Adjusting Beta

Can anyone tell me what the difference is between the Adjusted beta = (2/3)(Unadjusted beta) + (1/3)(1) and the whole levered/unlevered beta is? I think the levered/unlevered beta is for comparing similar companies, unlevering a public companies beta and then levering the beta of the company your trying to evaluate, but what is the above formula for? Thanks

above is for adjusting historical beta to a more current beta. kind of recognizing that the beta (historical) comes from a regression equation, and there is likely to be mean reversion. levered / unlevered beta is adjusting beta for differences in leverage between the public “comparable” company you picked and the target company.

Thanks CP