Stephen Brand
www.statisticsdoc.com
Dan,
First, I would use the regression weights from the boys to predict scores in
the girls. Your question is not simply whether the same predictors work as
well for boys and girls, but whether the same model (including the weights)
works as well for boys and girls. Running two separate regression analyses
allows the weights to be optimized for girls. The correlation between the
predicted and the observed scores is the cross-validity correlation. The
difference between the r-squared for boys and the square of the
cross-validity coefficient for girls is the degree of shrinkage in r-squared
between girls and boys. You can also perform this operation in reverse,
using the girls weights to generate predictions for boys.
I think that your question is nested within the larger question of whether
your model predicts differentially for boys and girls. I would suggest that
you combine the data from the boys and girls, add a predictor variable
representing sex to your model, and then add the cross-products between your
predictor variables and sex. Use a hierarchical order of entry. After you
have entered all of the variables in your model, and sex, enter the
interaction terms as a block - in one step. If the R-squared increment for
this step is significant, then your model makes differential predictions for
boys and girls.
The finding of a sex by predictor interaction is consistent with two general
possibilities: a.) that the direction of prediction is similar for both
groups but weaker for one group compared with another; or b.) that the
direction of the effects is different for the two groups. To look into
these interpretations, examine the beta weights for the regression equation
with the interactions, and plot predicted scores for boys and girls at
varying levels of the predictors.
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
Daniel Miller
Sent: Monday, November 13, 2006 7:56 PM
To:
[hidden email]
Subject: comparing R square values of two regressions?
Hi,
maybe someone can help me with this problem. I calculated two linear
regressions over the same variables but for two groups (boys and girls).
Now, i would like to compare the two R square values to see which model
explains more variance. Descriptivley the R square value of the one group
(boys) is higher than the R square value of the other group. Is it sound to
compare these two values like this? If so, how could I show that the
difference between the two R square values is significant?
Thanks a lot for your help,
Dan
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