I invite OP's attention to
https://www.drroyspencer.com/, specifically
Explaining Mauna Loa CO2 Increases with Anthropogenic and Natural Influences -- April 9th, 2022 if it's no longer top of page.
He was cited by someone he (and you) disagree[s] with, but he leans into statistical regression pretty heavily. It might be of interest.
Quote:
In addition to the master equation having a basis in physical processes, it avoids the problem of linear trends in two datasets being mistakenly attributed to a cause-and-effect relationship. Any time series of data that has just a linear trend is perfectly correlated with every other time series having just a linear trend, and yet that perfect correlation tells us nothing about causation.
But when we use the time derivative of the data, it is only the fluctuations from a linear trend that are correlated with another variable, giving some hope of inferring causation.
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