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Multiple regression model

  1. Oct 5, 2011 #1
    Consider the multiple regression model containing three independent variables
    y = B0 + B1x1 + B 2x2 + B 3x3 + u
    You are interested in estimating the sum of the parameters on x1 and x2; call this O1 = B1 + B 2
    a) Show that O hat1 = B hat 1 + B hat 2 is an unbiased estimator of O1.
    b) Find V ar(O hat 1) in terms of Var(B hat 1), Var(^B hat 2), and Corr(B hat 1, B hat 2).

    I get that for a) E(O hat1)= E(B hat 1 + B hat 2) = E(B hat 1) + E(B hat 2) = B1 + B2 makes it unbiased, but Im not sure what to do for b)


    help please

    should I post this in a different section?
     
  2. jcsd
  3. Oct 6, 2011 #2
    mainly looking for help in B)...where do I even start?
     
  4. Oct 6, 2011 #3

    Ray Vickson

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    Use the standard formula for the variance of a sum of random variables; see, eg.,
    http://en.wikipedia.org/wiki/Variance .

    RGV
     
  5. Oct 6, 2011 #4
    ok, thank you, so now i have this

    Var( O hat) = var( B hat 1 + B hat 2) = var( b hat 1) + var( b hat 2) + 2 Cov( B hat 1, B hat 2)

    Now, im supposed to have this in terms of Corr(B hat 1, B hat 2) also, how do I do that?

    This may sound dumb, but since Corr(x, y) = (cov(x,y))/( square root( var(x) var(y))......can i just multiply the whole right side of my equation by square root( var(x) var(y)) / square root( var(x) var(y)) then that would allow me to have the last term as 2Corr(x, y) square root( var(x) var(y)) ?
     
    Last edited: Oct 6, 2011
  6. Oct 6, 2011 #5

    Ray Vickson

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    How do you relate Cov to Corr? (It's in the book!)

    RGV
     
  7. Oct 6, 2011 #6
    Hi, I just editted my previous post, is that right?
     
  8. Oct 6, 2011 #7
    does my previous post look right?
     
  9. Oct 7, 2011 #8
    help?
     
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