Ramadan: Was Abubaker appointed by Rasoolallah (saww) as Khalifa or by the people?

at the time od death of holy prophet ...most of muslims were outside the medina ...and delayed the movement......ansaar claimed being in majority .......but mahir insisted thier claim being .....more time in being muslim........with holy prophet only from family members and 3/4 sahabas like salman ,abu zer ,............ then decided ..that from mahajir ...and from quresh...and being the oldest one .......[there is famous joke .... abu qaifa said to his son .....oh abu baker ...then i am the most qualifying person for the khalifat]..........2] hz umer confessed to hz abaas ...that it is the right of bnu hashim ...but peoples will take it ill and will make it tribal issue ...Ali is young and it will reach him ..there will be ample chances for him.....