I hope you can help me with the following problem: I have two sample groups. From the first group I know the explanatory variable x (pre-status) and from the second group I know the variable y (post-status). Unfortunately, I cannot measure them in the same experiment. Now, I would like to link these two groups in a regression analysis assuming that there is no structural difference between the two groups. Is it statistically valid to take all permutations of each sample from the first group and fit it against all y values from the second group? Afterwards, I plan to define the final model as the mean model of all permutation models. If this is indeed a common procedure, is there a name and / or literature for it? Finally, assuming x is only significant for some permutations, what statement can I make for the mean model?
Thank you for any hints and tipps. :-)
