Squared correlation coefficient of measured values versus predicted values in linear and monoexponential regressions

The correlation coefficient of measured values vs predicted values is widely used in pharmacokinetic and biopharmaceutical settings. When using linear and monoexponential regressions, we notice an interesting characteristic of the squared correlation coefficient of measured values vs predicted values, i.e. the squared correlation coefficient of measured y1 vs predicted (lambda)y2 is a constant regardless of different values of regression coefficients and is equal to the squared correlation coefficient of measured x1 vs measured y1.