I can proof:

**y(x) is an optimal regression ==> SST = SSR + SSE (*)**

Sketch of Proof: Proof that SST=SSR+SSE under the condition: y(x) is optimal <=> dR²/da=0 (1) and dR²/db=0 (2) for y(x).

(R² := 1 -SSE/SSR "R-Squared"). Then the conditions (1) and (2) let to an equation which proves (*)...

**My idea:**The proof of the above conjecture is “not easy” and maybe a little hard to understand. Easier would it be to construct a counterexample.

To construct a counterexample: define a Training Set TS= {observation-points}; a sLR-line which has condition (*), but is not an optimal sLR-line.

**My question:**Exist an easy conterexample? Or any other ideas?