Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 3.2, pp. 353-359   | 1 | 2 |

Chapter 3.2. The least-squares plane

R. E. Marsha* and V. Schomakerb

aThe Beckman Institute–139–74, California Institute of Technology, 1201 East California Blvd, Pasadena, California 91125, USA, and  bDepartment of Chemistry, University of Washington, Seattle, Washington 98195, USA
Correspondence e-mail:


Arley, N. & Buch, K. R. (1950). Introduction to the theory of probability and statistics. New York: John Wiley. London: Chapman & Hall.Google Scholar
Clews, C. J. B. & Cochran, W. (1949). The structures of pyrimidines and purines. III. An X-ray investigation of hydrogen bonding in aminopyrimidines. Acta Cryst. 2, 46–57.Google Scholar
Deming, W. E. (1943). Statistical adjustment of data. New York: John Wiley. [First edition 1938.]Google Scholar
Hamilton, W. C. (1961). On the least-squares plane through a set of points. Acta Cryst. 14, 185–189.Google Scholar
Hamilton, W. C. (1964). Statistics in physical science. New York: Ronald Press.Google Scholar
Ito, T. (1981a). Least-squares refinement of the best-plane parameters. Acta Cryst. A37, 621–624.Google Scholar
Ito, T. (1981b). On the least-squares plane through a group of atoms. Sci. Pap. Inst. Phys. Chem. Res. Saitama, 75, 55–58.Google Scholar
Ito, T. (1982). On the estimated standard deviation of the atom-to-plane distance. Acta Cryst. A38, 869–870.Google Scholar
Kalantar, A. H. (1987). Slopes of straight lines when neither axis is error-free. J. Chem. Educ. 64, 28–29.Google Scholar
Lybanon, M. (1984). A better least-squares method when both variables have uncertainties. Am. J. Phys. 52, 22–26.Google Scholar
Robertson, J. M. (1948). Bond-length variations in aromatic systems. Acta Cryst. 1, 101–109.Google Scholar
Schomaker, V. & Marsh, R. E. (1983). On evaluating the standard deviation of Ueq. Acta Cryst. A39, 819–820.Google Scholar
Schomaker, V., Waser, J., Marsh, R. E. & Bergman, G. (1959). To fit a plane or a line to a set of points by least squares. Acta Cryst. 12, 600–604.Google Scholar
Shmueli, U. (1981). On the statistics of atomic deviations from the `best' molecular plane. Acta Cryst. A37, 249–251.Google Scholar
Waser, J. (1973). Dyadics and variances and covariances of molecular parameters, including those of best planes. Acta Cryst. A29, 621–631.Google Scholar
Waser, J., Marsh, R. E. & Cordes, A. W. (1973). Variances and covariances for best-plane parameters including dihedral angles. Acta Cryst. B29, 2703–2708.Google Scholar
Whittaker, E. T. & Robinson, G. (1929). The calculus of observations. London: Blackie.Google Scholar