Can we nevertheless extract causality from correlation?
I would argue that, theoretically, we cannot. Practically speaking, however, we frequently settle for “very, very convincing correlations” as indicative of causation. A correlation may be persuasively described as causation if three conditions are met:
Completeness: The association itself (R²) is 100%. When we observe X, we always observe Y.
No bias: The association between X and Y is not affected by a third, omitted variable, Z.
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Can we nevertheless extract causality from correlation?
I would argue that, theoretically, we cannot. Practically speaking, however, we frequently settle for “very, very convincing correlations” as indicative of causation. A correlation may be persuasively described as causation if three conditions are met:
Completeness: The association itself (R²) is 100%. When we observe X, we always observe Y.
No bias: The association between X and Y is not affected by a third, omitted variable, Z.
Temporality: X temporally precedes Y.