In regression, if the residuals are correlated with X then what assumption has most likely been violated? 
*

*independence

*homoscedasticity



This question is from an online quiz with one "correct" answer, but I'm not sure I agree. I understand that the answer is homoscedasticity, but isn't independence violated here as well? Since heteroskedasticity indicates that residuals are correlated with X, then there is a dependency with x. Therefore, independence is also violated.
Could someone please explain?
 A: As both @AlecosPapadopoulos and @Glen_b note, there is a problem with the question.  Since they said the answer was 2 (heteroscedasticity), I wonder if they meant to ask: 'In regression, if the [standard deviation of the] residuals are correlated with X then what assumption has most likely been violated?'  However, that would be an awkward way to get at that idea (certainly not the question I would ask to probe that issue) and "are" should be "is" to maintain proper number agreement.  
An alternative interpretation would be 'In regression, if the residuals are correlated with X then [themselves,] what assumption has most likely been violated?'  This would make your choice of 1 (independence) correct.  A variable correlated with itself (at some lag) is autocorrelated, which @Stat discusses.  This can happen when the functional form of the variable is misspecified.  For example, if the relationship between $X$ and $Y$ is curvilinear, but a straight line is fit, then you may have, say, several negative residuals in a row, followed by several positive residuals in a row, followed by several negative residuals in a row again.  
In sum, the question is flawed.  Without more information from the asker, it is impossible to say exactly what the deal is.  
