arXiv:2509.14039v2 Announce Type: replace Abstract: In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant stepsize and study the explicit dependence of the convergence rate on the problem dimension $d$ and quantities related to the design matrix. When the number of iterations $n$ is known in advance, our results yield a normal approximation rate of order $\sqrt{\log{n}/n}$, provided that the sample size $n$ is large enough.