  Regression modeling is the workhorse of statistics and there is a vast
literature on estimation of the regression function. It is realized in recent
years that in regression analysis the ultimate aim may be the estimation of a
level set of the regression function, instead of the estimation of the
regression function itself. The published work on estimation of the level set
has thus far focused mainly on nonparametric regression, especially on point
estimation. In this paper, the construction of confidence sets for the level
set of linear regression is considered. In particular, $1-\alpha$ level upper,
lower and two-sided confidence sets are constructed for the normal-error linear
regression. It is shown that these confidence sets can be easily constructed
from the corresponding $1-\alpha$ level simultaneous confidence bands. It is
also pointed out that the construction method is readily applicable to other
parametric regression models where the mean response depends on a linear
predictor through a monotonic link function, which include generalized linear
models, linear mixed models and generalized linear mixed models. Therefore the
method proposed in this paper is widely applicable. Examples are given to
illustrate the method.
