Following is a model created from
> ols(mpg~wt+am+qsec, mtcars) Linear Regression Model ols(formula = mpg ~ wt + am + qsec, data = mtcars) Model Likelihood Discrimination Ratio Test Indexes Obs 32 LR chi2 60.64 R2 0.850 sigma 2.4588 d.f. 3 R2 adj 0.834 d.f. 28 Pr(> chi2) 0.0000 g 6.456 Residuals Min 1Q Median 3Q Max -3.4811 -1.5555 -0.7257 1.4110 4.6610 Coef S.E. t Pr(>|t|) Intercept 9.6178 6.9596 1.38 0.1779 wt -3.9165 0.7112 -5.51 <0.0001 am 2.9358 1.4109 2.08 0.0467 qsec 1.2259 0.2887 4.25 0.0002
The model seems good with total R2 of 0.85. However, partial R2 values seen on following plot do not add up to this value. They add up to approx 0.28.
> plot(anova(mod), what='partial R2')
Is there any relation between sum of all partial R2 and total R2 ? The analysis is done with
One way to understand partial R2 for a given predictor is that it equals the R2 that you would get if you first regress your independent variable on all other predictors, take the residuals, and regress those on the remaining predictor.
So if e.g. all predictors are perfectly identical (collinear), one can have decent R2, but partial R2 for all predictors will be exactly zero, because any single predictor has zero additional explanatory power.
On the other hand, if all predictors together explain the dependent variable perfectly, i.e. R2=1, then partial R2 for each predictor will be 1 too, because whatever is unexplained by all other predictors can be perfectly explained by the remaining one.
So the sum of all partial R2 can easily be below or above the total R2. They do not have to coincide even if all predictors are orthogonal. Partial R2 is a bit of a weird measure.
See this long thread for many more details: Importance of predictors in multiple regression: Partial R2 vs. standardized coefficients.