Hi Julie, often times applesauce can be used to replace up to 25% of the oil or butter (rather than eggs) in a recipe. You'll be better off using all vegan butter instead of a combination of butter and applesauce in this case. To replace the eggs, we typically recommend using Golden Flax Meal blended with water. (For full instructions use this article on our blog.) Keep in mind that eggs play a crucial role in the structure of cake, so the texture may be slightly different than what it otherwise would be in this recipe. (It's still worth giving it a shot, we think!) For the yogurt, we recommend using a plain soy yogurt, which tends to be the tangiest of all the non-dairy yogurts. Happy baking! Kye@KAF

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