Types of variation

The ideas of signal and noise correspond to explained and unexplained variation in a variable, X.

Explained variation
This is the amount that other variables in the data set explain differences between the values of X — the signal.
Unexplained variation
Some differences between the values of X cannot be explained in terms of the changing values of other variables in the data set. The unexplained variation is noise.

In some data sets, none of the variation in X can be explained in terms of other variables that have been recorded. In other data sets, some of the variation in X can be explained in terms of other variables whose values are available, but part of its variation remains unexplained.

A statistical analysis often separates and describes these two components of the variation. Both provide useful information.