If you have a very sound theoretical backing for your coefficients to be positive, then you could use bayesian regression method and set the prior distributions from positive distributions:    Here are some helpful links for bayesian regression:   1) Basic setup of model using proc Genmod: https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_genmod_sect007.htm   1a) How to change priors:  https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_genmod_sect012.htm   Alternatively (This might be the best proc to use in your case): Proc MCMC is another possible solution: 3) Proc MCMC linear regression: https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_mcmc_sect004.htm   Here note that I am assuming that you have very solid theoretical backing for your Beta coefficients to be positive. This is a very strong assumption and has to be based on evidence from prior literature or some other source.    ... View more