Fig. 1

Examples of residuals from two extreme scenarios. One thousand paired values were generated from a multivariate normal distribution to represent a cognitive score and brain measure indicative of atrophy. Variables in panels A and C were generated with correlations of r = 0.9 and r = 0.0 to show extreme scenarios. The variables in panel B were generated with a correlation of r = 0.5 to reflect what would be considered a strong yet realistic association between brain and cognitive measures. The cognitive score was regressed on the brain measure, and residuals from 100 randomly selected observations (for easier visualization) are plotted with color indicating the magnitude of the residuals (i.e., distance between predicted cognitive score and actual cognitive score). The dashed line represented the average cognitive score. When cognition and the brain are highly correlated (panel A), individuals with both higher and lower than average cognitive scores display a mix of positive and negative residuals. In contrast, when cognition and the brain are uncorrelated, individuals with high cognitive scores all have positive residuals and individuals with low cognitive scores have negative residuals