In the context of statistical data, the general concepts of signal and noise correspond to our ideas of explained and unexplained variation.

Data sets where all variation is unexplained

In some data sets, none of the variation in the variable of interest can be explained in terms of other variables that have been recorded.

Hotel no-shows and cancellations

Data sets with explained and unexplained variation

In many data sets, some of the variation in the variable of interest can be explained in terms of other variables, but part of its variation remains unexplained.

Experiment: Surface finish from lathe

Non-experimental data: Alcoholism and strength

(Note that the data matrix has 50 rows and 2 columns — it has been split here to fit better on the screen. Note also that the rows of the data matrix — individuals — have been sorted into order of lifetime alcohol consumption. Any ordering of the individuals is equally valid.)