Uncertain revised regression analysis with responses of logarithmic, square root and reciprocal transformations

Regression models are often called for to quantify relationships between the explanatory variables and the response variable. Mathematically, data should be collected and recorded as their true values, which turns out to be unrealistic for the real world. In this paper, we introduce uncertain variables to characterize such imprecise data, apply the most useful logarithmic, square root or reciprocal transformation to alleviate possible nonlinearity problems and estimate the disturbance terms for the obtained uncertain regression models, followed by confidence interval estimations and point predictions. For each type of models being proposed, namely the uncertain revised regression models, uncertain revised asymptotic regression models and uncertain revised Michaelis–Menten kinetics regression models, we give a numerical example, respectively, to illustrate our approach.