Error vector magnitude (EVM) is a metric for assessing the quality of m-ary quadrature amplitude modulation (mQAM) signals. Recently proposed deep learning techniques, e.g., feedforward neural networks (FFNNs) -based EVM estimation scheme leverage fast signal quality monitoring in coherent optical communication systems. Such a scheme estimates EVM from amplitude histograms (AHs) of short signal sequences captured before carrier phase recovery (CPR). In this work, we explore further complexity reduction by proposing a simple linear regression (LR) -based EVM monitoring method. We systematically compare the performance of the proposed method with the FFNN-based scheme and demonstrate its capability to infer EVM from an AH when the modulation format information is known in advance. We perform both simulation and experiment to show that the LR-based EVM estimation method achieves a comparable accuracy as the FFNN-based scheme. The technique can be embedded with modulation format identification modules to provide comprehensive signal information. Therefore, this work paves the way to design a fast-learning scheme with parsimony as a future intelligent OPM enabler.