<p>Linear regression can be applied to time
series data to extract model parameters such as the effective force and
friction constant matrices of the system. Even highly nonlinear systems can be
analyzed by linear regression, if the total amount of data is broken up into
shorter “time windows”, so that the dynamics is considered to be piece-wise
linear. Traditionally, linear regression has been performed on the equation of
motion itself (which approach we refer to as LRX). There has been surprisingly
little published on the accuracy and reliability of LRX as applied to time
series data. Here we show that linear regression can also be applied to the
time correlation function of the dynamical observables (which approach we refer
to as LRC), and that this approach is better justified within the context of
statistical physics, namely, Zwanzig-Mori theory. We test LRC against LRX on a
simple system of two damped harmonic oscillators driven by Gaussian random
noise. We find that LRC allows one to improve the signal to noise ratio in a
way that is not possible within LRX. Linear regression using time correlation
functions (LRC) thus appears to be not only better justified theoretically, but
it is more accurate and more versatile than LRX. <b></b></p>