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Prove That the Regression R2 Is Identical to the Square

Question 52

Essay

Prove that the regression R2 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 R2 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?

Correct Answer:

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The regression R2 = blured image , where ESS is given ...

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