I don't agree that there is not a correlation, it looks like there is from the chart (even though it's the wrong chart that you display).
It makes no sense to standardize for the cost off living, that's the point in the first place that NY etc have higher taxes partly because of the higher cost of living and therefore have higher wages and expenses and pay more federal tax. So the only relevant chart is the one you mentioned and linked to not the one displayed in the post. There does appear to be a pretty clear trend that blue states pay more in both local and federal taxes and that there is a strong correlation between states having high local and federal tax payments.
I'd certainly agree that -- all things being equal -- people in a city where costs of livings (and hence salaries) are twice as high will pay more in a progressive federal income tax system than people in a city where the cost of living (and hence salaries) are more reasonable. That's a different argument from the argument the economies are thriving in high tax states and thus they pay more in taxes, which is what I understood you to be saying in your previous post.
Also, note that I didn't say there wasn't a correlation, I said that the correlation wasn't that strong and that is was mostly the result of five states.
-Using data from every state but Deleware, there is a statistically significant correlation between federal tax paid per capita and state income/property tax paid per capita. However, the R^2 of the correlation is only 0.264
-Take out the five states I mentioned in my first post, and there is no statistically significant correlation between the two measures of tax burden in the remaining 44 states.
@Undecided, sure thing, I should have done a better job of documenting my sources in the original post but it was already getting rather long.
Federal tax revenue comes from Table 5 in this PDF:
https://www.irs.gov/pub/irs-soi/15databk.pdfState per capita income tax values:
https://taxfoundation.org/individual-income-tax-collections-per-capita/State per capita property tax values:
https://taxfoundation.org/property-tax-per-capita-2017/The federal data is from 2015, the state data is from 2014, which is not ideal.
Controlling for cost of living let me separate out the effects of cost of living:
The taxes in NY/San Fran etc are high because costs are high- teachers, police, firefighters etc all need to be paid more.
From the effects of differences in the actual strength of the economy between different states.