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Linear regression is used in signal analysis when other methods like artificial neural networks or support vector machines either lack the ability to represent the result in form of a signal or cannot be applied to continuous target values. However, signal noise may lead to unstable noisy solutions with bad performance on non-trained data, especially for underdetermined systems. This work develops a method to add statistical virtual noise with special properties such as band-limitation to the signals in order to reduce these properties in the solution signal. The results show stable solutions with significantly improved performance on non-trained data. The method is also tested on real EEG data.