I want to apply a quantile regression model to my data, and of course would like to understand at least in principle what quantile regression does to my data. Now I understand the basic concept and I learned minimizing the equation

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will give me a parameter vector for each quantile, which I will need to draw the different quantile regression lines and that

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is the regression line for the quantile 𝜏. But can somebody please tell me: how can this be rewritten to a form that I (obviously not being a mathematician) would recognize to be a linear equation. I thinking of something like

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