Relaxing the Assumptions Underlying Corrections for Restriction of Range

It is generally believed that the correction for restriction of range will yield exact correlational values only when the regression of z on x is both linear and homoscedastic. However it is shown that the correction formula can hold even for non-linear heteroscedastic relationships. A simple sufficient condition for the validity of the formula is described. Further, simple conditions for predicting when the formula will overestimate and underestimate are also described. The results are demonstrated in terms of a numerical example.