Can anybody explain how the following reduction happens:
2026-03-28 17:05:41.1774717541
Expected value of Bernoulli variable (for Linear regression model)
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\begin{align} \mathbb{E} \|y - (R*X) w\|^2 &= p \|y - X w\|^2 + (1-p) \|y\|^2 \\ &= p(\|y\|^2 - 2 y^\top X w + \|Xw\|^2) + (1-p) \|y\|^2 \\ &= (\|y\|^2 - 2 y^\top (p X w) + p^2 \|Xw\|^2) - p^2 \|Xw\|^2 + p \|Xw\|^2 \\ &= \|y - pXw\|^2 + p(1-p) \|Xw\|^2. \end{align}