One important thing to keep in mind is that the usage of “explains” in this statistical phrase is strongly misleading. I would call it straight-up wrong. From Joel Schneider’s Unfortunate statistical terms:
Variance explained: This term works if the predictor is a cause of the criterion variable. However, when it is simply a correlate, it misleadingly suggests that we now understand what is going on. I wish the term were something more neutral such as variance predicted.
Consider a faithful causal graph of this shape:
A <-- B --> C
Assume A and C are perfectly correlated. Trick question: How much variance does A explain of C? Answer: None. The association between A and C is purely statistical. A doesn’t explain anything of C. The “variance explained” phrase confuses correlation with causation. As Schneider says, “variance predicted” would be accurate, but unfortunately that’s not what statistics settled on.
The communication problem is that “variance explained” semantically implies measuring a causal effect, which it technically doesn’t do (in general).
One important thing to keep in mind is that the usage of “explains” in this statistical phrase is strongly misleading. I would call it straight-up wrong. From Joel Schneider’s Unfortunate statistical terms:
Consider a faithful causal graph of this shape:
A <-- B --> C
Assume A and C are perfectly correlated. Trick question: How much variance does A explain of C? Answer: None. The association between A and C is purely statistical. A doesn’t explain anything of C. The “variance explained” phrase confuses correlation with causation. As Schneider says, “variance predicted” would be accurate, but unfortunately that’s not what statistics settled on.
The communication problem is that “variance explained” semantically implies measuring a causal effect, which it technically doesn’t do (in general).
Agreed that the post is not about causality.