If you mean dependence among X elements, yes we do. If the variables (elements of X) are highly correlated, then we face "Multi-colinearity" problem which results in the coefficients "b" having large (inflated) variances, i.e., a small change in a variable may cause a big change in the corresponding "b". To detect this issue, you can use Variance Inflation Factor (VIF) = 1/ (1-R^2). VIF > 5-10 indicates multi-colinearity.