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I assume the question was how do you do median regression. A full explanation is available at the websites in the sources and related links below.

but unless you are a statistician you will regret reading them.

The simplest practical solution for the two variable case is to create the set of all possible slopes that could exist between all possible combinations of data points. You then order this set from low to high. The median slope is then passed through the median point X and the median point Y to find the intercept. There are a couple of methods to calculate confidence intervals, but I would just suggest a simple non-parametric test. If you have a multi-variate problem I would suggest visiting a statistician as there is no simple way to explain it.

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Q: How do you do median median regression?
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