Re: Sum of squared semi-partial correlations

Liesl wrote:
I was under the same impression as Shaun about squared semi-partial
correlations and their relationship to R squared.

Could someone please further clarify things here.

Thanks,
Liesl


SDW wrote:

Well - yes and no :)

From the text I primarily use (Tabachnick & Fiddel) I was under the
impression that the squared semi-partial correlation is the unique
variance in a DV attributable a single IV. So that the sum of all
squared semi-partial correlation PLUS the shared variance, equals R
square. Thus my concern over the results. From your response I take it
it isn't as simple as all that.

Should I be unconcerned about my results?


1. The squared multiple correlation of a set of variables with a
d.v. equals the sum of squares of the Pearson correlations of those
variables with the d.v. only if all the variables are mutually
unorrelated.

2. The semi-partial correlation of a predictor with the d.v. is the
ordinary Pearson correlation of the d.v. with the so-called "unique
part" of the predictor, where the "unique part" of a predictor is
defined as the residual when that predictor is regressed on the other
predictors. The unique part of a predictor is uncorrelated with all
the other predictors.

3. However, when the unique parts of all the predictors are
considered simultaneously, they are generally correlated with one
another. The only case in which the unique parts are all mutually
uncorrelated is when the original predictors are all mutually
uncorrelated. Hence, the squared multiple correlation equals the sum
of squared semi-partials only if all the predictors are mutually
uncorrelated.

.

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