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the blue figure that has been made using the principle of minimization of the sum of squares of deviations of the observed values from the regression lines over the whole domain of explanatory variable X (i.e. maximization of the coefficient of determination), while the partial regression is designed only to find the point where the horizontal trend changes into a sloping trend.
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The attached figure concerns the same data as shown in the blue graph in the infobox at the top of this page. Here, the wheat crop has a tolerance for soil salinity up to the level of EC=7.1 dS/m instead of 4.6 in the blue figure. However, the fit of the data beyond the threshold is not as well as in
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SegReg permits the introduction of one or two independent variables. When two variables are used, it first determines the relation between the dependent variable and the most influential independent variable, where after it finds the relation between the residuals and the second independent variable.
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As an alternative to regressions at both sides of the breakpoint (threshold), the method of partial regression can be used to find the longest possible horizontal stretch with insignificant regression coefficient, outside of which there is a definite slope with a significant regression coefficient.
183:(as a parameter for the fit of the regression lines to the observed data values) is selected as the true breakpoint. To assure that the lines at both sides of the breakpoint intersect each other exactly at the breakpoint, SegReg employs two methods and selects the method giving the best fit.
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The alternative method can be used for segmented regressions of Type 3 and Type 4 when it is the intention to detect a tolerance level of the dependent variable for varying quantities of the independent, explanatory, variable (also called predictor).
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During the input phase, the user can indicate a preference for or an exclusion of a certain type. The preference for a certain type is only accepted when it is statistically significant, even when the significance of another type is higher.
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SegReg recognizes many types of relations and selects the ultimate type on the basis of statistical criteria like the significance of the regression coefficients. The SegReg output provides statistical
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The breakpoint is found numerically by adopting a series tentative breakpoints and performing a linear regression at both sides of them. The tentative breakpoint that provides the largest
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Residuals are the deviations of observed values of the dependent variable from the values obtained by segmented regression on the first independent variable.
605:, 2002. Contribution to the project “Liquid Gold” of the International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands.
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Screenprint, data showing a tolerance level (threshold) of the wheat crop for soil salinity expressed in electric conductivity as ECe = 7.1 dS/m.
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of the regression lines and a confidence block for the breakpoint. The confidence level can be selected as 90%, 95% and 98% of certainty.
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where BP is the breakpoint, Y is the dependent variable, X the independent variable, A the
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the residual of Y. When two independent variables are present, the results may look like:
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When only one independent variable is present, the results may look like:
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analysis to determine the breakpoint where the relation between the
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A list of publications in which SegReg is used can be consulted.
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is BP of Z, Z is the second independent variable, C is the
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Segmented regression of residuals on number of irrigations.
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in the second set of equations into the first set yields:
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ILRI provides examples of application to magnitudes like
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To complete the confidence statements, SegReg provides an
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Drainage research in farmers' fields: analysis of data
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analysis of variance for segmented linear regression
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127:is a free and user-friendly tool for linear
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652:Pascal (programming language) software
577:confidence interval of the break-point
250:X > BP ==> Y = A
236:X < BP ==> Y = A
565:segmented regression with break-point
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269:, B the regression constant, and R
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617:List of publications using SegReg
369:Substituting the expressions of R
28:Screenshot of graphics tab sheet
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151:Screenprint of input tabsheet
17:Segmented regression software
451: ==> Y = A
429: ==> Y = A
407: ==> Y = A
385: ==> Y = A
299: ==> Y = A
281: ==> Y = A
181:coefficient of determination
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563:Statistical principles of
171:Screenprint of Anova table
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350:where, additionally, BP
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360:regression coefficient
335: ==> R
317: ==> R
267:regression coefficient
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575:determination of the
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647:Statistical software
545:Segmented regression
196:analysis of variance
161:Confidence intervals
137:independent variable
129:segmented regression
122:application software
82:Statistical software
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629:partial regression
627:Free software for
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139:changes abruptly.
133:dependent variable
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62:Microsoft Windows
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57:Operating system
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93:Proprietary
68:Available in
35:Developer(s)
518:Alternative
641:Categories
551:References
211:crop yield
163:are shown.
114:statistics
46:Written in
443:X > BP
421:X > BP
399:X < BP
377:X < BP
331:Z > BP
313:Z < BP
295:X > BP
277:X < BP
228:Equations
539:See also
143:Features
135:and the
95:Freeware
590:in the
588:F-tests
502:, and E
466:where E
459:.Z + E
437:.Z + E
415:.Z + E
393:.Z + E
202:table.
198:and an
101:Website
89:License
71:English
455:.X + C
433:.X + C
411:.X + C
389:.X + C
366:on Z.
343:.Z + D
325:.Z + D
303:.X + B
285:.X + B
254:.X + B
240:.X + B
217:, and
125:SegReg
120:, the
105:SegReg
50:Delphi
200:Anova
339:= C
321:= C
307:+ R
289:+ R
116:and
77:Type
506:= B
494:= B
490:, E
482:= B
478:, E
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244:+ R
112:In
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
