my question needs some explanation first;

i want to test the efficiency of formulas for weight prediction but since medical literature has studied this before from different populations and different linear regression formulas with different coefficients are derived. In previous studies, first a population is divided into two groups, first group is used for model building, second group is used for model verification. i want to see if these different coefficients are results of different populations or same populations after different randomizations in a study.

my question is:

how reliable are different linear regression formulas derived from the same populations after randomization differently? although each time, the distribution of the population for modeling and verification changes (which makes populations distinct), is there a way to compare linear regression formulas performance?

preliminary results show that although after different randomizations result different coefficients, weight predictions of formulas are close with similar mean absolute and mean relative errors.

sorry for my humble english and repeatedly using the word "different"