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Abstract Context. The problem of estimating the software size in the early stage of a software project is important, since the information obtained from estimating the software size is used for predicting the software development effort, including open-source Java-based information systems. The object of the study is the process of estimating the software size of open-source Java-based information systems. The subject of the study is the regression models for estimating the software size of open-source Java-based information systems. Objective. The goal of the work is the creation of the non-linear regression model for estimating the software size of open-source Java-based information systems on the basis of the Johnson multivariate normalizing transformation. Method. The model, confidence and prediction intervals of multiply non-linear regression for estimating the software size of open-source Java-based information systems are constructed on the basis of the Johnson multivariate normalizing transformation for non-Gaussian data with the help of appropriate techniques. The techniques to build the models, equations, confidence and prediction intervals of non-linear regressions are based on the multiple non-linear regression analysis using the multivariate normalizing transformations. The appropriate techniques are considered. The techniques allow to take into account the correlation between random variables in the case of normalization of multivariate non-Gaussian data. In general, this leads to a reduction of the mean magnitude of relative error, the widths of the confidence and prediction intervals in comparison with the linear models or nonlinear models constructed using univariate normalizing transformations. Results. Comparison of the constructed model with the linear model and non-linear regression models based on the decimal logarithm and the Johnson univariate transformation has been performed. Conclusions. The non-linear regression model to estimate the software size of open-source Java-based information systems is constructed on the basis of the Johnson multivariate transformation for SB family. This model, in comparison with other regression models (both linear and non-linear), has a larger multiple coefficient of determination, a larger value of percentage of prediction and a smaller value of the mean magnitude of relative error. The prospects for further research may include the application of other multivariate normalizing transformations and data sets to construct the non-linear regression model for estimating the software size of open-source Java-based information systems. References Kaczmarek J., Kucharski M. Size and effort estimation for

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