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Calculus and Beyond Homework Help
What is the correct formula for the reduced Chi square?
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[QUOTE="patric44, post: 6862536, member: 619921"] [B]Homework Statement:[/B] what is the correct formula of reduced Chi square [B]Relevant Equations:[/B] \Chi^2 Hi all I want to calculate the reduced Chi square and root mean square deviation RMSD of some data points that i have, but I am confused about the correct formula for each of them, which one is the correct one. I found this formula in a paper where they referred to it as the RMSD : $$ \chi=\sqrt{\frac{1}{N}\sum_{i}^{N}\left(\frac{(y_{i}-\tilde{y}_{i})}{\delta y_{i}}\right)^{2}} $$ and in some books the same formula with little modification (instead of ##N## they put the degrees of freedom) as : $$ \chi=\sqrt{\frac{1}{N-m}\sum_{i}^{N}\left(\frac{(y_{i}-\tilde{y}_{i})}{\delta y_{i}}\right)^{2}} $$ which one is reduced ##\chi^{2}## and which is RMSD if any of them?! another question why i read that we need to minimize the value of reduced ##\chi^{2}## to get the best fit, isn't the optimum value is 1 ?! , shouldn't we minimize 1-##\chi^{2}## or what? I will appreciate any help, thanks in advance [/QUOTE]
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What is the correct formula for the reduced Chi square?
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