I have two questions regarding standard multiple regression:
Why is my shared variance a negative number?
Should I only include the positive semipartial correlations when calculating uniquely explained variance?
I am trying to calculate the amount of shared variance explained in a regression model with four predictor variables, and this number is coming out negative (-.465).
According to Tabachnick & Fidell, (2001), uniquely explained variance is computed by adding up the squared semipartial correlations. Shared variance is computed by subtracting the uniquely explained variance from the R square.
My R square value = .325 (R = .570, Adj R square = .295, fwiw)
F(4, 91) = 10.941, p = .0005.
The semipartial correlation values are (significant predictors indicated by*, from the ‘Part’ column in SPSS output):
.172* -.174* .465* .164
I calculated that the predictors collectively uniquely explained 80% of the variance (0.801, which is the sum of POSITIVE semipartial correlation coefficients).
When calculating the shared variance, the figure comes out at -.48 (computed by subtracting the uniquely explained variance from the R square value; .32 - .80 = -.48). I’m not sure whether it is possible to have a negative value for shared variance, where have I gone wrong (if I have)?
Any advice would be greatly received.