If we have a dataset with two variables, X & Y, we can find the line of best fit using the empirical data (and whatever method suits you best).
However, what if know the true joint distribution of X & Y, how could we find the "true" line of best fit?
For example, if we have X & Y distributed uniformly such that 0 < X < 1, 0 < Y < 1 and X + Y < 1, the line of best fit should be the line y = -0.5x + 0.5.
Can this be generalised to any joint distribution? If not what are the limitations?