  We reexamine the classical linear regression model when the model is subject
to two types of uncertainty: (i) some of covariates are either missing or
completely inaccessible, and (ii) the variance of the measurement error is
undetermined and changing according to a mechanism unknown to the statistician.
By following the recent theory of sublinear expectation, we propose to
characterize such mean and variance uncertainty in the response variable by two
specific nonlinear random variables, which encompass an infinite family of
probability distributions for the response variable in the sense of (linear)
classical probability theory. The approach enables a family of estimators under
various loss functions for the regression parameter and the parameters related
to model uncertainty. The consistency of the estimators is established under
mild conditions on the data generation process. Three applications are
introduced to assess the quality of the approach including a forecasting model
for the S\&P Index.
