Hello,I have an analytical expression E[itex]_{i}[/itex] that I

[kassem84]

Hello,

I have an analytical expression E[itex]_{i}[/itex] that I want to fit it to some data E(Ref)[itex]_{i}[/itex] . I fitted this expression for N-points:
I have calculated the value of chi-squared using the following formula:
[itex]\chi^{2}[/itex]=[itex]\frac{1}{N-1}\sum_{i=1}^{N}\frac{(E_i-E(Ref)_i)^{2}}{σ_{i}^{2}}[/itex]

where:
σ[itex]_{i}[/itex]=error*E(Ref)[itex]_{i}[/itex]

Normally, I took the error =3-5%, and I got values of [itex]\chi^{2}[/itex]=0.01

Is this value reasonable? How can we judge on the values of [itex]\chi^{2}[/itex]?

Thanks in advance.

 

[Valerie Park]

The value of \chi^{2} is a measure of how well your fitted expression fits the data. Generally, the smaller the \chi^{2}, the better the fit. However, the exact value of \chi^{2} needed for a good fit depends on the number of data points and the degree of freedom (the number of fitting parameters). In general, a \chi^{2} of 1 or lower is considered to be a good fit. If the \chi^{2} is much larger than 1, then it means that your model does not fit the data very well.