In particular, the confidence band provides a size test of the null hypothesis H0 that the two regression lines are
the same if rejection occurs only when the band does not include the zero line for at least one x ∈ I . Indeed it can be
shown that the partial F test mention above is based on the hyperbolic confidence band given in Section 2.1 in this way,
and so the partial F test is only a by-product of the hyperbolic confidence band as the band provides more information
than simple inclusion of the zero line completely or exclusion of the zero line at one x at least.