  In this article we study the asymptotic behaviour of the least square
estimator in a linear regression model based on random observation instances.
We provide mild assumptions on the moments and dependence structure on the
randomly spaced observations and the residuals under which the estimator is
strongly consistent. In particular, we consider observation instances that are
negatively superadditive dependent within each other, while for the residuals
we merely assume that they are generated by some continuous function. In
addition, we prove that the rate of convergence is proportional to the sampling
rate $N$, and we complement our findings with a simulation study providing
insights on finite sample properties.
