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Fuzzy regression, a nonparametric method, can be quite useful in estimating the relationships among variables where the available data are very limited and imprecise, and variables are interacting in an uncertain, qualitative, and fuzzy way. Thus, it may have considerably practical applications in many management and engineering problems. But there is still lack of proper interpretation about fuzzy regression. In this paper, we provide an insight into regression intervals so that regression interval analysis, data type analysis and variable selections can be analytically performed. Numerical examples are provided for illustration.