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# FVCOVARIANCE procedure

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 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, 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.

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
```
Updated on March 7, 2019