You need to assess how well an equation fits the underlying data.

If you're simply fitting a curve through some data so you can conveniently interpolate the data, then choose whichever model best replicates your data. In this case you're not so concerned with smoothing the data or with statistical rigor. You can plot your data along with estimates using the fit curve and eyeball them to see how well they compare. You can also plot the residuals—differences between your actual *y*-value and the estimated *y*-value—and examine them to assess how well your data is represented or to determine if the residuals exhibit some unexpected structure. You can compute percentage differences to gauge how well your data is replicated. Further, you should examine how the trendline behaves between data points used to generate the trendline to make sure there are no unrealistic oscillations between data points. This can happen when you try to fit a higher-order polynomial trendline.

If you're interested in modeling the data from a statistical standpoint, or are trying to gain insight into a physical process, then you can perform some standard statistical calculations to help assess your trendline. Moreover, you should consider what your data represents. If your data represents some physical process, then let physics be your guide and choose a model that best represents the physical relationship between the variables underlying the data, if it is indeed known. ...

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