If $SSTO$ = $11489$, $SSE(X1, X2, X3)$ = $335$, $SSE(X1, X2, X4)$ = $990$, and $SSR(X1, X2)$ = $10493$, I want to find the value of $SSR(X4| X1, X2)$
I know that $SSR(X4| X1, X2)$ = $SSR(X1, X2, X4)$ - $SSR(X1, X2)$. I'm now faced with the problem of finding $SSR(X1, X2, X4)$. How may I go about it?
Recall that any regression that contains an intercept term satisfies the orthogonal decomposition of the total sum of squares, i.e., the model $$ y_i = \beta_0 + \beta_1x_{1i}+\beta_1x_{2i}+\beta_1x_{3i}+\epsilon_i, $$ satisfies $\text{SST} = \text{SSE}+\text{SSR}$, thus $$ SST=11489 = SSE(X_1, X_2, X_4) + SSR(X_1, X_2, X_4) = 990 + SSR(X_1, X_2, X_4), $$ hence, $$ \text{SSR}(X_1, X_2, X_4)=10499. $$