The Destructive Effect of Noise On Linear Regression

Mycroft Sowizral

When noise is present in both the independent and dependent variables, linear regression will be inaccurate. Noise in the regressor variable will lead to underestimation of the regression coefficient. Significant underestimation will occur if the signal-to-noise ratio is low. If the data is a time series, a low pass filter can be used to remove the noise. Regression on the smoothed data will give an accurate estimation of the regression coefficient. Several simulations are shown that demonstrate the results.