Anomaly detection for flight data is crucial in maintaining the safety and stability of unmanned aerial vehicles (UAVs), making it a topic of significant research and attention. However, existing anomaly detection methods often ignore the random noise of UAV flight data and lack effective parameter selection, resulting in inadequate anomaly detection performance. Furthermore, current methods generally face the problem of insufficient feature extraction capability. In this paper, a spatio-temporal correlation based on one-dimensional convolutional neural network (1D CNN), bidirectional long short-term memory (BiLSTM), and attention mechanism (AM) hybrid neural network with residual filtering (STC-1D CBiAM-RF) data-driven multiple regression framework is proposed for anomaly detection and recovery of UAV flight data. First, a correlation analysis method is used for parameter selection to reduce the dependence on expert knowledge. Second, a multiple regression model fusing attention mechanism is designed. It utilizes 1D CNN-BiLSTM as a feature extractor, guided by the attention mechanism, to enhance the learning of crucial information from UAV flight data. Then, to effectively mitigate the impact of random noise, a residual filtering method is introduced to smooth the residuals, thereby improving anomaly detection performance. Finally, anomaly detection is achieved by comparing the square of the smoothed residuals with the statistical threshold, and data recovery is achieved by replacing the anomalous data with the predicted data. The effectiveness of the proposed method is verified through a series of experiments using real UAV flight data injected with different anomaly types.