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In regression theory, the distribution of the error terms occupies a critical position, particularly when switching the data environment from probability theory to uncertainty theory. On the probabilistic platform, the variance-covariance matrix for standard regression model is assumed by an identity matrix with a positive constant multiplier. On the uncertain measure foundation, for given observational distributions, the variance-covariance is an interval-valued matrix. In this paper, we derive the interval-valued variance for given uncertain normal distribution. Further, we derive the interval-valued auto variance matrix for the observational error terms being the members of an uncertain canonical process. This new model may be regarded as an extension to the uncertain canonical process regression models, but its interval-valued variance-covariance matrix is also intrinsic to the uncertain canonical process, which results in an interval-valued weighted regression model.