# Correlation Matrix

A table showing correlations the between multiple variables.

The table is symmetric around the *main diagonal* (i.e., if you draw a line from the top-left corner to the bottom right corner, the numbers on one side of this line are the mirror of those on the other side. For this reason, sometimes only the portion of the correlation matrix above (or below) the main diagonal is shown.

## Example

The following correlation matrix shows correlations between viewing of a number of different television programs in Britain
^{[1]} Each of the numbers in the table is a correlation, showing the relationship between the viewing of the TV program shown in the row with the TV program shown in the column. The higher the correlation, the greater the overlap in the viewing of the programs. For example, the table shows that people who watch *World of Sport* frequently are more likely to watch *Professional Boxing* frequently than are people who watch *Today* (i.e., the correlation of .5 between *World of Sport* and *Professional Boxing* is higher than the correlation of .1 between *Today* and *Professional Boxing*).

Professional Boxing |
This Week |
Today | World of Sport |
Grandstand | Line-Up | Match of the Day |
Panorama | Rugby Special |
24 Hours | |
---|---|---|---|---|---|---|---|---|---|---|

Professional Boxing |
1.0 | .1 | .1 | .5 | .5 | .1 | .5 | .2 | .3 | .1 |

This Week |
.1 | 1.0 | .3 | .1 | .1 | .2 | .1 | .4 | .1 | .4 |

Today |
.1 | .3 | 1.0 | .1 | .1 | .2 | .0 | .2 | .1 | .2 |

World of Sport |
.5 | .1 | .1 | 1.0 | .6 | .1 | .6 | .2 | .3 | .1 |

Grandstand |
.5 | .1 | .1 | .6 | 1.0 | .1 | .6 | .2 | .3 | .1 |

Line-Up |
.1 | .2 | .2 | .1 | .1 | 1.0 | .0 | .2 | .1 | .3 |

Match of the Day |
.5 | .1 | .0 | .6 | .6 | .0 | 1.0 | .1 | .3 | .1 |

Panorama |
.2 | .4 | .2 | .2 | .2 | .2 | .1 | 1.0 | .1 | .5 |

Rugby Special |
.3 | .1 | .1 | .3 | .3 | .1 | .3 | .1 | 1.0 | .1 |

24 Hours |
.1 | .4 | .2 | .1 | .1 | .3 | .1 | .5 | .1 | 1.0 |

## See also

- Diagonalization for a discussion of how to improve interpretation of this correlation matrix.
- Principal Components Analysis for further analysis of this correlation matrix.

## References

- ↑ Ehrenberg, Andrew S. C. 1981. The Problem of Numeracy. The American Statistician 35 (May):67-70.