R. J. Oosterbaan
There are various kinds of curved (non-linear) regressions, for example those based on the power function, the second degree polynomial (i.e. the quadratic function), the S-curve functions, and the third degree polynomial (i.e. the cubic function). Free software to apply these functions is available as SegRegA. It uses a generalization of the standard functions by applying a transformation the values of the independent variable before fitting the selected function. Under the conditions at hand, one the these four kinds might be preferable. The decision can be made with the R2 magnitude, being the coefficient of explanation, for goodness of fit. When needed, confidence limits of R2 may be employed to tests its significance. The R2 is not always the ultimate criterion. Analysis of variance may also be required as well as theoretical considerations. In this article, data from literature on temperature trend in time and crop production against soil salinity as well as against depth of the water table are given as examples.
Curved (non-linear) regression, free software, coefficient of explanation, goodness of fit, confidence belt, analysis of variance, statistical significance testing
Cite this paper
R. J. Oosterbaan. (2021) Analysis of Different Curved Regressions using Free Software and Selection of the Appropriate Type Based on Statistical Tests for Goodness of Fit and Analysis of Variance. International Journal of Mathematical and Computational Methods, 6, 56-68