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Weighting Methods

We often don't have a good estimate of the variance (or standard deviation) for each data point. However, we may have a general idea of way the variance changes with the magnitude of the data. This provides a way to estimate the variance for each data point before or during non linear regression analysis.

Weighting schemes

Equal Weight
Reciprocal Variance
- Weighting Schemes
Iteratively Reweighted Least Squares (IRWLS)
Extended Least Squares (ELS)

With some data sets the variance is very similar and equal weights might be applied to all the data points. In most cases however, each data point estimate will have an estimate of its variance. This can be simplified by selection of a weighting scheme which may apply to the data set under consideration. The weighting scheme can be used to adjust the weight for each data point during the analysis using the iteratively reweighted least squares. The actual parameters of the weighting scheme are evaluated along with the model parameters with extended least squares.

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