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. (5 pts) (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. (5 pts)