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Suppose you are interested in the effect of a variable X on another variable Y, and you believe that when X=0, Y is also 0. So you decide to estimate the model: instead of the more standard Y=nX +e cho ta t (1) (a) Under the assumption E[Xe] = 0, derive the population coefficient 1. (5 marks) (b) Under what conditions is beta,?. (4 marks) (c) Now suppose you have data on X and Y and you want to estimate the effect of X on Y. Is there ever a reason to use the model in equation 1 instead of the one in equation 2? Explain. (3 marks). (d) (BONUS-5 marks) Suppose you really really dislike intercepts and you want to estimate a model with no intercept, and still recover the correct effect of X on Y (i.e., 3). Is there a transformation of tY and X in the data such that a regression of Y on X with no intercept will give you the same estimate of the effect of X on Y as estimating 3, in equation 2?