Econometric Methods

[bonles63]

Recall the regression model Yi = Beta0 + Beta1Xi + epsilon i. Prove that
Sum of Xiei=0.

I have no idea where to even start. If anyone can give me any ideas of how to even start this I would be SOOOOO grateful!

Thanks so much!

[Dragan]

Recall the regression model Yi = Beta0 + Beta1Xi + epsilon i. Prove that
Sum of Xiei=0.

I have no idea where to even start. If anyone can give me any ideas of how to even start this I would be SOOOOO grateful!

Thanks so much!

What you are doing (in effect) is showing that X and e are orthogonal to each other.

Use Sum(Xe) where e=(Y-Yhat).

So, Sum(X(Y-Yhat)).

Standardize: SumZX(Zy - rZX) because Yhat_ZY= rZX where r is the correlation coefficient.

Hence, Sum(ZXZY - rZX^2) = SumZXZY - rSumZX^2 = r(N-1) -r(N-1) = 0.

And this in one way to show that SumXe=0.

[bonles63]

so waht is z? we didn't talk about z's?
but thank you, becuase for the most part its starting to click!!! (sigh, thank god! )

shannon

[Dragan]

so waht is z? we didn't talk about z's?
but thank you, becuase for the most part its starting to click!!! (sigh, thank god! )

shannon

Z's are simply Zscores. You can take any set of data (X) and standardize it by using the linear transformation:

ZXi = (Xi-Xbar)/StdX

where ZXi will have a mean of zero and standard deviation of 1.