Introduction to Principal Components Analysis

Understanding the inverse equivalent width - luminosity relationship (Baldwin Effect), the topic of this meeting, requires extracting information on continuum and emission line parameters from samples of AGN. We wish to discover whether, and how, different subsets of measured parameters may correlate with each other. This general problem is the domain of Principal Components Analysis (PCA). We discuss the purpose, principles, and the interpretation of PCA, using some examples from QSO spectroscopy. The hope is that identification of relationships among subsets of correlated variables may lead to new physical insight.Comment: Invited review to appear in ``Quasars and Cosmology'', A.S.P. Conference Series 1999. eds. G. J. Ferland, J. A. Baldwin, (San Francisco: ASP). 10 pages, 2 figure

Spectral Properties From Lyman-alpha to H-alpha For An Essentially Complete Sample of Quasars I: Data

We have obtained quasi-simultaneous ultraviolet-optical spectra for 22 out of 23 quasars in the complete PG-X-ray sample with redshift, z<0.4, and M_B<-23. The spectra cover rest-frame wavelengths from at least Lyman-alpha to H-alpha. Here we provide a detailed description of the data, including careful spectrophotometry and redshift determination. We also present direct measurements of the continua, strong emission lines and features, including Lyman-alpha, SiIV+OIV], CIV, CIII], SiIII], MgII, H-beta, [OIII], He5876+NaI5890,5896, H-alpha, and blended iron emission in the UV and optical. The widths, asymmetries and velocity shifts of profiles of strong emission lines show that CIV and Lyman-alpha are very different from H-beta and H-alpha. This suggests that the motion of the broad line region is related to the ionization structure, but the data appears not agree with the radially stratified ionization structure supported by reverberation mapping studies, and therefore suggest that outflows contribute additional velocity components to the broad emission line profiles.Comment: 42 pages, 10 figures, 13 tables. Accepted by AJ. Supplemental figures not included. Full version available at http://physics.uwyo.edu/~shang/pgxpaper/ShangPaper.pd