Fig. 3

Examples of residuals from the ADNI dataset. Cognition residuals were calculated in a sample of Aβ+ individuals on the Alzheimer’s disease spectrum from the ADNI dataset. A ADNI-MEM, a composite measure of memory ability, was regressed on hippocampal volumes derived from structural MRI. Residuals are plotted with color indicating their magnitude. This figure represents a realistic association between the brain and cognition that can be expected in real samples. Panel B illustrates the high dependency of the cognition residual on cognition itself, with their correlation being 0.83 in the ADNI example. The blue dot in panel C represents the correlation between ADNI-MEM and hippocampal volume, for which 68% of the variance in the resulting residual is explained by the cognition variable. The red dot marks the point where the correlation between cognition and brain is 0.71 and therefore where 50% of the variance in the residual would be explained by cognition (i.e., squared correlation between the two variables). The blue dot falls perfectly along the simulated curve