In the present study, we demonstrated that the accuracy of the global signal regression is determined by the level of global noise by using simulation. When the global noise level is high, the global signal resembles global noise. When the global noise level is low, the global signal resembles the R-fMRI time courses of the largest cluster, but not global noise. We then showed, using real data, that the global signal is strongly correlated with the default mode network components PCC and precuneus. To answer the question as to whether or not the global signal should be considered a nuisance effect to be removed, we introduced a global negative index to quantify global noise levels. We demonstrated the monotonic relationship between the signal-to-global noise ratio and the global negative index. Finally, we discovered that there is a criterial global negative index associated with a criterial SGNR. Below this criterial global negative index, performing global signal regression induced less errors, therefore, it is highly suggested that the global regression be performed. Above this criterial global negative index, performing global signal regression induced more errors. Therefore, we suggest that the global signal regression not be performed. One can decide whether or not to apply this technique for each individual data set by comparing the global negative index of the data set to the criterial global negative index.

The findings of the monotonic relationship between SGNR and GNI is one of the most important components of the study. However, their relationship was obtained empirically, and it is important to understand the mechanisms. Theoretically, when SGNR is +∞, the global signal resembles the R-fMRI time courses of the largest cluster. Therefore, the GNI will approximate the percentage of the number of voxels that are negatively correlated with the largest cluster. When the SGNR is 0, the global signal will resemble the global noise, which will be positively connected to every voxel. Therefore, the GNI will be 0. When the SGNR is between 0 and +∞, the global signal will resemble a mixture of R-fMRI time courses of the largest cluster and global noise. Therefore, the GNI will depend on the ratio of the two components in this mixture, which is determined by the SGNR. As a result, the GNI may be used to estimate SGNR and gauge the *r* error.

The complete knowledge of global non-neural noise sources remains unclear. However, it has been demonstrated that the low-frequency respiratory volume, cardiac rate, white matter ROI signal and CSF ROI signal regressors had significant shared variances with the global signal (

23). Therefore, these non-neural noise correction techniques that were employed may generate the high SGNR observed here. It was observed that the SGNR varies from subject to subject. As a result, it is recommended that one determine the global negative index on a case-by-case basis, rather than simply excluding the global regression in data preprocessing. It also is possible to monitor the SGNR in a realtime manner and repeat scans when the abnormally low SGNR occurs.

This study has focused on the correlation-based analyses, one of the most popular methods employed in investigating resting-state functional interactions. Independent component analysis (ICA) is another technique that is frequently used to study functional interactions (

30–

32). Often, the global signal is removed in preprocessing before the ICA is employed. This may produce undesirable errors, as discussed in this study. To solve the problem, the effect of global signal regression in the ICA can be quantified using similar approaches outlined in the present study.

R-fMRI is an expanding field of research that has great potential in investigating neurological and psychiatric disorders. However, an essential consensus has not been reached in regard to using the global signal regression in preprocessing. While some studies emphasize the pitfalls of the correction technique (

19,

20), others (

22,

33) have shown the benefit of global regression. Because different imaging and preprocessing techniques have been used, direct comparison to the studies will be difficult. Nonetheless, the current study is a timely report demonstrating that the effect of the global signal regression is determined by the SGNR of the data. The SGNR can be estimated from the data based on the global negative index. By comparing the global negative index of the data set and the criterial global negative index, one can determine whether to include or exclude the global signal regression in minimizing errors in functional connectivity measures.