The parallel analysis method for determining the number of components to retain in a principal components analysis has received a recent resurgence of support and interest. However, researchers and practitioners desiring to use this criterion have been hampered by the required Monte Carlo analyses needed to develop the criteria. Two recent attempts at presenting regression estimation methods to determine eigenvalues were found to be deficient in several respects, and less accurate in general, than a simple linear interpolation of tabled random data eigenvalues. Tables are presented which permit accurate and easy determination of the parallel analysis criteria within a range of sample sizes (N=50 through 1,000) and number of variables (P=5 through 50) covered by the tables. A total of 12,000 unique data sets was created. The generated data provided the empirical criteria for comparison of regression equation estimates using S. J. Allen and R. Hubbard's (1986) estimation equations with those revised by G. J. Lautenschlager et al. Twelve tables present average eigenvalues and values for interpolations. (Author/SLD)