Question

Since prehistoric times what has been the correlation between atmospheric carbon dioxide level and global temperature

Answer 1

Answer:

The correlation based on one source of estimates of temperatures and CO2 levels (namely the Vostok data) is positive with an R^2 coefficient of about 0.75.

Explanation

There are only few sources of data for us to estimate this correlation over long periods of time. One of these are the "Vostok" ice core data that span some 400 thousand years of estimated temperature and CO2 levels (https://cdiac.ess-dive.lbl.gov/trends/co2/vostok.html). A paper referenced below shows the coefficient of determination of 0.75.

It should be pointed out that a correlation, and even more so causality between historical CO2 and temperatures has been subject of an ongoing scientific debate. This debate is further compounded by politically motivated factors. So it remains to be added: use care adopting conclusions of others in this active field of science, try to perform own analysis of raw/original sources yourself, whenever possible.

Reference: https://www.researchgate.net/publication/23226792_Global_warming_and_carbon_Dioxide_through_sciences