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Under the uncertain statistical framework by Liu [19], there is still a lack of an effective fitting method for uncertain linear models with Box-Cox transformation of response variables. For example, for the transformation parameter λ, the uncertain least squares estimation will produce a severely low estimation result. In this paper, we propose uncertain Box-Cox regression analysis by utilizing the uncertainty theory to model the imprecise data and applying a generalized Box-Cox transformation indexed by its parameter to validate classic regression assumptions. We use rescaled least squares to estimate unknown parameters and provide an estimate for noises followed by residual analysis for these uncertain Box-Cox regression models. We also give the forecast values and confidence intervals and use a numerical example to demonstrate our methodology. Our work sets a uniformed framework for Box-Cox transformation on the uncertain regression, and extends such regression from linear to nonlinear cases, taking the Johnson-Schumacher growth model as an example. INDEX TERMSUncertain box-cox regression model, rescaled least squares, residual analysis, uncertain box-cox linear regression model, uncertain box-cox Johnson-Schumacher growth model. ZAIYING ZHOU received the degree from the Department of Mathematical Sciences, Tsinghua University, in 2017. She has been a Teacher with the Center for Statistical Science, Tsinghua University. Her research interests include mathematical statistics and applications of statistical methods.YIPING HONG was born in Tianjin, China, in 1992. He received the B.S. degree in mathematics and applied mathematics from Tsinghua University, Beijing, China, in 2014, where he is currently pursuing the Ph.D. degree in statistics. His research interests include the statistical inference on the spatial and spatio-temporal covariance models, the network model analysis combined with spatial data, and the uncertainty theory. His awards and honors include the Excellent Undergraduate Thesis Award (Tsinghua University).

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