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

Least square estimators in linear regression models under negatively superadditive dependent random observations