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Linear algebra 1. Partition matrices: Consider using a partition matrix in OLS. That is, consider X = [X1, X2] and B = B2 where X1 is n x 1, X1 is n x 12, Bi is 1 X 1, B2 is 72 x 1, and r1 + 72 = ", the overall number of columns in X. When we take the inverse of a 2 x 2 partition matrix -CA-IBJ-1CA-1 -(A-BD-C)-1BD-1 [C D = (A-BC-'D)- (D - CA-1B)-1 Find the equations for B1 and B2 using the OLS estimator B = (X'X)-1X'y Programming 2. Newey-West estimator: Extend the linear model code we wrote in class to implement a Newey-West corrected OLS estimator with autocovariance term. The robust variance covariance matrix for this Newey-West estimator is Var(B) = (X'X)-1X'Sx(X'X)-1 where 62 01 O 01 01 n = 0 01 02 . . . 0 . . . % . You can either create a new inheriting class or you can add the functionality as an option in the least squares code that we wrote. CS Scanned with CamScanner