Two-dimensional slices through the joint confidence region in another
direction, for given values of β2, and the two-dimensional confidence region
for β0 and β3 ignoring β2 are shown in Figure 5.3. The strong negative
correlation between β0 and β3 is evident in the two-dimensional joint confidence
region and the slices from the three-dimensional region. Again, it
is clear that reasonable combinations of β0 and β3 are dependent on the
assumed value of β2, a result that is not evident from the two-dimensional
joint confidence region ignoring β2.