<- file stat 97betas.html ->

Beta greater than 1.0

=======================Rich Ulrich, 07 Mar 1997==========sse Subject: Re: Multiplicative composite's betas Message-ID: <5fpvmf$k0l@usenet.srv.cis.pitt.edu> In reference to a question about a standardized regression coefficient appearing as greater than 1.0, Dave Krantz (dhk@paradox.psych.columbia.edu) wrote: : You probably did not standardize the product, B*C, separately, : in which case the coefficients are not really betas. With : variables B, C, centered at 0 the correlation between each of them : and B*C is likely to be very small, so the coefficients of B and C : probably don't change very much when you add the product term; : but the other coefficients (including that of A) are not really betas : either, with B*C unstandardized. -- Is that another condemnation of spreadsheets being totally inadequate, and even WRONG, when it comes to producing statistics? I agree that putting in a non-centered product of the sort, B*C , will change the other terms, but so far as I know, the coefficients are still known as partial "b"s and partial betas, where "beta" is the convention for the standardized coefficient, the b divided by the standard deviation of the variable. : I have never had an application where I actually preferred the betas : to the raw unstandardized coefficients based on the original units : of all the variables. I like to think about what coefficients : mean by thinking about how much the response variable changes, in : its natural scale, for various changes in the explanatory variables, : on their natural scales. I suppose there are sometimes good reasons : for using betas, I've just never been in that situation. Raw coefficients can be interesting in ultimately explaining what was found, but I consider the betas to be useful in diagnosing collinearity. If the predictors are mutually uncorrelated, then each beta will be approximately equal to the first order r. Also, conversely, if each beta is approximately equal to its respective r, then the predictors are not interfering with each other. If two predictors are highly correlated so they share prediction, then each beta will be cut in half. If two predictors are highly correlated and there is a suppressor relation, then one beta will be given the opposite sign and both betas will be large. - Any beta over 1.0 is large enough to be considered 'large', in my experience. Any non-trivial beta (or b) with the wrong sign is a warning of the same thing, but you have to compare two parts of a listing to see that the regression and correlation differ.

Interpreting betas, "importance"

=======================Rich Ulrich, 15 Apr 1997==========spss From: wpilib+@pitt.edu (Richard F Ulrich) Subject: Re: interpreting standardized coefficeints (beta) Message-ID: <5j0i99$h8t@usenet.srv.cis.pitt.edu> Josh Kim (jkim4@WVU.EDU) wrote: : Hello...I am working to interpret the standardized ceofficients (betas) in a : regression equation. I want to be able to say what proportion of the : variance is explained by a given independent variable. I'd appreciate the help. -- If there is just one variable, then the beta is r. If the several predictor variables are all uncorrelated, then that is still true. Otherwise, there is not any single answer. You can find UNIQUE variance for a variable, after all the others. You can draw path diagrams, which indicate contributions, in assumed relationships. There is an equation such that total R-squared is the sum of beta(i) * r(i) which would be more intriguing if it were not possible for a single "contribution to variance", which this seems to be, to be negative or greater than 100%. If the intercorrelations are not great, then you might be able to draw that conclusion; but in that case, the univariate r should probably serve with less ambiguity.

Compare two BETAs?

=======================Rich Ulrich, 17 Apr 1997==========spss From: wpilib+@pitt.edu (Richard F Ulrich) Subject: Re: difference between two betas Message-ID: <5j5h68$74h@usenet.srv.cis.pitt.edu> Adrian Esterman (esterman.adrian@health.sa.gov.au) wrote: : Does anyone know how to test for the difference between two standardised : regression coefficients when comparing two multiple regressions? -- No. -- Or, to be more complete: No one knows. -- Further: after a bit of thought, I cannot imagine WANTING to compare two STANDARDIZED regression coefficients for the SAME variable. So you might mean, comparing two vastly different variables... From the results of univariate regression, that is the same as comparing two correlations. It can quickly become nonsensical from the results of multiple regression, given that they are "partial" coefficients by definition. If you make enough assumptions, then you can do an independent comparison of two normal deviates; but you probably ought to consult a statistician to figure out what kind of statement really says something useful about your data.

Understanding prediction equations.

=======================Rich Ulrich, 27 Jan 1997==========ssc Subject: Re: R-Sq. and Var. Explained Message-ID: <5cil9i$gn7@usenet.srv.cis.pitt.edu> << Michael Handel >> M. Handel (mjh@wjh.harvard.edu) wrote: : I estimated an ordinary regression model to which I added an additional : predictor, call it X2. R-squared increased by .01, so I assumed that X2 : explained 1% of the variance of Y net of effects of the other : predictors. However, when I subtract (B2 * X2) from Y, the variance of : Y declines by 6% not 1%. : I've been told that this is because the coeff. for X2, i.e., B2, still : includes some of the covariance of X2 with the other predictors, so that -- Well, that explanation is sometimes true, and might fit your data; and sometimes not at all appropriate. If you subtract that arbitrary amount from Y, it is possible for the resulting variance to INCREASE. You can't screw around with the equations by pulling out ONE term and have that term make sense. For a given, unchanging amount of R-squared, you could have a wide range of values of B2, some positive and some negative -- depending on what the whole set of intercorrelations are. The 1% is the difference between the EQUATION without X2 and the SECOND EQUATION with X2 - and they differ in other terms, unless X2 were totally uncorrelated with anything else (in which case, you would *not* face any puzzle). < FAQ edit: inserted "not" >

Interpreting betas

=======================Rich Ulrich, 16 Jun 1997==========csss Subject: significance question Message-ID: <5o45iv$67j@usenet.srv.cis.pitt.edu> Robert Flynn Corwyn (RBFLYNN@UALR.EDU) wrote: : I have encountered instances while using hierarchical regression where one : independent variable has a lower standardized beta than another but has a : significant T-value whereas the independent variable with the higher beta is : not significant. Could someone please explain this to me? If X does a really good job of predicting, all by itself, then there will be narrow confidence bands on X. If (Y-Z) were equal to that X, then there would be narrow bands on the difference; so the exact value of Y (or Z) would be extremely dependent on the Z (or Y), but there would be a WIDE band on Y or Z if you look at either axis alone. Graphically, you might imagine a line drawn up the main axis of the 1st Y-Z quadrant, with a narrow ellipse around it - the narrow width across the ellipse is the Confidence band on (Y-Z), even though the 'projection' onto the other two axes might take up as much of the scale as you care to show. So: You can have a HUGE beta that is hardly significant, if it is offset by a beta that is confounding it. By the way, any standardize coefficient greater than 1.0 HAS to have something confounding it... * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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