  This study investigated the problem posed by using ordinary least squares
(OLS) to estimate parameters of simple linear regression under a specific
context of special relativity, where an independent variable is restricted to
an open interval, (-c, c). It is found that the OLS estimate for the slope
coefficient is not invariant under Lorentz velocity transformation.
Accordingly, an alternative estimator for the parameters of linear regression
under special relativity is proposed. This estimator can be considered a
generalization of the OLS estimator under special relativity; when c approaches
to infinity, the proposed estimator and its variance converges to the OLS
estimator and its variance, respectively. The variance of the proposed
estimator is larger than that of the OLS estimator, which implies that
hypothesis testing using the OLS estimator and its variance may result in a
liberal test under special relativity.
