Scholarly articles about the correlation between CO2 and temperature.
We use a newly developed technique that is based on the information flow concept to investigate the causal structure between the global radiative forcing and the annual global mean surface temperature anomalies (GMTA) since 1850. Our study ...
www.ncbi.nlm.nih.gov
Graphs of CO2 and temperature over different time scales.
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Previously, we looked at the correlation between CO2 and temperature over the past 40 years. However, as I'm always saying, you need to look at the broader view, not just a single piece of the puzzle. The 40 year period was chosen to demonstrate that even during a period of long term warming...
skepticalscience.com
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Global annual average temperature (as measured over both land and oceans) has increased by more than 1.5°F (0.8°C) since 1880 (through 2012). Red bars show temperatures above the long-term average, and blue bars indicate temperatures below the long-term average. The black line shows atmospheric...
www.globalchange.gov
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This is the closest to the original question. The answer seems to come from climate science rather than statistics. Even though the graph has an R-squared value of 0.752, showing a consistent linear relationship between CO2 and temperature, climate science seems to indicate that increases in CO2 have a logarithmic relation to changes in temperature. The best numbers that I could find are for every doubling of CO2 global temperature increases 3C.
I have had three semesters of college statistics as part of my BSBA degree. From what I recall from regression analysis the graph seems to show a very high coefficient of determination between CO2 ...
stats.stackexchange.com
And if you know some statistics this website provides:
The average coefficient of determination (R-squared) turns out to be 0.752
Asynchrony between Antarctic temperature and CO2 associated with obliquity over the past 720,000 years
For the entire record, the 90% confidence ranges of the correlations (R-squared) of CO2 with δD, ΔTsite and ΔTsource are 0.68–0.73, 0.76–0.80 and 0.75–0.79, respectively.
And finally
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<p>When CO2 levels were higher in the past, solar levels were also lower. The combined effect of sun and CO2 matches well with climate.</p>
skepticalscience.com
The absorption of IR by CO2 was demonstrated in the lab in 1856. These days, the results of more accurate instrumentation in the lab provide us these data:
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"Engage atomic energy"??? Did you actually think that sounded like you knew what your were talking about?
Those laboratory experiments have shown that for the frequencies that CO2 absorbs, its concentrations in the atmosphere is sufficient to absorb 100% of radiated energy in a column length of less than 10 meters.
[Sadly shakes head]