Background to Least-Squares Methods

There are several reasons why the sum of squares, i.e. the sum of squared differences between the measured and modelled data, is used to define the quality of a fit and thus is minimised as a function of the parameters. It is instructive to consider alternatives to the sum of squares, (a) Minimal sum of differences - is not an option, as positive and negative differences cancel each other out. Huge deviations in both directions can result in zero sums. 

The higher the power the more weight is applied to the relatively large 

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In Chapter 4.1 Background to Least-Squares Methods, e.g. in Figure 4-3 and Figure 4-5, we have seen that for univariate data, the vector r of residuals and thus the sum of squares ssq, is a function of the measurement y and the parameters p of the model of choice. 

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