STAT 350: 95-3

Assignment 5: First Draft only

Part A

  1. In this question you will derive some of the formulas for case deleted statistics. Suppose that X is an tex2html_wrap_inline50 design matrix. Let tex2html_wrap_inline52 be the tex2html_wrap_inline54 row of X (so that, tex2html_wrap_inline58 is a column vector or dimension p). Let tex2html_wrap_inline62 be the design matrix with case i deleted and tex2html_wrap_inline66 the vector of n-1 responses with case i deleted.

    1. Use partitioned matrices to show

      displaymath72

    2. Show

      displaymath74

    3. Suppose B is an invertible symmetric tex2html_wrap_inline78 matrix and v is a column vector of dimension p. Show, by direct multiplication, that tex2html_wrap_inline84 is of the form

      displaymath86

      and give a formula for the scalar r.

    4. Apply to previous part to show

      displaymath90

      and give a formula for tex2html_wrap_inline92 in terms of the leverage tex2html_wrap_inline94 .

    5. Show tex2html_wrap_inline96 .
    6. Show that

      eqnarray32

    7. Deduce that tex2html_wrap_inline98 .
    8. Show that the tex2html_wrap_inline100 PRESS residual tex2html_wrap_inline102 is given by

      displaymath104

    9. Derive the formula for the tex2html_wrap_inline106 externally studentized (case deleted) residual.

  2. For the Nitrogen output in Wallabies data set from Assignment 3 do forward, backward, stepwise and all subsets regression.
  3. Problem 23.12, 23.13 parts c,d,e,f,g only and 23.14.
  4. Problem 25.11 parts a, b anc c, 25.12 part c.


Richard Lockhart
Mon Mar 3 14:02:07 PST 1997