Program for multiple linear regression with permutation test. The program includes regression through the origin.

Pierre Legendre
December 1999
Département de Sciences Biologiques
Université de Montréal
This program computes a multiple linear regression and performs tests of significance of the equation parameters using permutations. In this new version, the regression line can be forced through the origin. Permutation testing is recommended when the residuals of the regression equation are not normally distributed; it does not solve the problems caused by heteroscedasticity. Two permutation methods are available in the program:
  1. Permutation of the raw data.
  2. Permutation of residuals of the full regression model (ter Braak 1990, 1992).
Details about these permutation methods are given in Legendre & Legendre (1998, pp. 606-612) and in Anderson & Legendre (1999). Monte Carlo simulations conducted by Anderson & Legendre (1999) concluded that: Thus, permutation of raw data should not be used when the covariables contain (or may contain) outliers; permutation of residuals should be used in that case.

Program availability


  1. Anderson, M. J. & P. Legendre. 1999. An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model. Journal of Statistical Computation and Simulation 62: 271-303.
  2. Legendre, P. & Legendre, L. 1998. Numerical Ecology, 2nd English edition. Elsevier Science BV, Amsterdam. xv + 853 pages.
  3. "Legendre_Desdevises_JTB_in_press.pdf"
  4. Sokal, R. R. & F. J. Rohlf. 1995. Biometry - The principles and practice of statistics in biological research. 3rd edition. W. H. Freeman, New York.
  5. ter Braak, C. J. F. 1990. Update notes: CANOCO version 3.10. Agricultural Mathematics Group, Wageningen.
  6. ter Braak, C. J. F. 1992. Permutation versus bootstrap significance tests in multiple regression and ANOVA. 79-86 in: K.-H. Jöckel, G. Rothe & W. Sendler [eds.] Bootstrapping and related techniques. Springer-Verlag, Berlin.