The median regression function is defined and demonstrated by examples. A lemma with sufficient conditions for continuity and differentiation of the median regression function is proved. Its estimation from a random sample is deduced firstly based on the empirical distribution function and secondly based on a kernel estimation with Gaussian kernels. Both estimations are demonstrated by GALTONS historical example. A comparison between the empirical median regression function and the empirical regression of the first kind is made by an example. A hint for curve fitting with the median estimation equation is also given by an example.
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