ST790R -- Fall 2010

  Homework #2 -- due Thursday, 16 September 2010

  Exercises in Textbook: (*just turn in these)
  *2.14, 2.15 (on the computer you are using...)
   3.14 (find (4x3) L numerically only), 
    3.20, 3.21, 3.23(note error, see (5.9.4))

  *0) (similar to 3.23) Find the derivative of the determinant of
   a matrix with respect to one of its elements.  (Hint: use
   the result |I + ab'| = (1+b'a) )

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

  1) Let y = (4.82, 4.88, 4.70, 4.72, 4.88, 4.66, 4.94, 4.80)' and let
     x = (38, 40, 42, 44, 36, 42, 38, 40)' 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 Ramus Data from the file 'ramus.dat' in the course
     'rfiles' directory.  My old-fashioned code is
       Ramus <- t( matrix( scan("ramus.dat"), 4, 20) )
     which will make a 20x4 matrix.
 *3) Compute the sample covariance matrix using var(Ramus)
     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' ***