This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# VarianceEstimatorFunction

 VarianceEstimatorFunction is an option for LinearModelFit and NonlinearModelFit which specifies the variance estimator to use.
• VarianceEstimatorFunction defines the function for estimating the error variance scale for linear and nonlinear models with assumed normally distributed errors.
• With the setting VarianceEstimatorFunction->f, the variance scale is estimated by where is the list of residuals and w is the list of weights, as specified by the setting for the Weights option.
• The default setting Automatic estimates the variance scale by where is the weight for the th data point, is the th residual, is the number of data elements, and is the number of parameters in the model.
Use the default unbiased estimate of error variance:
Assume a known error variance:
Estimate the variance by the mean squared error:
Use the default unbiased estimate of error variance:
 Out[1]=
 Out[2]=
Assume a known error variance:
 Out[3]=
Estimate the variance by the mean squared error:
 Out[4]=
 Scope   (2)
Define the estimate within the FittedModel:
Use with a nonlinear model:
Estimate the variance by the mean absolute error:
 Applications   (1)
Fit a nonlinear model using measurement errors as weights:
Estimate the common error scale by :
Obtain standard errors for the parameters:
Compare with estimates using the default variance estimate:
Error estimates and confidence intervals involve variance estimates:
Use the default estimator:
Assume unit error scale:
Estimate by mean squared error:
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