Sorry, but there is so much confounding an analysis of this sort that I can take a 30s look at it and blow holes a mile wide through it. For instance, there is no correction in there for density. There is also the fundamental problem of attributing cause and effect -- if the lockdowns reduce transmission, then no correlation in the outcomes could be exactly your goal. Put another way, I'd like NYC to have the same case load per capita as rural Utah. If lockdowns achieve that, you would evidentially tell me that rural Utah, with no lockdown, is the same as NYC and therefore the lockdown was useless. That is not a sound analysis.
The way to do an analysis of this sort is to find very tightly constrained natural experiments. Sweden and Norway (or Sweden and Finland) is an interesting example. Germany and Austria (picking them randomly, I don't know how well-coordinated their lockdown policies are). Or you can pick city twins, like NYC and Mexico City and compare the results each got from their approach.
IOW, in order to say something meaningful about effect of lockdowns, you have to go narrow, not broad.