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Estimate a simple linear regression of y on x

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Suppose you estimate a simple linear regression of Y on X, and another simple linear regression of X on Y.

(a) Write down the condition that must hold for the estimated slope coefficient for a regression of Y on X and the estimated slope coefficient for a regression of X on Y to be reciprocals of one another? Hint: Look carefully at the formula for OLS slope estimator.

(b) Suppose you find that the estimated slope coefficient for a regression of Y on X is greater than the estimated slope coefficient for the regression of X on Y. Would that fact help you to make a decision as to whether X or Y should be your explanatory variable? Answer "Yes" or "No" and briefly explain.

Reference no: EM133068183

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