Solve I - IV Please!

Be aware that in the matrix equations that follow, the order in which symbols occurmattiers: in matrix murtlpi'i'catlon. the product depends on the order of the factors. Now we generalize the resurls of the previous section. by expanding to an arbitrary number of feature vectors. For any linear design problem in any number of d variables hg. .. . ,d . the model Y ~ P = rim +J32X2 + was can be solved using matrices as follows: I. compute G = X 'X . where)! is the data matrix whose columns are the feature vectors: II. compute H = G" . which Is the inverse matrix of G; ill. compute the optimal weights. organized in the column vector ' = HY'X. iv. the optimal prediction ls l3 = X'. In Fl, the transposition operation is written as tot} , and matrix multiplication is 96"?!) Here is a sample calculation that illustrates these steps. It begins by loading the pracma library that contains the matrix operation commands. library (pracma ) X= matrix(c( 2, 4,3,2, 1,3, 1, 1, 4,5,8,-1) , nrow=4, ncol=3) print (X) # # [ ,]] [,2] [,3] ## [1, ] 2 # # [2, ] 3 5 ## [3, ] 3 1 8 # # [4, ] 1 -1 G