On standardized axes, the regression slope of a linear function tells us the effect of regression to the mean on the data

On standardized axes (both variables as z-scores), the regression slope equals the correlation r (signal-to-noise relationship): slope 1 = no regression (we match extreme values exactly on each observation), slope 0 = full regression (every output is the mean), 0 < slope < 1 = partial regression to the mean.