Fig. 2

Correlation between cognition residual and cognition varies as a function of correlation between cognition and an adverse factor. One thousand paired values representing a cognitive score and brain measure indicative of atrophy were generated from a multivariate normal distribution with a correlation varying from 0 to 1. At each iteration, cognition was regressed on the brain measure and residuals were saved. The plot displays the correlation of residuals with the cognitive score and the association between cognition and brain increases. The red dot marks the point where the correlation between cognition and brain is 0.71. When the correlation between cognition and brain is smaller than this value, cognition will explain >50% of the variance in the residual measure (i.e., squared correlation between the two variables)