Solution
= Solution
{c}
Here both regressor columns are already centered, so $Z=XV$ and $X=ZV^T$. Writing $\beta=(\beta_1,\beta_2)^T$, the linear predictor is $X\beta=ZV^T\beta$. Thus
$$
\boxed{\widetilde\beta=V^T\beta,\qquad
\widetilde\beta_1=V_{11}\beta_1+V_{21}\beta_2,\quad
\widetilde\beta_2=V_{12}\beta_1+V_{22}\beta_2.}
$$
The intercept stays $\beta_0$, because centering made the transformation a rotation of the regressor columns without an added translation.