# OLS Regression equation [closed]

This question is primarily for my understanding; say we have a regression equation of the form Y = Xb, where X is a matrix of a few explanatory variables. If you are told that the vector 'b' does not exist, would this equation still have any value? Does it mean we are seeing a non-linear relationship between X and Y?

Thank you!

• More context, please. You’re always allowed to pick a b vector such that the matrix multiplication works out, so b not existing seems like nonsense to me unless there is additional information. (Such a b chosen at random is unlikely to be useful, sure, but it exists.)
– Dave
Sep 11 at 16:21
• I definitely agree that we need context here (and I think it should have been closed until the question was clarified). However I am confused by the additional comment. If Y and X are given, I am not sure we can always pick a $b$ to make the equation $Y=Xb$ true. How would we do that? Of course if you add in an error term you have lots of d.f. to play with. Sep 12 at 0:01