The present study addresses the problem of sequential least square multidimensional linear regression using a stochastic approximation process particularly in the case of a data stream. To avoid the phenomenon of numerical explosion which can be encountered and to reduce the computing time, we propose using a process with online standardized data instead of raw data and the use of several observations per step or all observations until the current step. Herein, we define and study the convergence of three processes with online standardized data: a classical process with a variable step-size and use of a varying number of observations per step, an averaged process with a constant step-size and use of a varying number of observations per step, and a process with a variable or constant step-size and use of all observations until the current step.