N.V. Prykhodko, PhD, Economics, S.B. Prykhodko, Dr.Sci.Tech.
Èlektron. model. 2018, 40(6):101-110
The techniques to build the models, equations, confidence and prediction intervals of nonlinear regressions on the basis of multivariate normalizing transformations for non-Gaussian data are considered. The examples of application of the techniques for the four-dimensional non-Gaussian data set for two cases such as: univariate and multivariate normalizing transformations are given. The values of the multiple coefficient of determination such as: the mean magnitude of relative error and the percentage of prediction which are given are better for the nonlinear regression model for the Johnson multivariate transformation compared to the univariate one. The widths of the prediction interval of non-linear regression on the basis of the Johnson multivariate transformation
are less than following Johnson univariate transformation for 26 of 30 rows of data. Approximately the same results are obtained for confidence intervals of nonlinear regression. In general, when constructing the models, equations, confidence and prediction intervals of non-linear regressions for multivariate non-Gaussian data, one should use multivariate normalizing transformations. Normalizing data with univariate transformations instead of multivariate one may lead to increasing of width of the confidence and prediction intervals of non-linear regression.
non-linear regression model, prediction interval, normalizing transformation,non-linear regression model, prediction interval, normalizing transformation,multivariate non-Gaussian data.
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