(i)
Suppose that \(N\) 2D points are measured with independent standard
deviations of \(\sigma\) in each coordinate. The RMS residual error (5.3)
for the best fit line using orthogonal regression is
\(\sigma \left(1 - 2 / n \right)^{1 / 2}\) because \(d = 2\) and
\(N = n\) [Ebe00].