I know that correlation does not imply causality but does an absence of correlation imply absence of causality?
Solved – Does no correlation imply no causality
causalitycorrelation
Related Solutions
Correlation is not sufficient for causation. One can get around the Wikipedia example by imagining that those twins always cheated in their tests by having a device that gives them the answers. The twin that goes to the amusement park loses the device, hence the low grade.
A good way to get this stuff straight is to think of the structure of Bayesian network that may be generating the measured quantities, as done by Pearl in his book Causality. His basic point is to look for hidden variables. If there is a hidden variable that happens not to vary in the measured sample, then the correlation would not imply causation. Expose all hidden variables and you have causation.
The quick answer is, no. You can easily come up with non-related data that when regressed, will pass all sorts of statistical tests. Below is an old picture from Wikipedia (which, for some reason has recently been removed) that has been used to illustrate data-driven "causality".
We need more pirates to cool the planet?
For time series, there is a term called "Granger Causality" that has a very specific meaning.
http://en.wikipedia.org/wiki/Granger_causality
Other than that, "causality" is in the eye of the beholder.
Best Answer
No. Any controlled system is a counterexample.
Without causal relationships control is clearly impossible, but successful control means - roughly speaking - that some quantity is being maintained constant, which implies it won't be correlated with anything, including whatever things are causing it to be constant.
So in this situation, concluding no causal relationship from lack of correlation would be a mistake.
Here's a somewhat topical example.