Multiple regression model

1. Oct 5, 2011

jasper90

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)

should I post this in a different section?

2. Oct 6, 2011

jasper90

mainly looking for help in B)...where do I even start?

3. Oct 6, 2011

Ray Vickson

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

RGV

4. Oct 6, 2011

jasper90

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
5. Oct 6, 2011

Ray Vickson

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

RGV

6. Oct 6, 2011

jasper90

Hi, I just editted my previous post, is that right?

7. Oct 6, 2011

jasper90

does my previous post look right?

8. Oct 7, 2011

help?