Quote by statdad
I'm a little confused about your question? Are you asking whether regressing X on Y will always give the same coefficients, or whether it is ever possible to get the same ones?

(X_i, Y_i), i=1,2,...n
Y hat is a fitted (predicted) value of Y based on fixed values of X.
Y hat = b0 + b1 *X with b0 and b1 being the leastsquare estimates.
For X hat, we are predicting the value of X from values of Y which would produce a different set of parameters, b0' and b1'. Is there any general mathematical relationship linking b0', b1' and b0, b1?
Thanks for answering!