This project attempts to describe the relationship between single sound-parameter variations and the brain's EEG signals by finding a linear regression model that accurately estimates the brain's state given a sound-parameter value. In this project the covariance matrix of each trial is considered a points in Riemannian space. Therefore, the statistical regression analyses use Riemannian geometry and Riemannian distance to find the linear model.

Two sound parameters were selected for the experiments, loudness and frequency. The raw EEG data obtained form the experiments was filtered to remove noise and artifacts. Different regression and cross validation methods were used to find a linear behavior in the data.

The relationship between single sound-parameter variation and the brain's state was found to be subject dependent. The linear models found for each subject validate the use of interpolation to estimate the state of the brain for any loudness or frequency value.