Regression - Expected Values and Variances of the OLS estimators
4 important questions on Regression - Expected Values and Variances of the OLS estimators
What four assumptions (SLR1-SLR4) are needed for unbiasedness of OLS?
SLR2 (Random sampling): We have random sample {(x(i),y(i));(i)=1,..,n} following SLR1's population model
SLR3 (Sample variation in the explanatory variable): The sample values x1,..,xn of the explanatory variable are not all the same
SLR4 (Zero conditional mean): E(u|x)=0
SLR1-SLR4 gives us E(^B0)=B0 and E(^B1)=B1
What additional assumption is needed for deriving variances of OLS estimators?
SLR5 (Homoskedasticity): var(u|x) = o2
SLR4 and SLR5 are equivalent to E[y|x]=B0+B1x and var(y|x)=o2
What is the sampling variance under SLR1-SLR5?
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How can the error variance and the standard error be estimated?
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