Nuisance regression is commonly used to reduce the influence of nuisance effects on functional connectivity (FC) estimates. Here we demonstrate that FC estimates across different scans are significantly correlated (prior to nuisance regression) with the norms of various nuisance signals including head motion regressors and signals from non-functional regions. We further show that nuisance regression does not necessarily eliminate the observed correlations between the FC estimates and nuisance norms. We demonstrate that the limited efficacy of nuisance regression is partly due to a theoretical bound that limits the difference in FC estimates obtained before and after regression.
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