More Testing, More Cases (?)

Pertaining to yesterday's post on the rise in cases, especially David's comment, here's the data I have on testing, which I record intermittently [viz. when I get around to it] from the John Hopkins site. (It's in their right-hand box, one arrow click over.) I don't know where to find historical data -- does anyone?)

I'm not exactly sure what to do with this. Surely the increase in cases is in some part due to an increase in testing -- test/case have doubled a doubling since late April -- but I don't know how to account for that in the number of cases, or the number of cases per day, to get a cleaner trend. If you do, please point it out in the comments. US deaths aren't rising, and the rate is trending down, so that says something meaningful. Can the spikes in Arizona and Texas and Florida be explained simply by more testing? I'm dubious but can be convinced by data and analysis, whether here or elsewhere. Maybe this.