Objectives: The pressure-reactivity index (PRx) is defined in terms of the moving correlation coefficient between intracranial pressure (ICP) and mean arterial pressure (MAP) and is a measure of cerebral autoregulation ability. Histograms of PRx against cerebral perfusion pressure (CPP) show U-shaped behaviour- the minimum reflecting optimal cerebral autoregulation (CPPopt). However U-shaped behavior may also occur by chance. To date there has been no evaluation of the statistical properties of these signals. Materials and Methods: We simulated PRx/CPP distributions using synthetic ICP and MAP signals from Gaussian noise with known cross-correlation. We calculated the statistical distribution of extrema in the PRx/CPP relationship. Results: The calculation of PRx on random data is statistically biased to show a U-shaped behavior when the signals are positively cross-correlated (equivalent to PRx>0). For PR<0, the bias is towards inverse U-shaped behavior. We demonstrate that this bias is eliminated by Fisher transforming the PRx data before CPPopt analysis. Conclusions: Cross-correlated signals are biased to show a U-shaped distribution. A “CPPopt-like” behavior will be observed more often than not even from random ICP and MAP signals that do not exhibit autoregulation unless PRx is Fisher transformed. Care must be taken in interpreting CPPopt in terms of physiology calculated from untransformed data