**Syntax**

` >>> FISHER`

**Parent Command**

` >> ERROR
`

**Subcommand**

` -
`

**Description**

The estimated error variance s_{0}^{2} represents the variance of the mean weighted residual and is thus a measure of goodness-of-fit:

The value s_{0}^{2} is used in the subsequent error analysis. For example, the covariance matrix of the estimated parameters, C_{pp}, is directly proportional to the scalar s_{0}^{2}. Note that if the residuals are consistent with the distributional assumption about the measurement errors (i.e., matrix C_{zz}), then the estimated error variance assumes a value close to one. s_{0}^{2} is also an estimate for the true or a priori error variance sigma_{0}^{2}. It can be shown that the ratio (s_{0}^{2}/sigma_{0}^{2}) follows an F-distribution with the two degrees of freedom f_{1}=m-n, and f_{2}=infinity. Therefore, it can be statistically tested to see whether the final match deviates significantly from the modeler’s expectations, expressed by matrix C_{zz}. This is called the Fisher Model Test. The user must decide whether the error analysis should be based on the a posteriori or a priori error variance (see commands `>>> POSTERIORI` and `>>> PRIORI`, respectively). The decision can also be delegated to the Fisher Model Test according to the following table:

Fisher Model Test | Error Variance | Comment |
---|---|---|

error either in the functional or stochastic model | ||

model test passed | ||

probably error in stochastic model |

**Example**

` > COMPUTATION
>> ERROR
>>> let the FISHER model test decide whether the
a priori or a posteriori error variance should be used
>>> confidence level 1-ALPHA : 95 %
<<<`

**See Also**

` >>> ALPHA | >>> POSTERIORI | >>> PRIORI
`