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When a linear regression model yields correlated errors it is claimed that the standard error of the estimators is under estimated. Can anyone give a proof of this fact? This is stated on page 94 of Introduction to Statistical Learning by James, Witten, Hastie, and Tibshirani

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  • $\begingroup$ Check this: stats.stackexchange.com/questions/114564/… $\endgroup$
    – Dole
    Commented Apr 10, 2016 at 1:13
  • $\begingroup$ A proof is impossible because the statement is false. When the errors are strongly negatively correlated, then the standard error of the estimators will be overestimated. Refer back to your source of the claim to check what additional assumptions or qualifications it is making--and please let us know what this source is. $\endgroup$
    – whuber
    Commented Apr 10, 2016 at 15:29

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