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I am having trouble understanding how i should approach the following problem: Given ๐‘ฆ๐‘– = ๐›ผ + ๐›ฝ๐‘ฅ๐‘– + ๐œ€๐‘– ๐‘– = 1, โ€ฆ , N with ๐œ€๐‘– ๐‘– = 1,2 โ€ฆ , N being a succession of IID Bernoulli variables with Pr({๐œ€๐‘– = 1}) = 1 , Pr({๐œ€๐‘– = 0}) = 1 โˆ’ P 0 < ๐‘ < 1 (p is a known parameter). Find the OLS estimators for ๐›ผฬ‚ e $\widehat{๐›ฝ}$.

From this thread, it would appear that the given residuals are missing the mean=0 and costant variance requirements for the ols to be BLUE.

What would the estimated $\widehat{Y}$ function look like? Would the ๐œ€๐‘– term disappear as usual?

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