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Mathematics
MATLAB, Maple, Mathematica, LaTeX
Weighting data points with fitted curve in Matlab
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[QUOTE="RUber, post: 5814632, member: 524408"] Fitting curves really is a black art. You can apply some standard methods, but when you want to apply some additional finesse, everyone will tell you it depends, so there are few authoritative standards. By definition, the un-weighted model will minimize your un-weighted error. By changing the weights, you are allowing for more error around points with more variability and hoping for less error around points with smaller variability. I think this is a smart application of the weighted model. Choosing the weights should be done in a way that helps. It seems like your goal is to still have a pretty good fit overall, so you do not want your weights to be too far out of proportion. Depending on your data, I would try to keep the weights between 0.5 and 1.5, so that the underweighted points aren't completely disregarded by the model. For comparison, if one point is weighted 1.5 and another has weight of 0.5, your model would be willing to trade up to 3 units of error around the lighter point in favor of 1 less unit error on the heavier point. If you have weights ranging from 0.1 to 10, then imagine how much total error you are allowing around the "unimportant" points, maybe to get just a fraction closer to your important points. I don't think that should matter. [/QUOTE]
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Weighting data points with fitted curve in Matlab
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