I think what you can start with is to explore the percentage of times a particular app was opened (relative to the total number of times all the apps together opened). If this percentage remains stable, then there's no increment.

In order to test for the presence of trend, you can use the Mann-Kendall test (obviously, applied to the percentages calculated as described above).

Your regression solution will not work because if you compare your app to the total apps then you are comparing a subset of the population to the population of which it is a member so the appropriate statement is subset.

What you can say is that your app makes up p% of the total and then follow the change in p. As Andrey Davydenko suggests you can follow the trend of p which may be what you were thinking. You might wish to see this link: https://www.bing.com/search?q=statistical+test+for+trend&qs=n&form=QBRE&sp=-1&ghc=1&pq=statistical+test+for+trend&sc=3-26&sk=&cvid=C9E744C821E446E9AF9018C3259244BF

BTW I would plot p versus month first of all.

Best, D. Booth

Okey thank you for the information. I will read about the Mann-Kendall test, I didn't know about it.

P.S. It is better to the logit(p) instead of p when applying the Mann-Kendall test as p is will be a biased estimate of the percentage under interest.