DATA:      Anderson (unpublished)
DIRECTORY: \CANOCO\SAMPLES\METHODS\MULTREGR
PROBLEM:   To relate y to predictors x1, ..., x5
ILLUSTRATION OF:
+ multiple linear regresion by using RDA
+ the partial tests and partial regression coefficients

_______________________________________________________________________________
FILE TYPE    |  FILE NAME    |         DESCRIPTION
-------------+---------------+-------------------------------------------------
 SPECIES     | y_var.dta     | 1 quantitative response variable (y) in 9 units
ENVIRONMENT  | x_vars.dta    | 5 predictor variables (x1-x5)
 DERIVED     | yx_vars.dta   | all data (y, x1- x5)
 PROJECTS    | multregr.con  | multiple regression of y on x1-x5
             | mltrgr.con    | idem, using yx_vars.dta as Species data
             | partialx.con  | regression of y on x1 with x2-x5 partialled out 
             |               |  (i.e. with covariables x2-x5 )
             | forward.con   | forward selection with permutation tests
-------------+---------------+-------------------------------------------------
The data set was created with Xi's from a random uniform on
the interval (0,3) and Y's were generated as Y = b1X1 + b2X2 + b3X3 + b4X4 +
b5X5 + e where b1=0.0, all other b's were 1.0 and e's are random exponential.
The data sets can use this to test that b1=0.0 and it is a true null.

Simulated data from M.J.Anderson (Sydney, Australia)
See Anderson et al. (1998) and Anderson & Legendre (1998).

      Y         X1        X2        X3        X4        X5
   8.34661   2.28957   2.45307   2.83369   0.84146   0.15786
   5.71341   0.04480   1.46076   0.58111   1.01206   2.34235
   6.55758   1.29107   1.02030   0.15994   1.12601   2.34261
   8.24781   2.09270   2.67383   0.13740   2.88279   2.49623
   5.34267   1.17646   2.42462   0.34709   0.58503   1.34091
   5.62812   1.75559   0.41774   1.05269   2.57238   1.16160
   6.43148   0.59789   2.86101   1.13440   0.35733   0.88738
   6.97709   2.14516   2.48327   2.33197   1.44982   0.09685
   3.62454   2.95367   0.03215   2.15445   0.94982   0.13403


Anderson, M.J., Robinson, J., Ter Braak, C.J.F.(1998): A note on the 
comparison of two methods of permutation for testing a partial coefficient
in a multiple regression model. Submitted

Anderson, M.J. & Legendre, P.(1998): An empirical comparison of permutation
methods for tests of partial regression coefficients in a linear model.
Submitted.