Forms the variance-covariance matrix for a list of variates (W. van den Berg).

### Options

`PRINT` = string tokens |
Printed output (`df` , `vcovariance` ); default `df` , `vcov` |
---|

`WEIGHTS`

= *variate* Provides weights for the units of the variates; default `*`

assumes that they all have weight one

`VCOVARIANCE` = symmetric matrix |
Saves the variance-covariance matrix |
---|---|

`DF` = scalar |
Saves the number of degrees of freedom of the (co)variances |

### Parameter

`DATA` = variates |
Variates for which the matrix is to be calculated |
---|

### Description

`FVCOVARIANCE`

calculates vcovariance matrices for a set of variates which should be listed by the `DATA`

parameter. The `WEIGHTS`

option can provide a variate of weights for the units of the variates; by default these are all assumed to have weight one. The vcovariance matrix can be saved using the `VCOVARIANCES`

option, and the degrees of freedom can be saved using `DF`

option.

Printed output is controlled by the `PRINT`

option with settings:

`vcovariance` |
prints the variance-covariance matrix, |
---|---|

`df` |
prints the degrees of freedom. |

By default both are printed.

Options: `PRINT`

, `WEIGHTS`

, `VCOVARIANCES`

, `DF`

.

Parameter: `DATA`

.

### Method

A `SSPM`

structure is set up for the `DATA`

variates, and its values are formed using the `FSSPM`

directive. The corrected sums of squares and products are divided by the residual degrees of freedom to give the variance covariance matrix.

### Action with `RESTRICT`

`FVCOVARIANCE`

takes account of restrictions on any of the variates.

### See also

Directive: `FSSPM`

.

Procedures: `FCORRELATION`

, `ROBSSPM`

.

Commands for: Calculations and manipulation.

### Example

CAPTION 'FVCOVARIANCE example',\ 'Data from Draper & Smith, 1981, Applied Regression Analysis.';\ STYLE=meta,plain VARIATE [VALUES=129,141,153,166,193,189,175,186,190,187,\ 195,206,198,192,191,200,200] Employees & [VALUES=21,22,22,20,25,23,20,23,20,20,\ 22,19,22,22,21,21,22] Operatingdays & [VALUES=7.107,6.373,6.796,9.208,14.792,\ 14.564,11.964,13.526,12.656,14.119,16.691,\ 14.571,13.619,14.575,14.556,18.573,15.618] Production & [VALUES=58.8,65.2,70.9,77.4,79.3,81,71.9,63.9,54.5,39.5,\ 44.5,43.6,56,64.7,73,78.9,79.4] Temperature & [VALUES=3.067,2.828,2.891,2.994,3.082,\ 3.898,3.502,3.06,3.211,3.286,3.542,\ 3.125,3.022,2.922,3.95,4.488,3.295] Wateruse FVCOVARIANCE Employees,Operatingdays,Production,Temperature,Wateruse