OLS unbiased

Understanding why and under what conditions the OLS regression estimate is unbiased.
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[@user-vf6eq5fb3z]

Finally a video that clarify that doesn't make sense assume that Xi is not random for most of our observations. Thank you so much!!

[@MalissaAli]

This is very easy to understand, thank you so much

[@alizzhimekariya904]

At 13:39, can we switch the ui to in front of [sigma (xi-xbar)/sigma(xi-xbar)^2) so that we can let sigma(xi-xbar)=0? Sry if I make a mistake, I'm just new to econometrics :p

[@billsundstrom8948]

Nope. If ui were a constant, we could factor it out and move it to the front of the sum as you propose. But it varies with i, so it cannot be factored out. This is a property of the maths involved, not the econometrics per se. Hope this helps, Bill

[@alizzhimekariya904]

@@billsundstrom8948 thank u so much for the explanation

[@priya7008]

Amazing video. Cleared everything up thanks

[@allwanamar1]

finally someone proving this . thank you very much .

[@thilinapremjayanth9372]

Thank you so much for the video. But i have a question. Here you mention that SIgma(Xi-X bar) is always zero. If SIgma(Xi-Xbar)Ubar=0 why SIgma(Xi-Xbar)Ui doesnt equal to zero?

[@cavidseyidli6871]

Thilina Premjayanth check that with sample (1,2,3,4,5) then u will see why it is not equal to 0

[@7479zm]

Thank for your videos, they are really helping me a lot. At 8:29, I lost you, you say that the sum of the deviation of x from its mean is equal to zero, I get that, did you not remain with Ubar of the last term?

[@rings4433]

Probs a bit late, but it's because of the average of the residuals is 0, not X.

[@Explorer982]

excellent. please do one for consistency !

[@williamcinemat7362]

great video ,thanks alot , so i was doing some revision and i encountered the question :econometric Q: Suppose we have n observations on the model Y=XB+U,where E(U)=0 and cov(u)=V n*n, V-completely known positive definite. suppose X n+1 is a new observation on an exogenous variables of the model,predict the corresponding Y n+1, the value of the endogenous variables? can you help me out?

[@gmayank32]

Thank you so much for this video. It is very useful. One thing I didn't understand that for a sample, how can X be fixed? From the video example of amount of fertilizers for different plots, I am assuming that a fertilizer amount is considered for a plot. If the sample is taken from this plot then we are calling it fixed X (amount of fertilizer), where dependent variable (yield maybe) is different at different point in time with errors?

[@williamsundstrom6103]

Mayank, that's a great question. You are of course correct that in non-experimental settings the X is not fixed across random samples. Under the standard least squares assumptions, given fixed X, E(b^) = b (pretend the b is beta). Another way to put this is that expected beta hat is equal to beta CONDITIONAL on the Xs:
E(b^ | X) = b
But when that is true, we can use the law of iterated expectations to conclude that
E(b^) = Ex(E(b^ | X)) = Ex(b) = b,
where Ex means expectation over the distribution of X.
The idea is that if the estimate is unbiased for any given random draw of Xs (treated provisionally as fixed), it will also be unbiased over over a large number of random draws of X, estimating unbiased beta^ each time and averaging across all the random draws.
Hope this makes some sense... Bill

[@gmayank32]

@@williamsundstrom6103 Thanks. It makes sense.

[@SonGoku-uv4pk]

Thanks so much

[@mercysereka5055]

Thanks alot, nice idea

[@sticky1963]

THANK YOU

[@UcheNnodi]

thanks

[@geetaverma8449]

Great explanation keep it up😄😍

[@citkat5743]

Appreciate this.

[@makwazamwanino3885]

he has a gift

[@williamsundstrom6103]

Thanks Makwaza! Glad it is helpful, wish I had more time to make more of these.

[@fatimajunejo3960]

thanks