Name		Name	Last commit message	Last commit date
live_demo		live_demo
.gitignore		.gitignore
00_diagram.png		00_diagram.png
A_linregress.png		A_linregress.png
Chi2.py		Chi2.py
Chi2eq0.pdf		Chi2eq0.pdf
Chi2eq0.tex		Chi2eq0.tex
Distribution_of_chi2.png		Distribution_of_chi2.png
DoF.py		DoF.py
Ensemble_of_linregress.png		Ensemble_of_linregress.png
GRAVEL_descent.png		GRAVEL_descent.png
GRAVEL_final0.png		GRAVEL_final0.png
GRAVEL_final1.png		GRAVEL_final1.png
GRAVEL_initial.png		GRAVEL_initial.png
MAXED_descent.png		MAXED_descent.png
Normalized_chi2_DoF.png		Normalized_chi2_DoF.png
Phase_space.png		Phase_space.png
README.md		README.md
Singular_log_likelihood.png		Singular_log_likelihood.png
UUnf.py		UUnf.py
Wiki_chi2.png		Wiki_chi2.png

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Chi2 = 0 proof

This repository is dedicated to proving that,

in an overdetermined system, a regressor should aim to achieve chi2 = degree of freedom = number of data points - number of parameters;

in an fully-/underdetermined system, a regressor should aim to achieve chi2 = 0.

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Chi^2 should equal 1 in over-determined fitting; but =0 at fully-/under-determined fitting. This repo contains the proof.

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