Multiple regression model

  • Thread starter jasper90
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  • #1
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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?
 

Answers and Replies

  • #2
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mainly looking for help in B)...where do I even start?
 
  • #3
Ray Vickson
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  • #4
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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)) ?
 
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  • #5
Ray Vickson
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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?

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

RGV
 
  • #6
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How do you relate Cov to Corr? (It's in the book!)

RGV

Hi, I just editted my previous post, is that right?
 
  • #7
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does my previous post look right?
 
  • #8
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help?
 

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