Least Square Estimators - Unbiased Proof

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The Simple Linear Regression Least Squared Estimators, b0 and b1, are unbiased. In this video I show the proof.

  1. Stats4Everyone
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Комментарии
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THE BEST explanation on this topic on YouTube! Many Thanks! One question though: 1:02 why can we make such assumption #1? Or what's the meaning of that assumption? Xi is nonrandom. Appreciate any advice!

kevinshao
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Thank you so much for the great explanation! One question: Is there difference of E[yi] and y_bar ; similar like E[epsilon_i] and epsilon_bar. One is expectation, the other is the average? For example if E[epsilon_i] = 0, then epsilon_bar, the average over sample, also should be zero, right?

Tyokok
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why sum of (x-xbar)ybar would be zero in 4.29 while it is not zero with sum of (xi-xbar)yi??

turkialajmi
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Hi! I would like to ask why X bar is nonrandom? Isnt the (sum of Xi)/n ? Since Xi can be any value, shouldn't X bar be a random variable?

ckk
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How is (Xi-Xbar)Xi = (Xi-Xbar)(Xi-Xbar)

ramitarajesh
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You lost me at the first step. Namely, E(S_xy / S_xx) is taking the expectation of both the numerator and the denominator

guojunma