In this paper, the variation of the weight matrix and its impact on the performance of regression analysis is examined. The large data matrix is primarily dominated by randomness, though it also contains a small amount of signal information. This paper investigates the relationship between weight matrix variation and its influence on the eigenvalue distribution of the data Gram matrix in random regression analysis, with the aim of enhancing the performance of regression models. One of the findings is that the size of the random matrix affects the movement of eigenvalues around the origin. Based on the consideration, a guideline for determining the appropriate size of weight matrix is described. The results are also expected to inform the improvement of models of neural network learning process.