In Skyrim attributes are health, stamina or magicka. The regeneration of each one if governed by the formula:
attribute regeneration per second = max * (base rate % * rate multiplier) + flat bonuses
Where:
max is the maximum attribute for the character, e.g. Altmer maximum stamina at the very beginning of the game is 90,
base rate % is the regeneration per second for that attribute for that race, represented as percentage over the max attribute. E.g. Altmer base stamina rate is 1.55%. Note that a few effects modify this:
the Apprentice stone increases magicka regen base rate by 0.75,
being vampire increases stamina and magicka regen,
having a summon active reduces the magicka regen by 0.40. See the Conjuration page for more info.
rate multiplier is the sum of every percentage-based regeneration bonus. Most regeneration bonuses fall in this value, for example
drinks, e.g. water increases the stamina rate multiplier by 1.15,
some standing stones bonuses, e.g. Lady increases the stamina regeneration by 1.4,
gear, e.g. Rigel's Armor Chest increases the stamina regeneration by 1.2
flat bonuses is anything flat-based that affects regeneration, for example
food, e.g. vegetable soup increases the stamina flat bonus by 0.8,
anything with the notation <value> / 100, like the tonic of stamina 80 / 100 increases the stamina flat bonus by 0.8 (the <value> / 100 representation is due to a limitation with the engine),
Altmer restores 1 magicka per second.
For example, the stamina regeneration per second of an Altmer with no stone nor blessing under the effect of water and vegetable soup is the following:
max = 90 (Altmer) + 20 (vegetable soup)
base rate = 1.55% (Altmer)
rate multiplier = 1.15 (water)
flat bonuses = 0.8 (vegetable soup)
stamina regeneration per second = 110 * 1.7825% + 0.8 = 2.76075