This paper proposes a new method for change detection and analysis using tensor regression. Change detection in our setting is to detect changes in the relationship between the input tensor and the output scalar while change analysis is to compute the responsibility score of individual tensor modes and dimensions for the change detected. We develop a new probabilistic tensor regression method, which can be viewed as a probabilistic generalization of the alternating least squares algorithm. Thanks to the probabilistic formulation, the derived change scores have a clear information-theoretic interpretation. We apply our method to semiconductor manufacturing to demonstrate the utility. To the best of our knowledge, this is the first work of change analysis based on probabilistic tensor regression.