It is shown that commonly used procedures for estimating parameters by regressing on pressure-derivative data are based on incorrect covariance matrices and thus violate the underlying statistical basis for nonlinear least-squares parameter estimation. Although the resulting estimates of model parameters may be reasonable, calculated confidence intervals are meaningless. Here, we show how to compute the correct derivative data covariance matrix that should be used for estimating parameters by nonlinear least squares. It is also shown that the information content of derivative data cannot be greater than the information content of pressure data, in the sense that regression on derivative data with the proper covariance matrix does not yield smaller confidence intervals than those obtained by regressing on pressure data only. In fact, we prove that matching a data set, including all interior derivative data plus two appropriate pressure points, yields exactly the same estimates and confidence intervals that would be obtained by regressing on pressure data only.