Personally it varies too much by situation to have a general rule, but something like the above is reasonable. I'd probably be more like 1 prod = 1.5 culture = 1.5 science = 2 faith = 3 gold, but there's certainly a lot of cases that it varies:
-Early game, before a pantheon, getting that first faith is big. Obviously 1 faith + 1 gold > 1 prod early, and before the pantheon, 1 faith + 1 gold > 2 prod. But once that pantheon drops, I basically stop caring about faith until much later, when I start seeing what I can do with it.
-And then depending on the game, I either value faith as equal to the other yields or virtually 0. If I'm not going religion, then most of the time I treat faith as a pure "bonus" resource. If I get enough faith to make it useful, great. Otherwise I ignore it. But if I'm going religion-heavy, then I might value it as much as science or culture, and more than production (my last game, where I had Valetta + Jesuit Education + Theocracy + Goddess of the Harvest, production meant virtually 0 for me, other than for being able to churn out builders to chop things)
-And in a general game, how I value science vs culture basically depends on how much of each I'm getting. If I'm lucky and get enough culture from city-states like Kumasi or Nan Mandol, then I might value science more. But other games where I really struggle for culture, then I might rather value 1 culture at 2 or more science (for example, if I'm thinking about which policy card to run, or which city-state to send an envoy to).