Active cell migration is essential in many physiological processes and in the function of some bioartificial tissues. Therefore, several investigators have recently attempted to quantitatively characterize random cell movement on isotropic substrata in vitro. A popular approach is to fit a theoretical expression for mean-squared cell displacement deriving from correlated random walk models to cell tracking data, yielding three objective cell movement indices: root-mean-squared speed, directional persistence time, and random motility coefficient (analogous to a molecular diffusion coefficient). The data are obtained typically by averaging cell displacements over a cell track composed of cell positions measured at equal time increments and frequently by further pooling such displacement data from tracks of different cells from the same population. We identify pitfalls introduced if an ordinary nonlinear least-squares regression analysis is used to fit the theoretical expression to the data as is commonly done and propose a generalized least-squares regression analysis as a remedy. This method estimates the cell movement indices and associated uncertainties much more accurately. It also predicts the precision of the indices based on their assumed true values and provides a means to address such issues as optimal sampling methods for data acquisition from cell tracks and handling errors associated with measuring cell position.