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321w4p1

# 321w4p1 - Assumptions in linear regression 1 E[u]=0 2...

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Assumptions in linear regression: 1. E[u]=0 2. E[u|X]=0 3. X and Y are iid random variables 4. Extreme values are unlikely 5. Relationship between Y&X is linear in parameters Under these assumptions, OLS provides useful estimates of population parameters

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Estimation using Method of Moments We can also estimate parameters β 0 and β 1 using two moments, E[u] and Cov(X,u). E[u] = E[Y- β 0 - β 1 X] = 0 and Cov(X,u) E[(X- μ X )(u- μ u )] = E[Xu] = E[X(Y- β 0 - β 1 X)] = 0
Our estimators satisfy the moment conditions: E [ Y 0 1 X ]= 0 E [ X Y 0 1 X ]= 0 , or E [ Y 0 1 X n 1 i = 1 n Y i 0 1 X i = Y 0 1 X = 0 which gives is the same condition as 6a, and E [ X Y 0 1 X n 1 i = 1 n X i Y i 0 1 X i = n 1 i = 1 n Y i X i 0 X n 1 1 i = 1 n X i 2 = 0 which gives is the same condition as 7a,

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So our method of moments estimator is the same as our least squares estimator.
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321w4p1 - Assumptions in linear regression 1 E[u]=0 2...

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