Measuring the Importance of Variables in Multiple Regression (1 of 3)
When predictor variables are correlated, as they normally are, determining
the relative importance of the predictor variables is a very complex
process. A detailed discussion of this problem is beyond the scope of this text.
The purpose of this section is to provide a few cautionary notes about
the problem.
First and foremost, correlation does not mean causation.
If the
regression coefficient for a predictor
variable is 0.75, this means that, holding everything else constant,
a change of one unit on the predictor variable is associated with a change
of 0.75 on the criterion. It does not necessarily mean that experimentally
manipulating the predictor variable one unit would result in a change
of 0.75 units on the criterion variable. The predictor variable may be
associated with the criterion variable simply because both are associated
with a third variable, and it is this third variable that is causally
related to the criterion. In other words, the predictor variable and this
unmeasured third variable are
confounded.