Could you rig a data set to have two lines of equally good (and best) fit? Or is it impossible?
2026-04-01 05:35:13.1775021713
Is it possible to have two lines of best fit?
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It is certainly possible (in mostly silly cases). For example, suppose you sample the same $x$ value twice and get two experimental $y$ values that differ. One such case might be getting the points $(0, -1)$ and $(0, 1)$ if we sample $x=0$ twice. Then, any line passing through the origin has SSE=2 which is the minimum possible. But of course there are many lines passing through the origin.
The root source of this problem is the fact that the "best-fit-slope", the $\beta$ in the formula here: http://en.wikipedia.org/wiki/Simple_linear_regression#Fitting_the_regression_line is undefined (division by $0$).