2. Consider the predicted values of Yi from a simple linear regression of Yi on Xi, which we refer to as Yi. Prove that the sample mean of Yi is equal to the sample mean of Yi (i.e. Y ). (3 points) 3. Consider the residuals (ui) from a simple linear regression. Prove that the sample mean of ui is equal to zero. (3 points) 4. Assume that Y and X are equal to zero. Prove that the sample covariance of Xi and ui is equal to zero. (3 points) 5. Suppose that you run a regression of Yi on Xi and obtain parameter estimates 1 and 2. Then, using the same data, you decide to run a regression of Yi on Xi, where Yi = 2Yi. Prove that both regressions have the same R2. (3 points)