# What happens in linear regression if Y's are not independently sampled?

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?

• 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. – StatsStudent Mar 19 '15 at 23:20
• @StatsStudent you should post that as an answer. Answers don't need to be technically involved to be helpful and correct – shadowtalker Mar 19 '15 at 23:31