Believe it or not, there is something called the "Suess effect" that uses the change in the atmospheric ratio of stable carbon isotopes, Carbon-13 and Carbon-12, that basically does what you asked. I.e., it fingers fossil fuel burning as the main cause of the increase in atmospheric CO2 concentration since the mid-1800s. The next step is determining the contribution of increasing CO2 to global warming, which is what is being done now. Better data means better results.
It is impossible to understand what kind of "error correction analyses" was done here.
What they say is "We took the data and changed it for an error and poof, the numbers look exactly like we want them to."
This is exactly the same thing that resulted in the "hockey stick fiasco."
So, what was the ratio of Carbon-13 to Carbon-12 molecules in the atmosphere, in say, the 1300's? Like I said, a couple hundred years of data, compared to who knows how many years before, does not impress me.
Let's just say I know something about science and the scientific method, for the record. And, let's just say I'm also an interested student of human nature...
In my opinion, we've got a LOT of inaccurate conclusions out there, resulting from the improper use of data, due to selfish interests of either individuals or groups, WHETHER THEY REALIZE IT OR NOT.
I have respect for the scientific community, but we/they are not flawless, and no matter how hard they try, they are NOT 100% objective. And even if they were, they do make mistakes.