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In this paper, we propose a new approach to justify a roundoff error impact on the accuracy of the linear least squares (LS) solution using QR decomposition. This decomposition is widely employed to invert a matrix in the linear detector of the multi-user multi-antenna receiver. Compared to existing numerical results, the suggested stochastic bound is far closer to actual errors. It was put through a half-precision format test and verified in real-world scenarios generated by the Quadriga 2.0 tool and in random randsvd ensemble. The results of experiments show that our method predicts errors that are extremely similar to those observed in simulations. The suggested method can be used to examine the roundoff error in many other applications that require matrix inverse operations.