In this paper we present an algorithm suitable to analyse linear models under the following robust conditions: the data is not received in batch but sequentially; the dependent variables may be either non-grouped or grouped, that is, imprecisely observed; the distribution of the errors may be general, thus, not necessarily normal; and the variance of the errors is unknown. As a consequence of the sequential data reception, the algorithm focuses on updating the current estimation and inference of the model parameters (slopes and error variance) as soon as a new data is received. The update of the current estimate is simple and needs scanty computational requirements. The same occurs with the inference processes which are based on asymptotics. The algorithm, unlike its natural competitors, has some memory; therefore, the storage of the complete up-to-date data set is not needed. This fact is essential in terms of computer complexity, so reducing both the computing time and storage requirements of our algorithm compared with other alternatives. Copyright © 2009 John Wiley & Sons, Ltd.