3. (Residual 85 Decomposition - 40) For the ordinary Multiple Linear Regression model Y N N (X )6, 0212\"\"), we use the OLS estimator for . X E Rn\"? has rank p. Denote the residual vector as e = Y Y. (a) Find X Te. You need to write out the dimension of the resulting matrix/ vector. (b) Explain the meaning of the equality in (a). (Hint: think about the columns of X) (c) What can we conclude if the linear model includes the intercept term? (d) Does the conclusion in (0) still holds when there is no intercept term but there is one column with the rst k