# Is it possible to fit a data curve to another data curve?

Is it possible to fit a data curve to another data curve?

I do not have the model for the black data curve or I don't want to model it. But I want to see how the red data curve fits/matches with the black one. Is it possible? I am looking for a non-parametric solution or a solution that can be arrived at even without plotting the two curves.

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Fitting process usually involves some kind of optimisation, so if you red-curve has some parametric expression, then yes you can fit it, using non-linear least squares for example. If the red curve is fixed then you can only calculate some metric which says how close your red curve is to the black curve. –  mpiktas Jul 28 '11 at 6:50
@mpiktas 'calculate some metric which says how close your red curve is to the black curve.' But what metric and how? –  Noble P. Abraham Jul 28 '11 at 10:36

It sounds like you want a goodness-of-fit measure. One possibility is the area between the curves. That is $$\int \left|f(x)-g(x)\right| dx$$ where $f(x)$ is the black curve and $g(x)$ is the red curve.