It is often necessary to perform linear fits to experimental data to estimate an extrapolated x-intercept. I've found that the precise choice of range of x-values used in the fit can often have a large influence on the resulting x-intercept even for data which shows only minimal curvature, appearing linear to the naked eye.
Using the range -5<x<0 gives an x-intercept of 0.339 with a 99% confidence interval of 0.333-0.342 . But a smaller fit range of -1<x<0 fives an x-intercept 0.377 with a 99% confidence interval of 0.376-0.378
Clearly the confidence interval is not capturing the full range of possibilities for the x-intercept. What would be a better way to quantify this uncertainty?