Are large coefficients resulting from a best-fit process bad or not?

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By performing the best fit of a data set, we can get an acceptable or even a good value of R^2. However, one or more of the best-fit coefficients might be quite large, or even exceptionally large, as shown in the figure here below.

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Are large coefficients resulting from a best-fit process bad or not?

Is there any rule of thumb to decide what to do in these kinds of situations? Should we just take another model (i.e. another equation to fit the data) or we can still use this model, despite the presence of large coefficients?

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