SegRegA :   Fitting of S-curves or sigmoids to cause-effect data.
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Summary: The amplified SegReg computer program (model, calculator), SegRegA, originally designed to perform a segmented (piecewise) linear regression, has been given the possibility to fit power curves, quadratic parabola's, cubic functions, and sigmoid S-curves to agricultural crop data,(see list of publications in which SegReg is used). An example of the application of the logistic S-curve can be found in the article: "Applying SegRegA to the annual average temperature trend from 1900 to 2020 in the Netherlands resulting from global warming; analysis by segmented linear regression types and curved functions such as the S-curve, Power curve, generalized quadratic and cubic regressions". Download from: average temperature.pdf The cubic functions are determined by matrices, determinants and matrix inversion. The third degree polygon can be used as a method to calculate and determine the salt tolerance of crops, see this article published in the International Journal of Agricultural Science and entitled "Crop tolerance to soil salinity, statistical analysis of data measured in farm lands". An overview of the use of S-curves is given in this text file Critical reviews: A critical review of the use of S-curves for the determination of a salt tolerance index for crops is to be found in this report           Another critical review of the use of S-curves with the same purpose in various published papers can be seen in this commentary Screenprint:

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Example of an S-curve model for crop yield and depth of the water table: Example of an inverted S-curve model for crop yield and soil salinity : Example of a cubic regression applied to crop yield and soil salinity yielding an S-curve :