Asymptotic confidence intervals are always centered on the best-fit value of the parameter, and extend the same distance above and below that value.

The 95% confidence intervals are computed by this equation:

 From [BestFit- t*SE]  TO  [BestFit+ t*SE]

where BestFit is the best fit value for the parameter, SE is its standard error,  and t is the value from the t distribution for the desired level of confidence (95% is standard) and the number of degrees of freedom (which equals the number of data points minus the number of parameters fit by regression). With 95% confidence and many degrees of freedom (more than a few dozen), this multiplier is very close to 1.96. Note that the value of t is not computed from your data, but is a constant that depends on the confidence level you choose, the number of data points, and the number of parameters.