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Analytical Exercise 1.1 (Proof that $$ \mathbf{b} $$ minimizes $$ SSR $$)
Let $$ \mathbf{b} $$ be the OLS estimator of $$ \boldsymbol{ \beta } $$. Prove that, for any hypothetical estimator $$ \tilde{ \boldsymbol{ \beta } } $$ of $$ \boldsymbol{ \beta } $$,