Linear, multivariate multiple (m independent, n dependent)
Requires two or more columns of measured data, with the dependent variables in the first column(s)
and the independents in consecutive columns. The program will ask for the number of dependent
variables. The output consists of four main parts.
An overall test of multivariate regression significance. The Wilks' lambda test statistic is computed as
the ratio of determinants
where E is the error (residuals) sum of squares and crossproducts, and H is the hypothesis
(predictions) sum of squares and crossproducts.
The Rao͛s F statistic is computed from the Wilks͛ lambda. With n the number of rows, p the number
of dependent variables and q the number of independent variables, we have:
Note that Rao͛s F can become negative. The F test has pq and m
+ 1- pq/2 degrees of freedom.
Tests on independent variables
The test for the overall effect of each independent variable (on all dependent variables) is based on a
similar design as the overall MANOVA above, but comparing the residuals of regression with and
without the independent variable in question.
Tests on dependent variables
See ͚Linear, n independent, one dependent͛ above for details of the ANOVA tests for the overall
effect of all independent variables on each dependent.
Regression coefficients and statistics
The complete set of coefficients and their significances for all combinations of independent and
Missing data supported by column average substitution.