Problem 4. (Extra Credit) A student wants to predict a variable, Y E R", from two other variables, X1 E R" and X2 E R", using multiple regression. The student defines a new variable X3 = X1 + X2 and uses multiple regression to predict Y from X1, X2, X3. Show why this method is problematic. Hint 1: Anxn is invertible Rank(A) = n. Hint 2: Rank(AB)