KNOWLEDGEBASE - ARTICLE #1388

Minor change in how Prism 5.02 and 5.0b do weighted nonlinear regression.

When you choose a weighting factor (Weights tab of nonlinear regression), Prism minimizes the weighted sum of squares rather than the absolute sum of squares. The commonly used weighting factors are based on the value of Y. Until Prism 5, Prism used the Y value of the data. With Prism 5, Prism weights by the Y value of the curve. This approach is much better, but it requires recomputing the weighting factors with every iteration. 

There is one situation where weighting by the Y values of the curve causes problems - when the initial values are really bad. The initial curve can be quite far from the points, and in some cases can have Y=0 for some X values, which makes weighting by 1/Y or 1/Y2 impossible.  To improve the fitting, even if the initial values generate a curve far from the data, we changed how Prism 5.02 and 5.0b do weighted regression. For the very first iteration, Prism now uses no weights. This first iteration brings the curve closer to the points. From then on, it uses the weighting function you specify. Essentially it uses the results of one iteration of unweighted fitting as the initial values for the weighted fit.

This change allows 5.02 to converge on a sensible curve in a few cases where earlier releases of Prism 5 could not. Beyond that, it should have a trivial effect on the results when the data really do define a curve. When the fit is ambiguous, different initial values can lead to different best fit values, but they all are pretty meaningless when the fit is ambiguous. 

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