The OLS estimator for the simple linear regression model can be written as
where
In the case for a sample size of three observations (T=3), this estimator can be written as:
where
Assume that the full set of assumption of the SLRM hold.
Without using summation notation, use the fact that to find .
Explain how the assumptions of the model are used to arrive at your answer.
i started by equating (definition of variance),
then using known results to
would greatly appreciate if anyone could help me derive without using any summation notation.
i suppose the end resut of [using a proof that uses summation notation) would be
and,
and