Elliptic Error Probable

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If we are going to make separate estimates of variance in each axis, $$s_x^2, s_y^2$$ note that the confidence interval in one dimension uses $$\chi^2$$ values with (n - 1) degrees of freedom, and:
$$\sigma_x^2 \in \left[\, \frac{(n-1)s_x^2}{\chi_2^2}, \ \frac{(n-1)s_x^2}{\chi_1^2} \,\right]$$