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What are some commonly used ways to examine how well a curve fits a given set of data? I am aware of the R Squared test but I was wondering if there are other tests that take into account the appearance of the curves as well.

To be more precise, I am trying to model the spread of diseases using various methods such as the classic differential equation SI model as well as others that take into account a bit of network structure. The latter models have a distinctly different appearance than the S shape of the SI model.

Thanks.

Sandeep Silwal
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    Your question needs to be clarified. Take account how? (And what shape is it?).... $R^2$ often isn't a good way to compare fits (especially nonlinear ones). If the number of parameters are equal in each case, why not just MSE? – Glen_b May 19 '14 at 05:15

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