How Prism computes the SE and CI of the slope and intercept in Deming regression.

Prism uses these standard calculations:

r = ((Sum[(Yi - YMean) * (Xi - XMean)])^2 / Sum[(Xi - XMean)^2])/ Sum[(Yi - YMean)^2]

SEslope = sqrt[Slope^2 * (1 - r) / (r * (n - 2))]
SEintercept = SEslope * sqrt[Sum(Xi^2) / n],

CIslope = Slope +(-) CriticalT(95%, N - 2)*SEslope
CIintercept = Intercept +(-) CriticalT(95%, N - 2)*SEintercept