Date: Tue, 24 May 2011 15:29:50 -0400 Rich Ulrich "SPSSX(r) Discussion" Rich Ulrich Re: interpretation of beta coefficent in quadratic regression To: alternativemail84@web.de <1306247821712-4422260.post@n5.nabble.com> text/plain; charset="iso-8859-1"

One of the first complexities for looking at standardized beta is the question of "How do *you* want to regard the impact of intercorrelations?"

- 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.

-- Rich Ulrich

---------------------------------------- > 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 > > Hello, > 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 > variable.

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