Curve Fitting and Multiple Experiments

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Say I do an an experiment 5 times, each of which gives you a list of data points. Do I fit a curve to each one separately and then average the parameters and their uncertainties? Or do I take the average of all the experiments and then do fit a single curve to that?

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My opinion is that each data point brings information. Since each of them is in error, treat all the data points in the same regression.