Question: Consider the following model Y; = X; 31 +u;, i = 1,...,n without an intercept. This model is used only under the assumption that E(Y)

Consider the following model Y; = X; 31 +u;, i = 1,...,n without an intercept. This model is used only under the assumption that E(Y) = E(X)= 0. We maintain this assumption here. (a) Derive the OLS estimator 3, for 51. Show your steps. (b) Given a dataset, suppose we know that the sample correlation coefficient between X 100 and Y is 0.5, the sample variance of X is 4 and that of Y is 60. Compute 31. (c) Now suppose we regress X on Y without an intercept. Given the information in (b), can you find the OLS estimate for the coefficient on Y?

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