The M_CORRELATE function computes the multiple correlation coefficient of a dependent variable and two or more independent variables.

This routine is written in the IDL language. Its source code can be found in the file m_correlate.pro in the lib subdirectory of the IDL distribution.

## Example

First, define the independent (X) and dependent (Y) data.

`X = [[0.477121, 2.0, 13.0], \$   [0.477121, 5.0, 6.0], \$   [0.301030, 5.0, 9.0], \$   [0.000000, 7.0, 5.5], \$   [0.602060, 3.0, 7.0], \$   [0.698970, 2.0, 9.5], \$   [0.301030, 2.0, 17.0], \$   [0.477121, 5.0, 12.5], \$   [0.698970, 2.0, 13.5], \$   [0.000000, 3.0, 12.5], \$   [0.602060, 4.0, 13.0], \$   [0.301030, 6.0, 7.5], \$   [0.301030, 2.0, 7.5], \$   [0.698970, 3.0, 12.0], \$   [0.000000, 4.0, 14.0], \$   [0.698970, 6.0, 11.5], \$   [0.301030, 2.0, 15.0], \$   [0.602060, 6.0, 8.5], \$   [0.477121, 7.0, 14.5], \$   [0.000000, 5.0, 9.5]]Y = [97.682, 98.424, 101.435, 102.266, 97.067, 97.397, \$   99.481, 99.613, 96.901, 100.152, 98.797, 100.796, \$   98.750, 97.991, 100.007, 98.615, 100.225, 98.388, \$   98.937, 100.617]`

Next, compute the multiple correlations of Y.

`; Compute the multiple correlation of Y on the first column of; X. The result should be 0.798816.PRINT, 'Multiple correlation of Y on 1st column of X:'PRINT, M_CORRELATE(X[0,*], Y); Compute the multiple correlation of Y on the first two columns; of X. The result should be 0.875872.PRINT, 'Multiple correlation of Y on 1st two columns of X:'PRINT, M_CORRELATE(X[0:1,*], Y); Compute the multiple correlation of Y on all columns of X. The; result should be 0.877197.PRINT, 'Multiple correlation of Y on all columns of X:'PRINT, M_CORRELATE(X, Y)`

IDL prints:

`Multiple correlation of Y on 1st column of X:`
`     0.798816`
`Multiple correlation of Y on 1st two columns of X:`
`     0.875872`
`Multiple correlation of Y on all columns of X:`
`     0.877196`

## Syntax

Result = M_CORRELATE( X, Y [, /DOUBLE] )

## Return Value

Returns the single or double-precision multiple correlation coefficient.

## Arguments

### X

An integer, single-, or double-precision floating-point array of m-columns and n-rows that specifies the independent variable data. The columns of this two dimensional array correspond to the n-element vectors of independent variable data.

### Y

An n-element integer, single-, or double-precision floating-point vector that specifies the dependent variable data.

## Keywords

### DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

## Version History

 4 Introduced

## Resources and References

J. Neter, W. Wasserman, G.A. Whitmore, Applied Statistics (Third Edition), Allyn and Bacon (ISBN 0-205-10328-6).