system
Given the following post, respond as if you're commenting on Reddit:
human
Can someone please tell me why we curve-fit?

I'm doing a physics project that includes Gaussian and Lorentzian 'fits', and I want to get a basic of understanding of why we curve-fit, and why those two fits are considered good.
gpt
"Curve-fitting" means different things to different people but in general when you are fitting a curve you are doing some form of  hypothesis testing.  **Hypothesis Testing** is the basis of science:

* Step 1) Make a hypothesis; 
* Step 2) Test hypothesis with data.

In many branches of science a good hypothesis requires expressing a proposed idea in a mathematical formula. For example, the mathematical expression of Newton's 2nd law is F=ma.  Suppose you wanted to test this hypothesis,  than you would take some mass, **m**, and push on it with a variety of forces, **F**, and measure the resulting acceleration, **a**.  A 'curve fit' in this case would be to see if your data (the measured accelerations as a function of forcing) provides a good fit to the hypothesized linear relation F=ma as opposed to some alternative hypothesis such as F= ma^2. By testing your model against the data you determine if it is consistent.  A key subdetail is that in many cases you have to be careful with understanding the measurement uncertainties of the data. In the real world with real data, you might not find a perfect relationship F=ma in your data but it's crucial to be able either reject the hypothesis or conclude it's statistically "close enough" given the uncertainty of your measurements. If your measurement quality is really poor, you'll find that you can't discriminate between competing hypotheses because all the different 'curve-fits' look as good as the next one.

In your specific case it sounds like you are testing whether the data is consistent with a hypothesis that the measurements will follow a specific type of distribution, either Gaussian or Lorentzian. By curve fitting you should (in optimal situations) be able to determine that one of these hypothesis provides a better fit to the data. Another key in any sort of experimental design is to insure that the data you get is going to be sufficient to conclusively test the hypothesis you start with.  If you get shitty data and you may be unable to draw any sort of conclusion from the 'curve fitting.'

The practice of "curve fitting' is often abused in many different ways (badly formed hypothesis, poor experimental design, neglecting data uncertainties, statistical trickery, etc...) Detailing all those cases would be a book-length rant.