@@ -26,7 +26,7 @@ All the above results are based on using residual bases to predict residual task

* To quantify how the diagonals of the correlation matrices differentiates from the off diagonal elements, we calculated the Kolmogorov–Smirnov test statistic as a measure of distance between the distributions of diagonal elements and off-diagonal elements (for a given sample size this statistic provides a comparable distance metric). We found using residual bases to make predictions further enhances the diagonal correlations ([Figure 11](figs/ukb_diag.png): UKB data; [Figure 12](figs/hcp_diag.png)), suggesting it has added advantage in capturing the individual variability in how subjects respond to tasks.

### 4. Prediction of amplitude of group-level activation maps

We also investigated whether amplitudes of group activation maps, which are the effect size (betas) of group-level contrast maps in explaning individual task activation maps, can be predicted by the amplitude of bases, which are the standard derivations of the individual time courses (in dual regression), across subjects. 80% of the subjects were taken as training data, and the rest 20% were used to evaluate the prediction. The process was repeated 1000 times for both UKB ([Figure 13](figs/ukb_amplitude_prediction.png)) and HCP ([Figure 14](figs/hcp_amplitude_prediction.png)) dataset.

We also investigated whether amplitudes of group activation maps can be predicted by the amplitude of bases across subjects (UKB: 1529 subjects; HCP: 967 subjects). Amplitudes of group-level activation maps are the effect sizes (betas) of the group-level contrast maps in explaning the individual task activation maps, while the amplitude of bases are the standard derivations of the individual time courses calculated in dual regression. 80% of the subjects were taken as training data, and the rest 20% were used to evaluate the prediction. The process was repeated 1000 times for both UKB ([Figure 13](figs/ukb_amplitude_prediction.png)) and HCP ([Figure 14](figs/hcp_amplitude_prediction.png)) dataset.