3
$\begingroup$

What happens in linear regression $Y\sim X$ when the $Y$'s are not independently sampled and, particularly, may be autocorrelated?

I believe the estimator will still work. But what will happen to the t-stat and the R-squared that measures the goodness of fit?

Any other implications I might not be aware of?

$\endgroup$
  • $\begingroup$ If the observations are not independent, then the least-squares estimates are still unbiased, however, the standard errors of your estimates can be seriously biased and very misleading, and lead to seriously biased incorrect conclusions from statistical tests. $\endgroup$ – StatsStudent Mar 19 '15 at 23:20
  • 1
    $\begingroup$ @StatsStudent you should post that as an answer. Answers don't need to be technically involved to be helpful and correct $\endgroup$ – shadowtalker Mar 19 '15 at 23:31
1
$\begingroup$

As @ssdecontrol indicated, here's an answer without much explanation:

If the observations are not independent, then the least-squares estimates are still unbiased, however, the standard errors of your estimates can be seriously biased and very misleading, and lead to seriously biased incorrect conclusions from statistical tests.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.