One of the first complexities for looking at standardized beta
is the question of "How do *you* want to regard the impact of
- I will interject here, before addressing the question itself,
than my own main use of beta has been to check for 'suppressor
variables', which are (usually) very serious trouble for interpretations.
- If any beta has the opposite sign if its zero-order correlation,
that is a sign of suppression taking place. If betas are not similar
to the zero-order correlations with outcome, that is a sign that
intercorrelations are indeed affecting the loadings, up or down.
- When X and X-squared are both used, and x is not zero-centered
(or near it), then there can be a *very* high correlation between
those two terms. Then, either the two terms account for the *same*
part of the outcome, and have coefficients that are smaller than
either would be by itself; or the "effective predictor using x" is
some version of c*x-x^2... a suppressor relationship.
So, if you want to look at the overall impact of x, you need to
construct one variable for x: use the proportions from the
raw b coefficients to make a composite variable for x so you can
look at the composite, if you are intending to examine the betas.
A separate way to consider the contributions is to look at the
"variance contributed at each step", looking at the entry of
X1 and X1^2 (in your problem) as the two variables entered at the
last step, and comparing the improvement in R^2 to the similar
improvement for entering X2 at the last step.
For interpretation, it is still essential to keep in mind that
these contributions do depend on the *range* of X1 and X2
that are actually present in the sample in the analysis.
> Date: Tue, 24 May 2011 07:37:01 -0700
> From: alternativemail84@WEB.DE
> Subject: interpretation of beta coefficent in quadratic regression
> To: SPSSX-L@LISTSERV.UGA.EDU
> I'm have a multiple Regression with a quadratic relationship. I use SPSS.
> I have three independent variables in my model x1;x1² and x2. x1² is the
> result of x1 *x1.
> x1² and x2 are significant terms and the whole model is significant, too.
> All is good.
> But I´m not sure how I should interpret the standardized betas of the
> indepedent variables.
> Which independent variable have the biggest influence of the dependent
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