Regression

Given a function \(f\) and a set of values \(x_i\), regression is the creation of a curve that approximates \(f\) from a set of points \(\left(x_i, y_i\right)\) where
\[ y_i = f\left(x_i\right) + \epsilon_i \]
and \(\epsilon_i\) are observations of some unknown random variables \(E_i\), typically assumed to have means of zero and to be independent of each other.