Uncertainty of result of spatial straightness least-square evaluation

According to the model of least-square evolution of spatial straightness, and the methods that ISO Guide to the Expression of uncertainty in Measurement (GUM)([1]) proposed, an uncertainty estimation formula is deduced after some factors are predigested or ignored. The estimation formula is tested with Monte Carlo Method on an actual measurement. The experiment shows that the result estimated with the formula deduced by this paper is accord with the result Monte Carlo method estimates. Besides, the using of the formula deduced needs less operation time. So it is useful inactual measurement.