Testing for multivariate normality of disturbances in the multivariate linear regression model

We suggest a characteristic test for testing the multivariate normal distribution of the disturbances in the multivariate linear regression model(MLRM). The test is based on the goodness-of-fit test for uniformity on the surface of a unit sphere. The asymptotic null distribution of the transformed residuals from the MLRM is obtained. An algorithm is given to approximate the critical values of the test by Monte Carlo simulation. The test possesses symmetry and can be easily computed for arbitrary dimension of the disturbance vectors.