/COMMENT
This is file MARS2WHW.BMD
for procedure 4R.
Because the output includes the eigenvalues and eigenvectors of the
correlation matrix, it can be used for diagnostic purposes regardless
of how you control which principal components enter the regression,
or whether you ultimately even use the principal components regression
results.
/PROBLEM
title is 'MARTIAN W vs. H and C; multicollinearity'.
/INPUT
file is 'mars2whw.dat'.
variables are 3.
format is free.
/VARIABLE
use = all.
names are W, H, C.
/REGRESS
title is 'PRINCIPAL COMPONENTS REGRESSION OF MARS W vs H and C'.
depend is 1.
independ are 2 to 3.
eigen.
limit = .01, .000000000001.
/COMMENT
Program 4R allows you several ways to decide which components to include.
The only way that makes sense, in terms of the development we have given
in Chapter 5, is to exclude only the very smallest eigenvalues. Because
we like to see sort of a "stepwise" result of including first the
component with the largest eigenvalue, then adding the next largest, and
so on through the smallest, we specify that the components to enter are
selected by their eigenvalues (eigen command in REGRESS paragraph
above). To ensure all components are entered, you must set the
eigenvalue entry limit below the value of the smallest eigenvalue. Thus,
the limit command above specifies "limit = .01, .000000000001." The
first number, .01, is the limit if you use the correlation method (so it
does not apply here) and the second is the eigenvalue limit. Any
component corresponding to an eigenvalue larger than the limit is
included. The result is a list of several regression equations starting
with the one including only the first component, then one obtained by
adding each successive component until all components are in,
corresponding to the ordinary least squares solution.
/END