<p>This paper considers univariate regressions involving processes with mean shifts and establishes the limiting behavior of the ordinary least squares estimator and the associated t-statistic. It is shown that, if shift magnitudes shrink at square-root rate for one variable while independent of sample size for the other, conventional t-ratio test may suffer severe size distortion, and hence, a spurious relationship is likely to be detected. For applied researchers, our theoretical results imply that the empirical findings must be interpreted cautiously whenever the mean shift is suspected for both variables.</p>