Linear Regression - important requirement I of beta: it should be unbiased, we need assumptions for this

5 important questions on Linear Regression - important requirement I of beta: it should be unbiased, we need assumptions for this

0.a 1st assumption: specification is correct.

That you truly believe that y depends on chosen x's, linearly & the error term.

1. 2nd assumption:epsilons on average or equal to zero

On average we don't make a mistake

4. Final one, we use it here but later on we relax it, we assume that the x-variables are not stochastic.

So we truly know what x is. Note that with a stochastic or random variable we don't know ex ante.
so regarding
y=xB+e
we truly know these
x not a variable, doesn't have covariance, so covariance between c and e is also 0. &we need this later on.

so these two, epsilons are zero on average and that x is non-stochastic, enough to show you that indeed my beta estimator is unbiased.
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0b:incorporated in 0a;

x-variables are ofcourse not multi collinear.

If x is a random variable, a term in true beta proof can be interpreted as a covariance between xi and ei.

If we later on relax the assumption of non stochastic then the assumption will become that the Covariance(xi, ei)=0 otherwise biased beta.

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