# Why is my shared variance negative?

I have two questions regarding standard multiple regression:

1. Why is my shared variance a negative number?

2. 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)?

Many thanks.

• Not positive semipartial correlation coefficients but squared ones. You may use Venn diagram (such as at the bottom of stats.stackexchange.com/a/73876/3277) to think about it all – ttnphns May 28 '14 at 6:53
• ...so, .325-(.172^2+.174^2+.465^2+.164^2)=.022 is the shared portion of explained variation in Y. No it isn't negative and cannot be negative. – ttnphns May 28 '14 at 7:04