Do I have to move all units in the area I have attacked?
Yes, you already moved those troops during the March Orders step.
The rule book indicates that all troops are moved or not moved during the March Order, before combat begins. If you wanted to leave some troops behind, you need to do so before you begin combat and you cannot add those units to your combat strength.

-When a player moves one or more units into an area containing units from another house, he starts a combat as the attacker.  See rules for combat on page 17.
-Before resolving combat, all other non-combat movement from the area assigned the March Order must be completed.

This is further supported by the rules for retreating on page 21. The retreating units are currently in the embattled area, and must retreat back to the area they marched from.

If the attacker lost the combat, his surviving units must retreat back to the area from which they marched.