Summary
This article explains a metrod to find out the regression line or plane by median similar to linear programing method
The regression line is y=a+bx if\(z = \sum {\left| {y_i - a - bx_i } \right|} \) is minimum.
We calculate the intersection of two straight linesi·e:
and we shall verify if the point found out produces a minimum inz. If that did not happen, changing sistematicaly the values ora andb we should have the solution.
Also, the regression plane is
is minimum.
We give, too, the disposition of data in order to make the shortest calculations, as you can see by the two examples.
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Béjar, J. Calculo practico de la regresion en mediana. Trabajos de Estadistica 8, 157–173 (1957). https://doi.org/10.1007/BF03006468
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DOI: https://doi.org/10.1007/BF03006468