Bootstrap sampling is a nonparametric method for estimating the standard error of a statistic. This paper describes the application of bootstrap sampling to estimate the error in local linear approximations of the dynamics on chaotic attractors reconstructed from time series measurements. We present an algorithm for identifying influential points, i.e., observations with an especially large effect on a least-squares fit, and an algorithm to estimate the standard error of regression coefficients obtained from total least squares. We also consider the application of bootstrap methods to assess the uncertainty in Lyapunov exponent computations from chaotic time series.