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PEARSON Function
Pearson Product-Moment Correlation Coefficient

The Pearson product-moment correlation coefficient is a statistical measurement of the correlation (linear association) between two sets of values.

The Pearson product-moment correlation coefficient for two sets of values, *x* and *y*, is
given by the formula:

where *x* and *y*
are the sample means of the two arrays of values.

The Excel RSQ function calculates the square of the Pearson Product-Moment Correlation Coefficient for two supplied sets of values.

The format of the function is :

RSQ( array1, array2 )

Where array1 and array2 are two arrays of numeric values and are of equal length.

A | B | |
---|---|---|

1 | array1 | array2 |

2 | 2 | 22.90 |

3 | 7 | 33.49 |

4 | 8 | 34.50 |

5 | 3 | 27.61 |

6 | 4 | 19.5 |

7 | 1 | 10.11 |

8 | 6 | 37.90 |

9 | 5 | 31.08 |

Columns A and B of the above spreadsheet on the right contain two arrays of values.

The square of the Pearson Product-Moment Correlation Coefficient of the values in columns A and B of the spreadsheet can be calculated using the Excel Rsq function, as follows:

=RSQ( A2:A9, B2:B9 )

This gives the result **0.71166629**.

Note that this result is the square of 0.843603159, which is the Pearson Product-Moment Correlation Coefficient for the two arrays of values.

Further examples of the Excel Rsq function can be found on the Microsoft Office website.

If you get an error from the Excel Rsq function this is likely to be one of the following :

Common Errors

#N/A | - | Occurs if the two supplied data arrays have different lengths |

#DIV/0! | - | Occurs if either of the supplied data arrays has length 1 (i.e. contain just one data value) |