threshold). 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, a version was made permitting the use of weight factors, preferred
regression type or type exclusion. Although manipulative, it is available on request.
In September 2010, the SegReg program was provided with new functionalities thanks to a request by
Kirsten Otis.
On 4 December 2011, the SegReg program was given an extended ANOVA table and a Fisher F-test
calculator was added, thanks to a suggestion by Ryan O'Donnell.
More details are found in the program itself.
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Start:
The mathematical model starts clicking on SegReg.Exe.
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Documentation:
A paper on the statistical principles of segmented regression with break-point,
including the determination of its confidence interval, can be inspected
in here.
A note on the construction of the confidence interval of the breakpoint in functions of
type 2, called bptype2, can also be downloaded.
The construction of confidence intervals of the regression segments
separated by the breakpoint is described in this text.
The principles of regression analysis in general can be found in this
lecture note.
Furter, the analysis of variance (Anova) and the F-test for segmented linear regression
with break-point, as used in SegReg, is briefly discussed in
this paper. There is also a Fisher F-test
calculator.
A lecture note on statistical analysis with examples of SegReg applications is found
in a document called Data Analysis.
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Download:
SegReg
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