please show the details

Q6. Consider the linear regression model y = X + f, where X is n x K and [3 is K x 1. After obtaining the OLS estimates (3) and the residuals (6), you add the residuals to the regression and run the OLS estimation on the following equation: y=X+eqv+v Note that 12 is the regression error term. Let 5 and 3 be the OLS estimates of {3 and 7 from the new regression. (a) Using the results in the partitioned regression, write 2:} using matrices like X, y and M. You must clearly dene the M matrix in this specic example. ' A (b) Prove or disprove: 5 = E (c) What is the value of '54