When describing some experimental results, if two physical quantities (let's call them a and b) seem to depend on each other, it is often desirable to say what happened with one of them if the other went up or down, using the words increase and decrease. If, for example, a = b, then there may be several choices of the same phrase:
- We observed an increase in b with an increase in a.
- We observed an increase in b with increasing a.
- We observed increasing b with increasing a.
Personally, I tend to use the 1st version because both "increases" are nouns, which gives the sentence a semblance of self-consistency. However, thinking like that, two gerunds in 3rd would also make the sentence self-consistent. Besides, I cannot quite justify why the 2nd could be wrong.
The question is, which one of the example sentences is correct, and if more than one, then what are the differences between them (e.g. maybe there are situations when one should be preferred over the other).