Prove That the Regression $R ^ { 2 }$ Is Identical to the Square of the Correlation Coefficient Between

Prove that the regression $R ^ { 2 }$ is identical to the square of the correlation coefficient between two variables Y and X . Regression functions are written in a form that suggests causation running from X to Y . Given your proof, does a high regression $R ^ { 2 }$ present supportive evidence of a causal relationship? Can you think of some regression examples where the direction of causality is not clear? Is without a doubt?

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