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Solving for a matrix finding the unique sym matrix (Regression Analys)

  1. Feb 5, 2014 #1
    1. The problem statement, all variables and given/known data

    A)Determine the elements of the matrix G such that GY = (Y1 +Y2 + Y3, Y3-Y1, 0.5Y1 - 0.5Y3 +2Y2)'
    B)Find the unique symmetric matrix A such that Y'AY = Y'GY.

    Y=
    [2
    7
    6]

    2. Relevant equations



    3. The attempt at a solution
    I know that Y1=2, Y2=7, and Y3=6. That means the right hand matrix should be

    Z=
    [15
    4
    12]

    So:
    GY=Z
    GYY'=ZY'
    G=ZY'(YY')^1

    Using proc IML in SAS I get something like:
    0.3370787 1.1797753 1.011236
    0.0898876 0.3146067 0.2696629
    0.2696629 0.9438202 0.8089888

    However, I was talking to a friend, and he just matched up the coefficients and got
    G=
    1 1 1
    -1 0 1
    .5 2 -.5

    This also makes sense to me, so I don't understand why our numbers would be so different. Did I do something wrong in my equation above?

    For part B, I did the same thing

    Y'AY = Y'GY
    Y'AYY'=Y'GYY'
    Y'AYY'(YY')^-1 = Y'GYY'(YY')^-1
    Y'A=Y'G
    YY'A=YY'G
    (YY')^-1YY'A=YY')^-1YY'G
    A=G

    However, G is not symmetric (in either case). I'm not sure what else I can do.

    Thanks in advance for the help.
     
  2. jcsd
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