How good is the sinusoidal fit?

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SUMMARY

The discussion centers on evaluating the goodness of fit for a sinusoidal curve applied to a set of data points. The primary method suggested is the chi-squared statistic, which quantifies how well the curve fits the data. Additionally, the concept of comparing the sinusoidal fit to a flat line using the sum of squares is introduced, although details are lacking. The F-test is also mentioned as a potential method for assessing fit quality, prompting a request for further explanation on its application.

PREREQUISITES
  • Understanding of chi-squared statistics for curve fitting
  • Familiarity with sum of squares in statistical analysis
  • Basic knowledge of F-tests in hypothesis testing
  • Experience with sinusoidal functions and their applications in data modeling
NEXT STEPS
  • Research the application of chi-squared statistics in curve fitting
  • Explore the concept of sum of squares and its relevance in model comparison
  • Learn about the F-test and its use in comparing nested models
  • Investigate additional goodness-of-fit measures beyond chi-squared and F-test
USEFUL FOR

Data analysts, statisticians, and researchers involved in curve fitting and model evaluation will benefit from this discussion, particularly those working with sinusoidal models and seeking to improve their statistical analysis skills.

astropi
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First off, this is NOT a homework question! That is, I'm not doing this for any course. So then, here's the question:

I have some data points to which I fit a sinusoidal curve. I get the best (min) chi-square. Now, the question becomes how good a fit is my sinusoid? I was thinking that I could compare my sinusoid with a flat line and see which is a better fit to the data points. How would people suggest I go about doing this? One person suggested a sum of squares, but could not provide me with more than that (he does not remember much except that it "generally works"). I was hoping someone could provide me with much more details (a reference to look up, some examples perhaps?) I know Wikipedia has tons of pages on sum of squares, but I'm not sure which page to go to. Also, if people have other ideas other than sum of squares I am certainly open to it. I know there is something called an F-test, but I don't know how appropriate that would be here? Anyway, I'm hoping for help! Thanks, and yes my statistics is extremely rusty...
 
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Simon Bridge said:
The chi-squared statistic is actually the measure of how good the curve fits the data.
http://en.wikipedia.org/wiki/Goodness_of_fit

Thanks for the response, but that's not what I'm looking for here. I have a few options I'm playing with, but I would still be interested in understanding the F-test if someone can explain how it can be applied to what I described above.
 

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