Question

explain why the sum of the squared semipartials does not equal the squared multiple R when independent variables are correlated.

Answer 1

There is a simple answer of your question, semi-partial correlation ells us about the uniqueness of the contribution devoted by the independent variable in the regression equation.

Basically the sum of squared semi-partial correlation tells us how much R² will decrease if the independent variable is removed from the regression equation.

For the record semi-partial correlation is mainly used in step-wise regression, where instead of analyst the software decides that which variables need the removal and which one proceed to next step.