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coefficient of correlation, regression

Help is given with coefficient of correlation, regression, etc.


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if you can't read it clearly, please refer to the attached WORD file.
<br>3.13 X1, X2, X3 are uncorrelated, i.e. cov(Xi,Xj)=0 for all I<>j
<br>Let Var(Xi)=S
<br>Then Var(X1+X2)=E([(X1+X2)-E(X1+X2)]^2)=E([X1+X2-E(X1)-E(X2)]^2)
<br>= E(([X1-E(X1)]+[X2- E(X2)])^2)=E(([X1-E(X1)]^2+[X2- E(X2)]^2+[X1-E(X1)]* [X2- E(X2)]
<br>= E([X1-E(X1)]^2)+E([X2- E(X2)]^2)+E([X1-E(X1)]* [X2- E(X2)])
<br>= var(X1)+ var(X2)+cov(X1,X2)=S+S+0=2S
<br>in the same way, we can prove that Var(X3+X2)=2S
<br>Now, Cov[(X1+X2),( X3+X2)]=E([(X1+X2)-E(X1+X2)]*[(X3+X2)-E(X3+X2)])
<br>=E{([X1-E(X1)]+[X2-E(X2)])* ([X3-E(X3)]+[X2-E(X2)])}
<br>=E{[X1-E(X1)]* [X3-E(X3)]+ [X2-E(X2)]* [X3-E(X3)]+ [X2-E(X2)]* [X1-E(X1)]+[X2-E(X2)]* [X2-E(X2)]}= E{[X1-E(X1)]* [X3-E(X3)]}+ E{[X2-E(X2)]* [X3-E(X3)]}+ E{[X2-E(X2)]* [X1-E(X1)]}+E{[X2-E(X2)]* ...

Solution Summary

This job explores coefficient of correlation, regression, and other terms.