Egg Substitution for Cake Mix *Allergies*?

My daughter and I are allergic to eggs. I am making a betty crocker cake mix, and usually do the can of soda method because it is easy. Well I do not have an soda or carbonated beverage of any sort in my house and therefore have resulted to using a 1/4 cup of Plain Fat Free Yogurt for every egg called for and have otherwise followed the directions precisely. What I am wondering as my cake bakes is what will the end outcome be. Will it be the right texture and density? Have any of you had experience with using Yogurt for Egg substitution before and if so what else does yogurt work well for?