Posted by
Dominic Lusinchi on
Jan 04, 2007; 4:31pm
URL: http://spssx-discussion.165.s1.nabble.com/Sign-on-regression-coef-tp1072952p1072955.html
Lisa,
I haven't followed the thread very carefully, so this may be redundant...
To see how it is possible to have a positive correlation (r) between a
predictor (X1) and the outcome (Y) and a negative regression coefficient b1,
it is useful to look at the formula for the standardized coefficient for a
2-predictor model:
b1 = [ryx1 - (ryx2 x rx1x2)] / [1 - (rx1x2)^2]
in which "b1" is the standardized regression coefficient for x1, "ryx1" the
correlation between y and x1, "ryx2" the correlation between y and x2, and
"rx1x2" the correlation between x1 and x2. ("x" is the multiplication sign
in he numerator and "^" the exponentiation sign in the denominator.)
Now we can see that if the term "ryx2 x rx1x2" is larger than the
correlation between y and x1, we get a negative coefficient. In order for
that term to be larger than ryx1, we must have ryx2>ryx1 and the correlation
between the two predictors must be high enough so that when it multiplies
ryx2, the product is still larger than ryx1.
Good luck, and best for the New Year to all.
Dominic Lusinchi
Statistician
Far West Research
Statistical Consulting
San Francisco, California
415-664-3032
www.farwestresearch.com
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of
Lisa Stickney
Sent: Wednesday, January 03, 2007 12:50 PM
To:
[hidden email]
Subject: Re: Sign on regression coef?
My thanks to all for your comments, help & insight.
Best,
Lisa
----- Original Message -----
From: "Statisticsdoc" <
[hidden email]>
To: <
[hidden email]>
Sent: Wednesday, January 03, 2007 10:38 AM
Subject: Re: Sign on regression coef?
> Lisa,
>
> David's example is a good one. Another example that comes to mind has
> been
> reported in research on self-esteem in early adolescence. In a study by
> David Dubois, peer self-esteem and academic self-esteem both correlated
> with
> students' academic performance, and with one another. However, when both
> academic and peer self-esteem were entered into a reqression equation to
> predict students' academic performance, the beta weight for peer-self
> esteem
> is negative. Students' who have high levels of peer self-esteem relative
> to
> academic self-esteem have poorer performance. Illustratively, students
> with
> high peer and low academic self-esteem do poorly, while those who have low
> peer and high academic self-esteem perform well. A key issue to examine
> with supressor variables is the relationship between the unique variance
> in
> the predictors and the criterion variable. In this example, the unique
> variance of peer self-esteem (the portion that is not shared with academic
> self-esteem) has a negative association with acsdemic performance. Such
> situations can arise even when the predictor variables have a moderate
> correlation (.4 to .5), depending on how the remaining unique variance is
> associated with the criterion variable.
>
> HTH,
>
> Stephen Brand
>
> For personalized and professional consultation in statistics and research
> design, visit
> www.statisticsdoc.com
>
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:
[hidden email]]On Behalf Of
> Lisa Stickney
> Sent: Tuesday, January 02, 2007 8:51 PM
> To:
[hidden email]
> Subject: Sign on regression coef?
>
> Can anyone tell me when/why this might occur? Thanks in advance.
>
> Best,
> Lisa
>
> Lisa T. Stickney
> Ph.D. Candidate
> The Fox School of Business
> and Management
> Temple University
>
[hidden email]
>