ST758 -- Fall 2011

  Homework #2 -- due Thursday, 15 September 2011

  Exercises in Textbook: (*just turn in these)
   2.14, 2.15 (on the computer you are using...), *2.26
   *3.14 but use p'=(.7,.1,.1.,1) (find (4x3) L numerically only), 
    3.20, 3.21, *3.23

  R Exercises:(just turn in 2), 3), 4) )

  1) Let y = (225, 215, 209, 175, 163, 135, 153, 125)' and let
     x = (37, 41, 41, 45, 45, 49, 49, 53)' be the covariate of
     a simple linear regression model, where the first column of
     the design matrix X is one, and the second column is x. 
     Compute y'Pone y, y'(Px-Pone)y, and y'(I-Px)y, where
     Pone is a matrix with each element equal to 1/n (here n=8),
     and Px is X*inv(X'X)X' the usual symmetric projection matrix.
  2) Read in the Cork Data from the file 'cork.dat' in the course
     'rfiles' directory.  Use 'readtable' or my old-fashioned code 
       Cork <- t( matrix( scan("cork.dat"), 4, 28) )
     which will make a 28x4 matrix.
  3) Compute the sample covariance matrix using var(Cork)
     and call this matrix V
  4) Partition the matrix V into the first two and last two rows/
     columns and compute V11 - V12*inv(V22)*V21
     *** use only 'chol' and 'forwardsolve'