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In particular this is the go to approach in case of solving a least squares problem that lacks a unique solution, how does being the closest point to the origin among all the solutions make it any better than the others?

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  • $\begingroup$ The method you describe is so arbitrary that I wonder whether you could provide a credible reference. It would be less arbitrary to apply this criterion to the standardized coefficients. $\endgroup$ – whuber Sep 25 '20 at 16:09
  • $\begingroup$ The least norm solution is the one provided through singular value decomposition whenever one calculates the pseudo-inverse. $\endgroup$ – Essam Sep 25 '20 at 16:11
  • $\begingroup$ @whuber This is a standard topic taught in most linear algebra courses. I think what's missing in the question is how this mathematical topic relates to statistics. Perhaps this should be migrated to math.stackexchange if no additional information is given? $\endgroup$ – Eric Perkerson Sep 25 '20 at 17:57
  • $\begingroup$ For example, Gilbert Strang does this exact thing near the beginning of this video lecture: ocw.mit.edu/courses/mathematics/… $\endgroup$ – Eric Perkerson Sep 25 '20 at 18:13
  • $\begingroup$ This is the solution you will find if you regularize the problem as ridge regression ... showing why it is natural. $\endgroup$ – kjetil b halvorsen Sep 25 '20 at 21:46

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